shithub: purgatorio

ref: a8083462e62459b2ae8a243dc4ba88416eba03b1

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pentagonal prism
pentagonal dipyramid
2 5|2
(4.4.5)
dihedral group
D
2{5}+5{4}
0 10 15 7 10 1 0 0 2 2 3 20 2 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8737108351  0.0000000000  0.4864456563
-0.3018596695  0.8199093629  0.4864456563
-0.6651309335 -0.5665434359  0.4864456563
 0.5718511657  0.8199093629 -0.0271086873
 0.7485628941 -0.5665434359 -0.3445027268
-0.9669906029  0.2533659270 -0.0271086873
-0.2024936222 -0.9166865354 -0.3445027268
 0.4467032247  0.2533659270 -0.8580570704
-0.5043532916 -0.0967771725 -0.8580570704
 0.2978495106  0.4270509831  0.5067318540
-0.5036584607  0.1319660113  0.5067318540
 0.2978495106 -0.8090169944  0.5067318540
 0.6877395818  0.1319660113 -0.1935543450
-0.2978495106  0.8090169944 -0.5067318540
-0.6091275581 -0.3454915028 -0.1935543450
 0.1271969263 -0.3454915028 -0.6263550179
4 0 2 4 1 
4 0 3 6 2 
5 0 1 5 7 3 
4 1 4 8 5 
5 2 6 9 8 4 
4 3 7 9 6 
4 5 8 9 7 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 4 0 
3 2 6 3 
3 4 5 1 
3 5 6 2 
3 6 4 3 
3 4 5 6 
pentagonal antiprism
pentagonal deltohedron
|2 2 5
(3.3.3.5)
dihedral group
D
2{5}+10{3}
1 10 20 12 10 1 0 0 2 2 4 20 2 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8944271910  0.0000000000  0.4472135955
 0.2763932023  0.8506508084  0.4472135955
-0.7236067977  0.5257311121  0.4472135955
-0.7236067977 -0.5257311121  0.4472135955
 0.7236067977 -0.5257311121 -0.4472135955
 0.7236067977  0.5257311121 -0.4472135955
-0.8944271910 -0.0000000000 -0.4472135955
-0.2763932023 -0.8506508084 -0.4472135955
-0.0000000000 -0.0000000000 -1.0000000000
 0.2763932023  0.2008114159  0.4472135955
-0.1055728090  0.3249196962  0.4472135955
-0.3416407865 -0.0000000000  0.4472135955
 0.2763932023 -0.8506508084  0.4472135955
 0.5527864045  0.0000000000 -0.1055728090
 0.4472135955  0.3249196962  0.1055728090
-0.2763932023  0.8506508084 -0.4472135955
-0.5527864045 -0.0000000000  0.1055728090
-0.4472135955 -0.3249196962 -0.1055728090
 0.1055728090 -0.3249196962 -0.4472135955
 0.3416407865  0.0000000000 -0.4472135955
-0.2763932023 -0.2008114159 -0.4472135955
3 0 2 1 
3 0 3 2 
3 0 4 3 
5 0 1 5 8 4 
3 1 6 5 
3 1 2 6 
5 2 3 7 9 6 
3 3 4 7 
3 4 8 7 
3 5 9 8 
3 5 6 9 
3 7 8 9 
4 3 0 1 2 
4 3 4 5 0 
4 5 6 1 0 
4 6 7 2 1 
4 7 8 3 2 
4 3 9 10 4 
4 10 6 5 4 
4 6 11 8 7 
4 11 9 3 8 
4 9 10 6 11 
pentagrammic prism
pentagrammic dipyramid
2 5/2|2
(4.4.5/2)
dihedral group
D
5{4}+2{5/2}
2 10 15 7 10 2 0 0 2 2 3 20 2 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9987422138  0.0000000000  0.0501397095
-0.9033708188  0.4259192097  0.0501397095
 0.6354709497 -0.7704950886  0.0501397095
 0.0953713949  0.4259192097 -0.8997205810
 0.0182143157 -0.7704950886  0.6371856536
-0.2678998691 -0.3445758789 -0.8997205810
 0.6059995679  0.4761921529  0.6371856536
-0.8851565032 -0.3445758789 -0.3126746369
-0.2973712509  0.9021113626 -0.3126746369
 0.2129596049  0.9510565163  0.2239189798
-0.5982071492 -0.7694208843  0.2239189798
 0.2129596049 -0.1004057079  0.2239189798
 0.2536312703 -0.7694208843 -0.5862274998
-0.2129596049  0.1004057079 -0.2239189798
 0.7549598948  0.2938926261 -0.5862274998
-0.6233436208  0.2938926261  0.7246170401
4 0 2 4 1 
4 0 3 6 2 
5 0 1 5 7 3 2
4 1 4 8 5 
5 2 6 9 8 4 2
4 3 7 9 6 
4 5 8 9 7 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 4 0 
3 2 6 3 
3 4 5 1 
3 5 6 2 
3 6 4 3 
3 4 5 6 
pentagrammic antiprism
pentagrammic deltohedron
|2 2 5/2
(3.3.3.5/2)
dihedral group
D
10{3}+2{5/2}
3 10 20 12 10 2 0 0 2 2 4 20 2 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9870590084  0.0000000000 -0.1603574566
-0.1885114962  0.9688905521 -0.1603574566
-0.9150540242 -0.3700832595 -0.1603574566
 0.5380310318 -0.8275313256 -0.1603574566
-0.0720049843 -0.8275313256  0.5567828907
-0.3050180081 -0.3700832595 -0.8774978039
 0.1440099685  0.4574480661 -0.8774978039
 0.6545375437  0.5114424860  0.5567828907
-0.8430490399  0.4574480661  0.2828596527
 0.5593892211  0.6787159473  0.4758448931
-0.7730568906  0.4194695241  0.4758448931
-0.2641077641 -0.8389390482  0.4758448931
 0.5593892211 -0.3035309991  0.4758448931
 0.4273353390 -0.8389390482 -0.3369952245
 0.3457215516  0.4194695241 -0.8393580447
-0.5593892211  0.3035309991 -0.4758448931
-0.1632275749 -0.5184928463 -0.8393580447
 0.9362844655  0.0990233222 -0.3369952245
-0.1824939766  0.0990233222  0.9782077132
-0.8546706780 -0.5184928463 -0.0265179270
-0.0311736929  0.9991621492 -0.0265179270
3 0 2 1 
3 0 3 2 
3 0 4 3 
5 0 1 5 8 4 2
3 1 6 5 
3 1 2 6 
5 2 3 7 9 6 2
3 3 4 7 
3 4 8 7 
3 5 9 8 
3 5 6 9 
3 7 8 9 
4 3 0 1 2 
4 3 4 5 0 
4 5 6 1 0 
4 6 7 2 1 
4 7 8 3 2 
4 3 9 10 4 
4 10 6 5 4 
4 6 11 8 7 
4 11 9 3 8 
4 9 10 6 11 
pentagrammic crossed antiprism
pentagrammic concave deltohedron
|2 2 5/3
(3.3.3.5/3)
dihedral group
D
10{3}+2{5/3}
4 10 20 12 10 3 0 0 2 2 4 20 2 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8944271910  0.0000000000 -0.4472135955
-0.7236067977  0.5257311121 -0.4472135955
 0.2763932023 -0.8506508084 -0.4472135955
 0.2763932023  0.8506508084 -0.4472135955
-0.2763932023  0.8506508084  0.4472135955
-0.2763932023 -0.8506508084  0.4472135955
-0.8944271910  0.0000000000  0.4472135955
 0.7236067977 -0.5257311121  0.4472135955
-0.0000000000  0.0000000000 -1.0000000000
 0.3035309991  0.9341723590  0.1875924741
-0.7946544723 -0.5773502692  0.1875924741
 0.9822469464  0.0000000000  0.1875924741
 0.3035309991  0.2205281794  0.1875924741
 0.6070619982 -0.0000000000  0.7946544723
-0.1875924741 -0.5773502692 -0.7946544723
-0.3035309991 -0.2205281794 -0.1875924741
-0.6070619982 -0.0000000000 -0.7946544723
 0.1875924741  0.5773502692  0.7946544723
 0.7946544723  0.5773502692 -0.1875924741
-0.9822469464  0.0000000000 -0.1875924741
-0.3035309991 -0.9341723590 -0.1875924741
3 0 2 1 
3 0 3 2 
3 0 4 3 
5 0 1 5 8 4 3
3 1 6 5 
3 1 2 6 
5 2 3 7 9 6 3
3 3 4 7 
3 4 8 7 
3 5 9 8 
3 5 6 9 
3 7 8 9 
4 3 0 1 2 
4 3 4 5 0 
4 5 6 1 0 
4 6 7 2 1 
4 7 8 3 2 
4 3 9 10 4 
4 10 6 5 4 
4 6 11 8 7 
4 11 9 3 8 
4 9 10 6 11 
tetrahedron
tetrahedron
3|2 3
(3.3.3)
tetrahedral group
A4
4{3}
5 4 6 4 4 1 0 0 2 1 3 24 3 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9428090416  0.0000000000 -0.3333333333
-0.4714045208  0.8164965809 -0.3333333333
-0.4714045208 -0.8164965809 -0.3333333333
 0.4714045208  0.8164965809  0.3333333333
-0.9428090416  0.0000000000  0.3333333333
 0.4714045208 -0.8164965809  0.3333333333
-0.0000000000  0.0000000000 -1.0000000000
3 0 2 1 
3 0 3 2 
3 0 1 3 
3 1 2 3 
3 2 0 1 
3 2 3 0 
3 3 1 0 
3 1 2 3 
truncated tetrahedron
triakistetrahedron
2 3|3
(6.6.3)
tetrahedral group
A4
4{6}+4{3}
6 12 18 8 12 1 0 0 2 2 3 24 3 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.7713892158  0.0000000000  0.6363636364
-0.6428243465  0.4264014327  0.6363636364
 0.2999846950 -0.7106690545  0.6363636364
 0.8999540851  0.4264014327 -0.0909090909
-0.9856639980  0.1421338109 -0.0909090909
-0.5142594772  0.8528028654 -0.0909090909
-0.0428549564 -0.9949366763 -0.0909090909
 0.5571144337  0.1421338109 -0.8181818182
 0.2571297386  0.8528028654 -0.4545454545
-0.6856793030 -0.5685352436 -0.4545454545
 0.0857099129 -0.5685352436 -0.8181818182
 0.2461829820  0.8164965809  0.5222329679
-0.6564879519 -0.5443310540  0.5222329679
 0.2461829820 -0.1632993162  0.5222329679
 0.8206099399 -0.5443310540 -0.1740776560
-0.4923659639  0.3265986324  0.1044465936
 0.3938927711  0.3265986324 -0.3133397807
-0.4103049699  0.2721655270 -0.8703882798
-0.1477097892 -0.4898979486 -0.3133397807
6 0 2 6 9 4 1 
6 0 3 7 10 5 2 
3 0 1 3 
6 1 4 8 11 7 3 
3 2 5 6 
3 4 9 8 
6 5 10 11 8 9 6 
3 7 11 10 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 3 2 
3 3 5 0 
3 4 6 1 
3 0 6 4 
3 1 7 3 
3 3 6 5 
3 5 0 6 
3 6 7 1 
3 7 3 6 
octahemioctahedron
octahemioctacron
3/2 3|3
(6.3/2.6.3)
tetrahedral group
A4
4{6}+4{3}+4{3/2}
7 12 24 12 12 0 1 0 0 3 4 24 3 1 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8660254038  0.0000000000  0.5000000000
-0.8660254038  0.0000000000  0.5000000000
-0.2886751346  0.8164965809  0.5000000000
 0.2886751346 -0.8164965809  0.5000000000
 0.8660254038  0.0000000000 -0.5000000000
 0.5773502692  0.8164965809  0.0000000000
-0.5773502692 -0.8164965809  0.0000000000
-0.8660254038 -0.0000000000 -0.5000000000
-0.2886751346  0.8164965809 -0.5000000000
 0.2886751346 -0.8164965809 -0.5000000000
-0.0000000000  0.0000000000 -1.0000000000
 0.0000000000  1.0000000000  0.0000000000
-0.4714045208  0.3333333333  0.8164965809
-0.9428090416 -0.3333333333  0.0000000000
 0.4714045208 -0.3333333333  0.8164965809
 0.4714045208 -0.3333333333 -0.8164965809
 0.9428090416  0.3333333333  0.0000000000
-0.9428090416 -0.3333333333  0.0000000000
 0.4714045208 -0.3333333333  0.8164965809
 0.0000000000  1.0000000000  0.0000000000
-0.0000000000 -1.0000000000  0.0000000000
 0.4714045208 -0.3333333333 -0.8164965809
-0.4714045208  0.3333333333 -0.8164965809
6 0 1 5 11 8 2 
3 0 2 3 2
6 0 3 9 11 10 4 
3 0 1 4 
6 1 4 7 8 9 6 
3 1 6 5 2
3 2 8 7 
6 2 7 10 5 6 3 
3 3 6 9 
3 4 10 7 2
3 5 10 11 
3 8 11 9 2
4 3 0 1 2 
4 3 4 5 0 
4 6 0 1 7 
4 8 7 1 2 
4 9 2 3 4 
4 5 7 10 0 
4 8 4 5 7 
4 6 4 9 7 
4 11 0 6 4 
4 11 2 8 4 
4 10 2 9 7 
4 10 0 11 2 
tetrahemihexahedron
tetrahemihexacron
3/2 3|2
(4.3/2.4.3)
tetrahedral group
A4
3{4}+2{3}+2{3/2}
8 6 12 7 6 0 1 1 1 3 4 24 3 1 -1
 0.0000000000  0.0000000000  1.0000000000
 1.0000000000  0.0000000000  0.0000000000
-1.0000000000  0.0000000000  0.0000000000
-0.0000000000  1.0000000000  0.0000000000
-0.0000000000 -1.0000000000  0.0000000000
 0.0000000000  0.0000000000 -1.0000000000
 0.0000000000  1.0000000000  0.0000000000
-0.5773502692  0.5773502692  0.5773502692
-1.0000000000  0.0000000000  0.0000000000
 0.5773502692 -0.5773502692  0.5773502692
-0.0000000000  0.0000000000 -1.0000000000
 0.5773502692  0.5773502692 -0.5773502692
-0.5773502692 -0.5773502692 -0.5773502692
4 0 1 5 2 
3 0 2 3 2
4 0 3 5 4 
3 0 1 4 
4 1 4 2 3 
3 1 3 5 2
3 2 5 4 
4 3 0 1 2 
4 3 4 5 0 
4 6 0 1 4 
4 5 2 1 4 
4 6 2 3 4 
4 5 0 6 2 
octahedron
hexahedron
4|2 3
(3.3.3.3)
octahedral group
S4
8{3}
9 6 12 8 6 1 0 0 2 1 4 48 4 0 -1
 0.0000000000  0.0000000000  1.0000000000
 1.0000000000  0.0000000000  0.0000000000
 0.0000000000  1.0000000000  0.0000000000
-1.0000000000  0.0000000000  0.0000000000
 0.0000000000 -1.0000000000  0.0000000000
 0.0000000000  0.0000000000 -1.0000000000
 0.5773502692  0.5773502692  0.5773502692
-0.5773502692  0.5773502692  0.5773502692
-0.5773502692 -0.5773502692  0.5773502692
 0.5773502692 -0.5773502692  0.5773502692
 0.5773502692 -0.5773502692 -0.5773502692
 0.5773502692  0.5773502692 -0.5773502692
-0.5773502692  0.5773502692 -0.5773502692
-0.5773502692 -0.5773502692 -0.5773502692
3 0 2 1 
3 0 3 2 
3 0 4 3 
3 0 1 4 
3 1 5 4 
3 1 2 5 
3 2 3 5 
3 3 4 5 
4 3 0 1 2 
4 3 4 5 0 
4 5 6 1 0 
4 6 7 2 1 
4 7 4 3 2 
4 4 5 6 7 
hexahedron
octahedron
3|2 4
(4.4.4)
octahedral group
S4
6{4}
10 8 12 6 8 1 0 0 2 1 3 48 4 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9428090416  0.0000000000  0.3333333333
-0.4714045208  0.8164965809  0.3333333333
-0.4714045208 -0.8164965809  0.3333333333
 0.4714045208  0.8164965809 -0.3333333333
 0.4714045208 -0.8164965809 -0.3333333333
-0.9428090416  0.0000000000 -0.3333333333
 0.0000000000  0.0000000000 -1.0000000000
 0.4082482905  0.7071067812  0.5773502692
-0.8164965809  0.0000000000  0.5773502692
 0.4082482905 -0.7071067812  0.5773502692
 0.8164965809  0.0000000000 -0.5773502692
-0.4082482905  0.7071067812 -0.5773502692
-0.4082482905 -0.7071067812 -0.5773502692
4 0 2 4 1 
4 0 3 6 2 
4 0 1 5 3 
4 1 4 7 5 
4 2 6 7 4 
4 3 5 7 6 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 4 0 
3 5 3 2 
3 4 5 1 
3 3 4 5 
cuboctahedron
rhombic dodecahedron
2|3 4
(3.4.3.4)
octahedral group
S4
6{4}+8{3}
11 12 24 14 12 1 0 0 2 2 4 48 4 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8660254038  0.0000000000  0.5000000000
 0.2886751346  0.8164965809  0.5000000000
-0.8660254038  0.0000000000  0.5000000000
-0.2886751346 -0.8164965809  0.5000000000
 0.8660254038  0.0000000000 -0.5000000000
 0.5773502692 -0.8164965809  0.0000000000
-0.5773502692  0.8164965809  0.0000000000
 0.2886751346  0.8164965809 -0.5000000000
-0.8660254038  0.0000000000 -0.5000000000
-0.2886751346 -0.8164965809 -0.5000000000
 0.0000000000  0.0000000000 -1.0000000000
 0.4082482905  0.2886751346  0.7071067812
-0.4082482905  0.5773502692  0.7071067812
-0.4082482905 -0.2886751346  0.7071067812
 0.4082482905 -0.5773502692  0.7071067812
 0.8164965809 -0.2886751346  0.0000000000
 0.8164965809  0.5773502692  0.0000000000
 0.0000000000  0.8660254038  0.0000000000
-0.8164965809  0.2886751346 -0.0000000000
-0.8164965809 -0.5773502692  0.0000000000
-0.0000000000 -0.8660254038 -0.0000000000
 0.4082482905 -0.5773502692 -0.7071067812
 0.4082482905  0.2886751346 -0.7071067812
-0.4082482905  0.5773502692 -0.7071067812
-0.4082482905 -0.2886751346 -0.7071067812
3 0 2 1 
4 0 3 7 2 
3 0 4 3 
4 0 1 6 4 
3 1 5 6 
4 1 2 8 5 
3 2 7 8 
3 3 9 7 
4 3 4 10 9 
3 4 6 10 
4 5 11 10 6 
3 5 8 11 
4 7 9 11 8 
3 9 10 11 
4 3 0 1 2 
4 3 4 5 0 
4 5 6 1 0 
4 1 7 8 2 
4 8 9 3 2 
4 4 10 11 5 
4 9 10 4 3 
4 6 12 7 1 
4 11 12 6 5 
4 12 13 8 7 
4 13 10 9 8 
4 10 11 12 13 
truncated octahedron
tetrakishexahedron
2 4|3
(6.6.4)
octahedral group
S4
8{6}+6{4}
12 24 36 14 24 1 0 0 2 2 3 48 4 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.6000000000  0.0000000000  0.8000000000
-0.4000000000  0.4472135955  0.8000000000
-0.0666666667 -0.5962847940  0.8000000000
 0.8000000000  0.4472135955  0.4000000000
 0.5333333333 -0.5962847940  0.6000000000
-0.8666666667  0.2981423970  0.4000000000
-0.2000000000  0.8944271910  0.4000000000
-0.5333333333 -0.7453559925  0.4000000000
 0.9333333333  0.2981423970 -0.2000000000
 0.4000000000  0.8944271910  0.2000000000
 0.6666666667 -0.7453559925  0.0000000000
-0.6666666667  0.7453559925  0.0000000000
-0.9333333333 -0.2981423970  0.2000000000
-0.4000000000 -0.8944271910 -0.2000000000
 0.5333333333  0.7453559925 -0.4000000000
 0.8666666667 -0.2981423970 -0.4000000000
 0.2000000000 -0.8944271910 -0.4000000000
-0.5333333333  0.5962847940 -0.6000000000
-0.8000000000 -0.4472135955 -0.4000000000
 0.0666666667  0.5962847940 -0.8000000000
 0.4000000000 -0.4472135955 -0.8000000000
-0.6000000000 -0.0000000000 -0.8000000000
 0.0000000000 -0.0000000000 -1.0000000000
 0.2581988897  0.5773502692  0.7745966692
-0.6024640761 -0.1924500897  0.7745966692
 0.2581988897 -0.2886751346  0.7745966692
 0.9467292624 -0.1924500897  0.2581988897
-0.5163977795  0.5773502692  0.3872983346
 0.0860662966 -0.9622504486  0.2581988897
 0.6454972244  0.5773502692  0.0000000000
-0.9467292624  0.1924500897 -0.2581988897
-0.0860662966  0.9622504486 -0.2581988897
-0.6454972244 -0.5773502692 -0.0000000000
 0.6024640761  0.1924500897 -0.7745966692
 0.5163977795 -0.5773502692 -0.3872983346
-0.2581988897 -0.5773502692 -0.7745966692
-0.2581988897  0.2886751346 -0.7745966692
6 0 2 7 10 4 1 
6 0 3 8 13 6 2 
4 0 1 5 3 
6 1 4 9 16 11 5 
4 2 6 12 7 
6 3 5 11 17 14 8 
4 4 10 15 9 
6 6 13 19 22 18 12 
6 7 12 18 20 15 10 
4 8 14 19 13 
6 9 15 20 23 21 16 
4 11 16 21 17 
6 14 17 21 23 22 19 
4 18 22 23 20 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 6 0 
3 5 3 2 
3 4 7 1 
3 0 8 4 
3 1 9 5 
3 3 10 6 
3 6 8 0 
3 5 11 3 
3 8 7 4 
3 7 9 1 
3 9 12 5 
3 10 8 6 
3 11 10 3 
3 12 11 5 
3 8 13 7 
3 7 12 9 
3 10 13 8 
3 12 10 11 
3 13 12 7 
3 10 13 12 
truncated hexahedron
triakisoctahedron
2 3|4
(8.8.3)
octahedral group
S4
6{8}+8{3}
13 24 36 14 24 1 0 0 2 2 3 48 4 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.5395042868  0.0000000000  0.8419828529
-0.4604957132  0.2810846377  0.8419828529
 0.2466110680 -0.4798414911  0.8419828529
 0.8419828529  0.2810846377  0.4604957132
-0.8651239283  0.1987568534  0.4604957132
-0.5722307095  0.6785983445  0.4604957132
 0.1348760717 -0.8773551980  0.4604957132
 0.9768589246  0.1987568534 -0.0790085736
 0.7302478566  0.6785983445  0.0790085736
-0.9768589246 -0.1987568534  0.0790085736
-0.2697521434  0.9596829823  0.0790085736
-0.2697521434 -0.9596829823  0.0790085736
 0.2697521434 -0.9596829823 -0.0790085736
 0.8651239283 -0.1987568534 -0.4604957132
 0.2697521434  0.9596829823 -0.0790085736
-0.7302478566 -0.6785983445 -0.0790085736
-0.8419828529 -0.2810846377 -0.4604957132
-0.1348760717  0.8773551980 -0.4604957132
 0.5722307095 -0.6785983445 -0.4604957132
 0.4604957132 -0.2810846377 -0.8419828529
-0.5395042868  0.0000000000 -0.8419828529
-0.2466110680  0.4798414911 -0.8419828529
-0.0000000000  0.0000000000 -1.0000000000
 0.1987568534  0.7071067812  0.6785983445
-0.5380560257 -0.5000000000  0.6785983445
 0.1987568534 -0.1213203436  0.6785983445
 0.8191406634 -0.5000000000  0.2810846377
-0.4798414911  0.2928932188  0.4457402063
 0.6444970597  0.2928932188  0.1164290691
-0.8191406634  0.5000000000 -0.2810846377
 0.0341012848 -0.7071067812  0.1164290691
 0.5380560257  0.5000000000 -0.6785983445
-0.6444970597 -0.2928932188 -0.1164290691
-0.0341012848  0.7071067812 -0.1164290691
-0.1987568534 -0.7071067812 -0.6785983445
 0.4798414911 -0.2928932188 -0.4457402063
-0.1987568534  0.1213203436 -0.6785983445
8 0 2 6 11 15 9 4 1 
8 0 3 7 12 16 10 5 2 
3 0 1 3 
8 1 4 8 14 19 13 7 3 
3 2 5 6 
3 4 9 8 
8 5 10 17 21 22 18 11 6 
3 7 13 12 
8 8 9 15 18 22 23 20 14 
3 10 16 17 
3 11 18 15 
8 12 13 19 20 23 21 17 16 
3 14 20 19 
3 21 23 22 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 3 2 
3 3 5 0 
3 4 6 1 
3 0 6 4 
3 1 7 3 
3 3 8 5 
3 8 0 5 
3 6 9 1 
3 0 10 6 
3 1 11 7 
3 11 3 7 
3 3 12 8 
3 8 10 0 
3 9 11 1 
3 6 11 9 
3 8 6 10 
3 11 12 3 
3 11 8 12 
3 6 13 11 
3 8 13 6 
3 11 8 13 
small rhombicuboctahedron
deltoidal icositetrahedron
3 4|2
(4.3.4.4)
octahedral group
S4
18{4}+8{3}
14 24 48 26 24 1 0 0 2 2 4 48 4 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.6675992222  0.0000000000  0.7445208382
-0.0977676425  0.6604015517  0.7445208382
-0.6389637427  0.1934271362  0.7445208382
-0.0977676425 -0.6604015517  0.7445208382
 0.5698315797  0.6604015517  0.4890416764
 0.9727633538  0.1934271362  0.1277395809
 0.5698315797 -0.6604015517  0.4890416764
-0.3337996111  0.9339488311  0.1277395809
-0.7367313852 -0.4669744155  0.4890416764
-0.8749957112  0.4669744155  0.1277395809
-0.3337996111 -0.9339488311  0.1277395809
 0.3337996111  0.9339488311 -0.1277395809
 0.8749957112 -0.4669744155 -0.1277395809
 0.7367313852  0.4669744155 -0.4890416764
 0.3337996111 -0.9339488311 -0.1277395809
-0.5698315797  0.6604015517 -0.4890416764
-0.9727633538 -0.1934271362 -0.1277395809
-0.5698315797 -0.6604015517 -0.4890416764
 0.0977676425  0.6604015517 -0.7445208382
 0.6389637427 -0.1934271362 -0.7445208382
 0.0977676425 -0.6604015517 -0.7445208382
-0.6675992222 -0.0000000000 -0.7445208382
 0.0000000000 -0.0000000000 -1.0000000000
 0.3302007759  0.3826834324  0.8628562095
-0.2553967884  0.2959899757  0.8628562095
-0.4269143440 -0.2705980501  0.8628562095
 0.3302007759 -0.3826834324  0.8628562095
 0.8938887595 -0.2705980501  0.3574067443
 0.7661903653  0.2959899757  0.4719117310
 0.1367736397  0.9238795325  0.3574067443
-0.5636879836  0.6532814824  0.5054494651
-0.9339488311  0.0000000000  0.3574067443
-0.4050047633 -0.7145830136  0.4719117310
 0.1367736397 -0.9238795325  0.3574067443
 0.7571151198  0.6532814824  0.0000000000
 0.9339488311  0.0000000000 -0.3574067443
 0.6165823904 -0.7145830136  0.0809672526
-0.1367736397  0.9238795325 -0.3574067443
-0.6165823904  0.7145830136 -0.0809672526
-0.7571151198 -0.6532814824  0.0000000000
-0.8938887595  0.2705980501 -0.3574067443
-0.1367736397 -0.9238795325 -0.3574067443
 0.4050047633  0.7145830136 -0.4719117310
 0.5636879836 -0.6532814824 -0.5054494651
 0.4269143440  0.2705980501 -0.8628562095
-0.3302007759  0.3826834324 -0.8628562095
-0.7661903653 -0.2959899757 -0.4719117310
-0.3302007759 -0.3826834324 -0.8628562095
 0.2553967884 -0.2959899757 -0.8628562095
4 0 2 5 1 
3 0 3 2 
4 0 4 9 3 
4 0 1 7 4 
4 1 6 13 7 
3 1 5 6 
4 2 8 12 5 
4 2 3 10 8 
4 3 9 17 10 
3 4 11 9 
4 4 7 15 11 
4 5 12 14 6 
4 6 14 20 13 
3 7 13 15 
4 8 16 19 12 
3 8 10 16 
4 9 11 18 17 
4 10 17 22 16 
4 11 15 21 18 
3 12 19 14 
4 13 20 21 15 
4 14 19 23 20 
4 16 22 23 19 
3 17 18 22 
4 18 21 23 22 
3 20 23 21 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 7 8 2 1 
4 2 9 10 3 
4 5 11 6 0 
4 4 12 11 5 
4 10 13 4 3 
4 6 14 15 7 
4 8 16 9 2 
4 15 17 8 7 
4 16 18 10 9 
4 11 19 14 6 
4 13 20 12 4 
4 12 21 19 11 
4 18 20 13 10 
4 14 22 17 15 
4 17 23 16 8 
4 23 24 18 16 
4 21 22 14 19 
4 20 25 21 12 
4 24 25 20 18 
4 22 24 23 17 
4 21 22 24 25 
truncated cuboctahedron
disdyakisdodecahedron
2 3 4|
(4.6.8)
octahedral group
S4
6{8}+8{6}+12{4}
15 48 72 26 48 1 0 0 2 3 3 48 4 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.4213179058  0.0000000000  0.9069130180
-0.0205668596  0.4208156152  0.9069130180
-0.3330265737 -0.2580737859  0.9069130180
 0.4007510462  0.4208156152  0.8138260361
 0.6841248285 -0.2580737859  0.6821811637
-0.3741602929  0.5835574446  0.7207390541
-0.3826793651 -0.6230452339  0.6821811637
-0.6866200070 -0.0953319565  0.7207390541
 0.6429911093  0.5835574446  0.4960071997
 0.6344720372 -0.6230452339  0.4574493093
 0.9263648917 -0.0953319565  0.3643623273
-0.4528990160  0.8137091469  0.3643623273
-0.7071868666  0.3254836587  0.6276520721
-0.7362727984 -0.4603034045  0.4960071997
-0.1198724423 -0.8811190198  0.4574493093
 0.5642523862  0.8137091469  0.1396304730
 0.9057980321  0.3254836587  0.2712753454
 0.8767121003 -0.4603034045  0.1396304730
 0.3014454635 -0.8811190198  0.3643623273
-0.7859255897  0.5556353610  0.2712753454
-0.2106589529  0.9764509762  0.0465434910
-0.8270593089 -0.5556353610  0.0851013814
-0.2106589529 -0.9764509762  0.0465434910
 0.8270593089  0.5556353610 -0.0851013814
 0.2106589529  0.9764509762 -0.0465434910
 0.7859255897 -0.5556353610 -0.2712753454
 0.2106589529 -0.9764509762 -0.0465434910
-0.8767121003  0.4603034045 -0.1396304730
-0.3014454635  0.8811190198 -0.3643623273
-0.9057980321 -0.3254836587 -0.2712753454
-0.5642523862 -0.8137091469 -0.1396304730
 0.7362727984  0.4603034045 -0.4960071997
 0.1198724423  0.8811190198 -0.4574493093
 0.7071868666 -0.3254836587 -0.6276520721
 0.4528990160 -0.8137091469 -0.3643623273
-0.9263648917  0.0953319565 -0.3643623273
-0.6344720372  0.6230452339 -0.4574493093
-0.6429911093 -0.5835574446 -0.4960071997
 0.6866200070  0.0953319565 -0.7207390541
 0.3826793651  0.6230452339 -0.6821811637
 0.3741602929 -0.5835574446 -0.7207390541
-0.6841248285  0.2580737859 -0.6821811637
-0.4007510462 -0.4208156152 -0.8138260361
 0.3330265737  0.2580737859 -0.9069130180
 0.0205668596 -0.4208156152 -0.9069130180
-0.4213179058 -0.0000000000 -0.9069130180
-0.0000000000 -0.0000000000 -1.0000000000
 0.1824857240  0.1916223125  0.8259425910
-0.3588578683  0.1651647923  0.8259425910
 0.1824857240 -0.5334020968  0.8259425910
 0.6734372751  0.1651647923  0.5978648424
 0.1150758511  0.8458618109  0.5208409981
-0.4869154353 -0.3271197492  0.6388327969
 0.7107416431 -0.3271197492  0.3742195883
-0.5282559191  0.5187420617  0.4517230027
-0.4805150176 -0.7290726662  0.2753141970
-0.9764509762  0.0000000000  0.2157394053
 0.6694011593  0.5187420617  0.1871097942
 0.5517801258 -0.7290726662  0.0472364484
 0.9764509762  0.0000000000 -0.2157394053
-0.5517801258  0.7290726662 -0.0472364484
 0.0413404837 -0.8458618109  0.1871097942
 0.4805150176  0.7290726662 -0.2753141970
-0.0413404837  0.8458618109 -0.1871097942
-0.6694011593 -0.5187420617 -0.1871097942
-0.1150758511 -0.8458618109 -0.5208409981
 0.5282559191 -0.5187420617 -0.4517230027
-0.7107416431  0.3271197492 -0.3742195883
-0.1824857240  0.5334020968 -0.8259425910
-0.6734372751 -0.1651647923 -0.5978648424
 0.4869154353  0.3271197492 -0.6388327969
 0.3588578683 -0.1651647923 -0.8259425910
-0.1824857240 -0.1916223125 -0.8259425910
4 0 2 4 1 
6 0 3 8 13 6 2 
8 0 1 5 10 19 15 7 3 
6 1 4 9 17 11 5 
8 2 6 12 21 25 16 9 4 
4 3 7 14 8 
4 5 11 18 10 
4 6 13 20 12 
6 7 15 23 31 22 14 
8 8 14 22 30 36 28 20 13 
4 9 16 24 17 
6 10 18 26 35 27 19 
8 11 17 24 32 39 34 26 18 
6 12 20 28 37 29 21 
4 15 19 27 23 
6 16 25 33 40 32 24 
4 21 29 33 25 
4 22 31 38 30 
8 23 27 35 41 45 43 38 31 
4 26 34 41 35 
4 28 36 42 37 
8 29 37 42 46 47 44 40 33 
6 30 38 43 46 42 36 
4 32 40 44 39 
6 34 39 44 47 45 41 
4 43 45 47 46 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 4 0 
3 2 6 3 
3 4 7 1 
3 5 8 2 
3 1 9 5 
3 3 10 4 
3 2 11 6 
3 6 12 3 
3 4 13 7 
3 7 9 1 
3 9 8 5 
3 8 14 2 
3 10 15 4 
3 12 10 3 
3 11 12 6 
3 14 11 2 
3 13 9 7 
3 4 16 13 
3 9 17 8 
3 8 18 14 
3 12 15 10 
3 15 16 4 
3 11 19 12 
3 18 11 14 
3 13 20 9 
3 16 21 13 
3 9 22 17 
3 17 18 8 
3 12 23 15 
3 15 21 16 
3 19 24 12 
3 18 19 11 
3 20 22 9 
3 21 20 13 
3 22 18 17 
3 24 23 12 
3 23 21 15 
3 18 24 19 
3 21 22 20 
3 22 25 18 
3 24 21 23 
3 25 24 18 
3 21 25 22 
3 24 21 25 
snub hexahedron
pentagonal icositetrahedron
|2 3 4
(3.3.3.3.4)
octahedral group
S4
6{4}+32{3}
16 24 60 38 24 1 0 0 2 2 5 48 4 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.6907659000  0.0000000000  0.7230784683
 0.2898753354  0.6270006527  0.7230784683
-0.4474773703  0.5262333434  0.7230784683
-0.6654371656 -0.1853399775  0.7230784683
-0.1110152292 -0.6817867317  0.7230784683
 0.5797506708 -0.6817867317  0.4461569367
 0.9806412354 -0.1853399775  0.0631811688
 0.8230392005  0.5262333434  0.2137403629
 0.2432885297  0.9678940186  0.0631811688
-0.4940641761  0.8671267092  0.0631811688
-0.9340544297  0.2861072869  0.2137403629
-0.6516662110 -0.7277679621  0.2137403629
 0.0253287344 -0.9976806078  0.0631811688
 0.6188503599 -0.7277679621 -0.2955977425
 0.7626814402 -0.0845726681 -0.6412210887
 0.6050794053  0.6270006527 -0.4906618946
-0.1110152292  0.8123406303 -0.5725192742
-0.7511236604  0.4416606752 -0.4906618946
-0.9202834751 -0.2563206977 -0.2955977425
-0.4146615192 -0.7663593998 -0.4906618946
 0.1788601062 -0.4964467542 -0.8494408059
 0.1713729895  0.2401260565 -0.9554950421
-0.4687354417 -0.1305538986 -0.8736376625
 0.3408933659  0.2179597953  0.8503402074
-0.0547860790  0.4008905646  0.8503402074
-0.3868745963  0.1185023459  0.8503402074
-0.2699126456 -0.3014331152  0.8503402074
 0.3408933659 -0.4008905646  0.8503402074
 0.7825540411 -0.3014331152  0.4284162431
 0.8671267092  0.1185023459  0.3476229160
 0.6270006527  0.4008905646  0.5770183396
 0.4714472644  0.7373527058  0.3476229160
-0.1200630282  0.8785468151  0.4623206278
-0.6520001425  0.5838213339  0.3476229160
-0.7115733209  0.2179597953  0.5770183396
-0.9324036585 -0.2596964552  0.2513586457
-0.4964467542 -0.5544219364  0.5770183396
-0.2563206977 -0.8368101551  0.3476229160
 0.1717480296 -0.8208260257  0.4284162431
 0.4254660340 -0.8368101551  0.0743010482
 0.7575545513 -0.5544219364  0.0743010482
 0.8211454788 -0.3468166421 -0.3036964718
 0.9324036585  0.2596964552 -0.2513586457
 0.5810194223  0.7373527058 -0.0743010482
 0.2563206977  0.8368101551 -0.3476229160
-0.1257667992  0.9202834751 -0.1550943753
-0.4714472644  0.7373527058 -0.3476229160
-0.7575545513  0.5544219364 -0.0743010482
-0.9057181469  0.1638858728 -0.1990208196
-0.6905915802 -0.6084958589 -0.1990208196
-0.3618751065 -0.8662095526 -0.0743010482
 0.1200630282 -0.8785468151 -0.4623206278
 0.5424279846 -0.4549644871 -0.6209447838
 0.3868745963 -0.1185023459 -0.8503402074
 0.5350381919  0.2720337177 -0.7256204361
 0.2313212079  0.5838213339 -0.7017381110
-0.3408933659  0.4008905646 -0.8503402074
-0.7439626034  0.0190448965 -0.5770183396
-0.6270006527 -0.4008905646 -0.5770183396
-0.2449131559 -0.4843638846 -0.7695468803
-0.0411941310 -0.1344864753 -0.9311335345
3 0 2 1 
3 0 3 2 
3 0 4 3 
3 0 5 4 
4 0 1 6 5 
3 1 7 6 
3 1 8 7 
3 1 2 8 
3 2 9 8 
4 2 3 10 9 
3 3 11 10 
3 3 4 11 
4 4 12 19 11 
3 4 5 12 
3 5 13 12 
3 5 6 13 
3 6 14 13 
3 6 7 14 
3 7 15 14 
4 7 8 16 15 
3 8 9 16 
3 9 17 16 
3 9 10 17 
3 10 18 17 
3 10 11 18 
3 11 19 18 
3 12 20 19 
3 12 13 20 
4 13 14 21 20 
3 14 15 21 
3 15 22 21 
3 15 16 22 
3 16 17 22 
4 17 18 23 22 
3 18 19 23 
3 19 20 23 
3 20 21 23 
3 21 22 23 
5 4 0 1 2 3 
5 4 5 6 7 0 
5 7 8 9 1 0 
5 9 10 11 2 1 
5 11 12 13 3 2 
5 13 14 15 4 3 
5 15 16 17 5 4 
5 17 18 19 6 5 
5 19 20 8 7 6 
5 20 21 22 9 8 
5 22 23 24 10 9 
5 24 25 12 11 10 
5 12 26 27 14 13 
5 27 28 16 15 14 
5 28 29 18 17 16 
5 29 30 31 19 18 
5 31 32 21 20 19 
5 32 33 23 22 21 
5 33 34 25 24 23 
5 34 35 26 12 25 
5 35 36 28 27 26 
5 36 37 30 29 28 
5 37 33 32 31 30 
5 33 34 35 36 37 
small cubicuboctahedron
small hexacronic icositetrahedron
3/2 4|4
(8.3/2.8.4)
octahedral group
S4
6{8}+6{4}+8{3/2}
17 24 48 20 24 2 0 0 -4 3 4 48 4 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.6675992222  0.0000000000  0.7445208382
-0.6389637427  0.1934271362  0.7445208382
-0.0977676425  0.6604015517  0.7445208382
-0.0977676425 -0.6604015517  0.7445208382
 0.9727633538  0.1934271362  0.1277395809
 0.5698315797  0.6604015517  0.4890416764
 0.5698315797 -0.6604015517  0.4890416764
-0.7367313852 -0.4669744155  0.4890416764
-0.8749957112  0.4669744155  0.1277395809
-0.3337996111  0.9339488311  0.1277395809
-0.3337996111 -0.9339488311  0.1277395809
 0.8749957112 -0.4669744155 -0.1277395809
 0.7367313852  0.4669744155 -0.4890416764
 0.3337996111  0.9339488311 -0.1277395809
 0.3337996111 -0.9339488311 -0.1277395809
-0.9727633538 -0.1934271362 -0.1277395809
-0.5698315797  0.6604015517 -0.4890416764
-0.5698315797 -0.6604015517 -0.4890416764
 0.6389637427 -0.1934271362 -0.7445208382
 0.0977676425  0.6604015517 -0.7445208382
 0.0977676425 -0.6604015517 -0.7445208382
-0.6675992222  0.0000000000 -0.7445208382
 0.0000000000  0.0000000000 -1.0000000000
 0.1367736397  0.9238795325  0.3574067443
-0.1057888136  0.1226030622  0.3574067443
-0.9339488311 -0.0000000000  0.3574067443
 0.1367736397 -0.1585126678  0.3574067443
 0.9339488311 -0.0000000000 -0.3574067443
 0.3173664407  0.1226030622  0.1954722392
-0.3868542724 -0.0000000000  0.1480427208
 0.3302007759 -0.3826834324  0.8628562095
 0.0566534965  0.3826834324  0.1480427208
-0.1677584658 -0.2959899757  0.1954722392
-0.1367736397 -0.9238795325 -0.3574067443
 0.3868542724 -0.0000000000 -0.1480427208
 0.2553967884 -0.2959899757  0.0335377341
-0.2553967884  0.2959899757 -0.0335377341
-0.3302007759  0.3826834324 -0.8628562095
-0.0566534965 -0.3826834324 -0.1480427208
 0.1677584658  0.2959899757 -0.1954722392
-0.3173664407 -0.1226030622 -0.1954722392
-0.1367736397  0.1585126678 -0.3574067443
 0.1057888136 -0.1226030622 -0.3574067443
8 0 2 9 17 20 13 5 1 
3 0 3 2 2
8 0 4 11 18 22 17 10 3 
4 0 1 7 4 
8 1 6 14 20 23 21 15 7 
3 1 5 6 2
4 2 8 16 9 
8 2 3 6 5 12 15 11 8 
4 3 10 14 6 
3 4 8 11 2
8 4 7 12 19 23 22 16 8 
4 5 13 19 12 
3 7 15 12 2
3 9 10 17 2
8 9 16 18 21 19 13 14 10 
4 11 15 21 18 
3 13 20 14 2
3 16 22 18 2
4 17 22 23 20 
3 19 21 23 2
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 7 8 2 1 
4 2 9 10 3 
4 5 7 11 0 
4 4 8 7 5 
4 10 12 4 3 
4 6 10 9 7 
4 0 13 14 6 
4 8 14 13 2 
4 2 15 7 9 
4 7 12 10 11 
4 11 14 16 0 
4 4 16 14 8 
4 15 4 12 7 
4 14 17 10 6 
4 0 18 2 13 
4 2 17 14 15 
4 10 19 14 11 
4 4 18 0 16 
4 19 4 15 14 
4 18 10 17 2 
4 10 19 4 18 
great cubicuboctahedron
great hexacronic icositetrahedron
3 4|4/3
(8/3.3.8/3.4)
octahedral group
S4
6{4}+8{3}+6{8/3}
18 24 48 20 24 4 0 0 -4 3 4 48 4 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9968739365  0.0000000000  0.0790085736
 0.4556778364  0.8866314650  0.0790085736
-0.8508851285  0.5193766874  0.0790085736
-0.8508851285 -0.5193766874  0.0790085736
 0.0427591319  0.8866314650  0.4604957132
 0.1459888080  0.5193766874 -0.8419828529
 0.1459888080 -0.5193766874 -0.8419828529
-0.3952072921  0.3672547776 -0.8419828529
 0.8081259966 -0.3672547776  0.4604957132
-0.4984369683 -0.7345095553  0.4604957132
-0.4984369683  0.7345095553  0.4604957132
-0.8081259966  0.3672547776 -0.4604957132
 0.3952072921 -0.3672547776  0.8419828529
 0.4984369683 -0.7345095553 -0.4604957132
 0.4984369683  0.7345095553 -0.4604957132
-0.0427591319 -0.8866314650 -0.4604957132
-0.1459888080  0.5193766874  0.8419828529
-0.1459888080 -0.5193766874  0.8419828529
-0.4556778364 -0.8866314650 -0.0790085736
 0.8508851285  0.5193766874 -0.0790085736
 0.8508851285 -0.5193766874 -0.0790085736
-0.9968739365  0.0000000000 -0.0790085736
 0.0000000000  0.0000000000 -1.0000000000
 0.2596883437  0.1585126678  0.2810846377
-0.0959283710  0.3412793093  0.2810846377
-0.3042438195  0.0000000000  0.2810846377
 0.2596883437 -0.9238795325  0.2810846377
 0.3042438195  0.0000000000 -0.2810846377
 0.2877851131  0.3412793093 -0.0734203966
 0.7345095553 -0.0000000000 -0.6785983445
-0.1075664339  0.3826834324 -0.1164290691
-0.6269431213 -0.3826834324 -0.6785983445
-0.4234483164  0.1413625185 -0.0734203966
-0.2596883437 -0.1585126678 -0.2810846377
-0.7345095553 -0.0000000000  0.6785983445
-0.0397348323  0.1413625185 -0.4279254308
 0.0397348323 -0.1413625185  0.4279254308
 0.1075664339 -0.3826834324  0.1164290691
 0.6269431213  0.3826834324  0.6785983445
 0.4234483164 -0.1413625185  0.0734203966
-0.2877851131 -0.3412793093  0.0734203966
-0.2596883437  0.9238795325 -0.2810846377
 0.0959283710 -0.3412793093 -0.2810846377
8 0 2 9 17 20 13 5 1 3
3 0 3 2 
8 0 4 11 18 22 17 10 3 3
4 0 1 7 4 
8 1 6 14 20 23 21 15 7 3
3 1 5 6 
4 2 8 16 9 
8 2 3 6 5 12 15 11 8 3
4 3 10 14 6 
3 4 8 11 
8 4 7 12 19 23 22 16 8 3
4 5 13 19 12 
3 7 15 12 
3 9 10 17 
8 9 16 18 21 19 13 14 10 3
4 11 15 21 18 
3 13 20 14 
3 16 22 18 
4 17 22 23 20 
3 19 21 23 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 7 8 2 1 
4 2 9 10 3 
4 5 7 11 0 
4 4 8 7 5 
4 10 12 4 3 
4 6 10 9 7 
4 0 13 14 6 
4 8 14 13 2 
4 2 15 7 9 
4 7 12 10 11 
4 11 14 16 0 
4 4 16 14 8 
4 15 4 12 7 
4 14 17 10 6 
4 0 18 2 13 
4 2 17 14 15 
4 10 19 14 11 
4 4 18 0 16 
4 19 4 15 14 
4 18 10 17 2 
4 10 19 4 18 
cubohemioctahedron
hexahemioctacron
4/3 4|3
(6.4/3.6.4)
octahedral group
S4
4{6}+3{4}+3{4/3}
19 12 24 10 12 0 1 1 -2 3 4 48 4 1 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8660254038  0.0000000000  0.5000000000
-0.8660254038  0.0000000000  0.5000000000
 0.2886751346  0.8164965809  0.5000000000
-0.2886751346 -0.8164965809  0.5000000000
 0.8660254038  0.0000000000 -0.5000000000
 0.5773502692 -0.8164965809 -0.0000000000
-0.5773502692  0.8164965809  0.0000000000
-0.8660254038 -0.0000000000 -0.5000000000
 0.2886751346  0.8164965809 -0.5000000000
-0.2886751346 -0.8164965809 -0.5000000000
 0.0000000000 -0.0000000000 -1.0000000000
 0.0000000000  1.0000000000  0.0000000000
-0.4082482905  0.5773502692  0.7071067812
-0.9428090416  0.3333333333  0.0000000000
 0.4082482905 -0.5773502692  0.7071067812
 0.4714045208  0.3333333333 -0.8164965809
 0.8164965809  0.5773502692  0.0000000000
-0.8164965809 -0.5773502692  0.0000000000
 0.4714045208  0.3333333333  0.8164965809
 0.4082482905 -0.5773502692 -0.7071067812
-0.4082482905  0.5773502692 -0.7071067812
6 0 1 5 11 8 2 
4 0 2 7 3 3
6 0 3 9 11 10 4 
4 0 1 6 4 
6 1 6 10 8 7 3 
4 1 3 9 5 3
4 2 8 10 4 
6 2 4 6 5 9 7 
4 5 6 10 11 
4 7 9 11 8 
4 3 0 1 2 
4 3 4 5 0 
4 6 0 1 7 
4 1 4 5 2 
4 6 2 3 7 
4 5 7 8 0 
4 8 4 3 7 
4 9 7 1 4 
4 9 0 6 4 
4 9 2 5 7 
4 8 2 6 4 
4 8 0 9 2 
cubitruncated cuboctahedron
tetradyakishexahedron
4/3 3 4|
(8/3.6.8)
octahedral group
S4
6{8}+8{6}+6{8/3}
20 48 72 20 48 4 0 0 -4 3 3 48 4 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.6998542122  0.0000000000  0.7142857143
 0.4607079005  0.5268245902  0.7142857143
-0.6939926379 -0.0903888097  0.7142857143
 0.1708187941  0.5268245902  0.8326324464
 0.9956048929 -0.0903888097  0.0245104108
 0.2274231631  0.9632603706  0.1428571429
 0.5090227516 -0.2182178902  0.8326324464
-0.9755922264 -0.2182178902  0.0245104108
-0.9272773753  0.3460469708  0.1428571429
-0.0624659433  0.9632603706  0.2612038750
 0.2191336452 -0.2182178902  0.9509791785
 0.7140053045 -0.2182178902 -0.6652648928
 0.7623201555  0.3460469708 -0.5469181607
-0.0541764254  0.8354312901 -0.5469181607
-0.4665694748  0.8728715609 -0.1428571429
-0.0200126666  0.3086066999  0.9509791785
 0.3440655318 -0.8354312901  0.4285714286
-0.8106350066  0.3989955096  0.4285714286
-0.6798415456 -0.3086066999 -0.6652648928
-0.8789625242 -0.3989955096  0.2612038750
-0.3440655318  0.8354312901 -0.4285714286
 0.2332847374  0.8728715609 -0.4285714286
 0.6798415456  0.3086066999  0.6652648928
 0.0541764254 -0.8354312901  0.5469181607
 0.8789625242  0.3989955096 -0.2612038750
 0.0200126666 -0.3086066999 -0.9509791785
 0.8106350066 -0.3989955096 -0.4285714286
-0.3499271061  0.9258200998  0.1428571429
-0.2191336452  0.2182178902 -0.9509791785
-0.7140053045  0.2182178902  0.6652648928
 0.0624659433 -0.9632603706 -0.2612038750
-0.3499271061 -0.9258200998  0.1428571429
-0.7623201555 -0.3460469708  0.5469181607
 0.3499271061  0.9258200998 -0.1428571429
-0.5090227516  0.2182178902 -0.8326324464
 0.9755922264  0.2182178902 -0.0245104108
-0.2274231631 -0.9632603706 -0.1428571429
 0.3499271061 -0.9258200998 -0.1428571429
 0.9272773753 -0.3460469708 -0.1428571429
-0.1708187941 -0.5268245902 -0.8326324464
-0.9956048929  0.0903888097 -0.0245104108
-0.2332847374 -0.8728715609  0.4285714286
-0.4607079005 -0.5268245902 -0.7142857143
 0.6939926379  0.0903888097 -0.7142857143
 0.4665694748 -0.8728715609  0.1428571429
-0.6998542122  0.0000000000 -0.7142857143
 0.0000000000  0.0000000000 -1.0000000000
 0.0639145403  0.0290133127  0.1565580108
-0.0852193870  0.1594308745  0.1565580108
 0.0639145403 -0.9855985597  0.1565580108
 0.1704387741  0.1594308745  0.0521860036
 0.9258200998 -0.0000000000 -0.3779644730
-0.1588456165  0.0000000000  0.0648484514
-0.9258200998 -0.0000000000  0.3779644730
 0.1588456165  0.0000000000 -0.0648484514
-0.0109660014  0.1691019787 -0.0268611081
-0.0675698741 -0.1127346525  0.1997903117
-0.1880882870  0.1127346525 -0.0954183045
-0.3725212402 -0.1691019787 -0.9124869568
 0.1880882870 -0.1127346525  0.0954183045
 0.0675698741  0.1127346525 -0.1997903117
-0.0639145403  0.9855985597 -0.1565580108
 0.0109660014 -0.1691019787  0.0268611081
 0.3725212402  0.1691019787  0.9124869568
-0.0639145403 -0.0290133127 -0.1565580108
-0.1704387741 -0.1594308745 -0.0521860036
 0.0852193870 -0.1594308745 -0.1565580108
8 0 2 7 16 23 11 4 1 3
6 0 3 9 15 6 2 
8 0 1 5 12 26 19 8 3 
6 1 4 10 22 13 5 
8 2 6 14 29 40 31 17 7 
8 3 8 18 33 41 30 20 9 3
8 4 11 24 37 43 35 21 10 
8 5 13 27 36 44 39 25 12 3
8 6 15 22 10 21 34 28 14 3
6 7 17 32 20 30 16 
6 8 19 29 14 28 18 
8 9 20 32 38 27 13 22 15 
6 11 23 36 27 38 24 
6 12 25 34 21 35 26 
8 16 30 41 46 47 44 36 23 
8 17 31 42 45 37 24 38 32 3
8 18 28 34 25 39 45 42 33 
8 19 26 35 43 47 46 40 29 3
6 31 40 46 41 33 42 
6 37 45 39 44 47 43 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 6 0 
3 2 7 3 
3 4 8 1 
3 0 9 4 
3 5 10 2 
3 1 11 5 
3 3 8 6 
3 6 12 0 
3 2 13 7 
3 7 11 3 
3 4 10 8 
3 8 11 1 
3 0 14 9 
3 9 15 4 
3 5 16 10 
3 10 17 2 
3 11 9 5 
3 8 13 6 
3 3 8 11 
3 12 14 0 
3 6 15 12 
3 13 16 7 
3 17 13 2 
3 7 12 11 
3 16 8 10 
3 4 17 10 
3 14 5 9 
3 15 18 4 
3 11 15 9 
3 5 18 16 
3 8 13 16 
3 17 6 13 
3 7 14 12 
3 6 19 15 
3 15 12 11 
3 16 19 7 
3 18 17 4 
3 14 18 5 
3 15 16 18 
3 17 19 6 
3 19 14 7 
3 19 15 16 
3 14 17 18 
3 17 19 14 
great rhombicuboctahedron
great deltoidal icositetrahedron
3/2 4|2
(4.3/2.4.4)
octahedral group
S4
18{4}+8{3/2}
21 24 48 26 24 5 0 0 2 2 4 48 4 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9968739365  0.0000000000  0.0790085736
-0.8508851285  0.5193766874  0.0790085736
 0.4556778364  0.8866314650  0.0790085736
-0.8508851285 -0.5193766874  0.0790085736
 0.1459888080  0.5193766874 -0.8419828529
 0.0427591319  0.8866314650  0.4604957132
 0.1459888080 -0.5193766874 -0.8419828529
-0.4984369683 -0.7345095553  0.4604957132
-0.3952072921  0.3672547776 -0.8419828529
 0.8081259966 -0.3672547776  0.4604957132
-0.4984369683  0.7345095553  0.4604957132
 0.4984369683 -0.7345095553 -0.4604957132
-0.8081259966  0.3672547776 -0.4604957132
 0.3952072921 -0.3672547776  0.8419828529
 0.4984369683  0.7345095553 -0.4604957132
-0.1459888080  0.5193766874  0.8419828529
-0.0427591319 -0.8866314650 -0.4604957132
-0.1459888080 -0.5193766874  0.8419828529
 0.8508851285  0.5193766874 -0.0790085736
-0.4556778364 -0.8866314650 -0.0790085736
 0.8508851285 -0.5193766874 -0.0790085736
-0.9968739365  0.0000000000 -0.0790085736
 0.0000000000  0.0000000000 -1.0000000000
 0.2596883437  0.9238795325  0.2810846377
-0.0959283710  0.3412793093  0.2810846377
-0.7030040762  0.6532814824  0.2810846377
 0.2596883437 -0.9238795325  0.2810846377
 0.3357492986  0.6532814824 -0.6785983445
 0.2877851131  0.3412793093 -0.0734203966
-0.6269431213 -0.3826834324 -0.6785983445
-0.0760609549  0.2705980501  0.9596829823
 0.7345095553  0.0000000000 -0.6785983445
-0.4234483164  0.1413625185 -0.0734203966
-0.6269431213  0.3826834324 -0.6785983445
 0.9626924199  0.2705980501  0.0000000000
-0.7345095553  0.0000000000  0.6785983445
-0.0397348323  0.1413625185 -0.4279254308
 0.6269431213 -0.3826834324  0.6785983445
 0.0397348323 -0.1413625185  0.4279254308
-0.9626924199 -0.2705980501  0.0000000000
-0.3357492986 -0.6532814824  0.6785983445
 0.6269431213  0.3826834324  0.6785983445
 0.4234483164 -0.1413625185  0.0734203966
 0.0760609549 -0.2705980501 -0.9596829823
 0.7030040762 -0.6532814824 -0.2810846377
-0.2596883437  0.9238795325 -0.2810846377
-0.2877851131 -0.3412793093  0.0734203966
-0.2596883437 -0.9238795325 -0.2810846377
 0.0959283710 -0.3412793093 -0.2810846377
4 0 2 5 1 
3 0 3 2 2
4 0 4 9 3 
4 0 1 7 4 
4 1 6 13 7 
3 1 5 6 2
4 2 8 12 5 
4 2 3 10 8 
4 3 9 17 10 
3 4 11 9 2
4 4 7 15 11 
4 5 12 14 6 
4 6 14 20 13 
3 7 13 15 2
4 8 16 19 12 
3 8 10 16 2
4 9 11 18 17 
4 10 17 22 16 
4 11 15 21 18 
3 12 19 14 2
4 13 20 21 15 
4 14 19 23 20 
4 16 22 23 19 
3 17 18 22 2
4 18 21 23 22 
3 20 23 21 2
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 7 8 2 1 
4 2 9 10 3 
4 5 11 6 0 
4 4 12 11 5 
4 10 13 4 3 
4 6 14 15 7 
4 8 16 9 2 
4 15 17 8 7 
4 16 18 10 9 
4 11 19 14 6 
4 13 20 12 4 
4 12 21 19 11 
4 18 20 13 10 
4 14 22 17 15 
4 17 23 16 8 
4 23 24 18 16 
4 21 22 14 19 
4 20 25 21 12 
4 24 25 20 18 
4 22 24 23 17 
4 21 22 24 25 
small rhombihexahedron
small rhombihexacron
3/2 2 4|
(8.4.8/7.4/3)
octahedral group
S4
3{8}+6{4}+6{4/3}+3{8/7}
22 24 48 18 24 0 0 1 -6 4 4 48 4 0 2
 0.0000000000  0.0000000000  1.0000000000
 0.6675992222  0.0000000000  0.7445208382
-0.6389637427 -0.1934271362  0.7445208382
 0.2849157898 -0.6037480552  0.7445208382
-0.0977676425  0.6604015517  0.7445208382
 0.9727633538 -0.1934271362  0.1277395809
 0.5698315797  0.6604015517  0.4890416764
-0.3540479528 -0.7971751914  0.4890416764
-0.7367313852  0.4669744155  0.4890416764
-0.8749957112 -0.4669744155  0.1277395809
 0.5900799214 -0.7971751914  0.1277395809
 0.0488838213  0.9906023276  0.1277395809
 0.8749957112  0.4669744155 -0.1277395809
 0.7367313852 -0.4669744155 -0.4890416764
-0.0488838213 -0.9906023276 -0.1277395809
-0.9727633538  0.1934271362 -0.1277395809
-0.5900799214  0.7971751914 -0.1277395809
-0.5698315797 -0.6604015517 -0.4890416764
 0.3540479528  0.7971751914 -0.4890416764
 0.6389637427  0.1934271362 -0.7445208382
 0.0977676425 -0.6604015517 -0.7445208382
-0.6675992222 -0.0000000000 -0.7445208382
-0.2849157898  0.6037480552 -0.7445208382
-0.0000000000 -0.0000000000 -1.0000000000
 0.1367736397 -0.9238795325  0.3574067443
-0.0849802448 -0.1913417162  0.3574067443
 0.8938887595  0.2705980501  0.3574067443
 0.1367736397  0.1585126678  0.3574067443
-0.4269143440  0.2705980501  0.8628562095
 0.3018740276 -0.1913417162  0.2093640235
-0.3868542724 -0.0000000000  0.1480427208
-0.8938887595 -0.2705980501 -0.3574067443
-0.1651003879  0.3498543840  0.1480427208
-0.1367736397  0.9238795325 -0.3574067443
 0.4269143440 -0.2705980501 -0.8628562095
 0.3868542724 -0.0000000000 -0.1480427208
 0.2217538845  0.3498543840 -0.0000000000
-0.2217538845 -0.3498543840 -0.0000000000
 0.1651003879 -0.3498543840 -0.1480427208
-0.3018740276  0.1913417162 -0.2093640235
-0.1367736397 -0.1585126678 -0.3574067443
 0.0849802448  0.1913417162 -0.3574067443
8 0 2 9 17 20 13 5 1 
4 0 3 7 2 
8 0 4 11 18 19 13 10 3 7
4 0 1 6 4 3
8 1 3 7 9 15 16 11 6 7
4 1 5 10 3 
4 2 8 15 9 3
8 2 7 14 20 23 22 16 8 7
4 4 8 16 11 
8 4 6 12 19 23 21 15 8 
8 5 12 18 22 21 17 14 10 7
4 5 13 19 12 3
4 6 11 18 12 
4 7 9 17 14 3
4 10 13 20 14 
4 15 21 22 16 
4 17 21 23 20 3
4 18 22 23 19 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 1 4 5 2 
4 2 8 9 3 
4 5 10 11 0 
4 9 12 4 3 
4 7 13 4 1 
4 6 9 8 7 
4 0 13 4 6 
4 10 14 2 5 
4 2 12 4 8 
4 10 12 9 11 
4 11 2 14 0 
4 7 14 10 13 
4 4 15 9 6 
4 15 7 8 4 
4 0 16 10 13 
4 2 17 10 12 
4 9 17 2 11 
4 7 16 0 14 
4 15 10 16 9 
4 17 7 15 10 
4 9 17 7 16 
stellated truncated hexahedron
great triakisoctahedron
2 3|4/3
(8/3.8/3.3)
octahedral group
S4
8{3}+6{8/3}
23 24 36 14 24 7 0 0 2 2 3 48 4 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8722604191  0.0000000000 -0.4890416764
-0.1277395809  0.8628562095 -0.4890416764
-0.8348463621 -0.2527247326 -0.4890416764
-0.4890416764  0.8628562095  0.1277395809
-0.7819348952 -0.6101314769  0.1277395809
 0.9251718860 -0.3574067443  0.1277395809
 0.2180651048  0.9675382212  0.1277395809
-0.2709765716 -0.6101314769 -0.7445208382
 0.5638697904 -0.3574067443  0.7445208382
 0.2709765716  0.6101314769  0.7445208382
-0.4361302096  0.5054494651  0.7445208382
-0.4361302096 -0.5054494651  0.7445208382
 0.4361302096 -0.5054494651 -0.7445208382
 0.7819348952  0.6101314769 -0.1277395809
 0.4361302096  0.5054494651 -0.7445208382
-0.5638697904  0.3574067443 -0.7445208382
 0.4890416764 -0.8628562095 -0.1277395809
-0.2180651048 -0.9675382212 -0.1277395809
-0.9251718860  0.3574067443 -0.1277395809
 0.1277395809 -0.8628562095  0.4890416764
-0.8722604191 -0.0000000000  0.4890416764
 0.8348463621  0.2527247326  0.4890416764
 0.0000000000 -0.0000000000 -1.0000000000
 0.1459106924  0.1691019787  0.0854725047
-0.1886469447  0.1195731559  0.0854725047
 0.1459106924 -0.9855985597  0.0854725047
-0.0177019353  0.1195731559 -0.2063488801
 0.0604381877 -0.4082482905 -0.9108680249
-0.7649573325 -0.4082482905  0.4981702648
 0.0177019353 -0.1195731559  0.2063488801
 0.8504298372 -0.1691019787  0.4981702648
 0.1886469447 -0.1195731559 -0.0854725047
 0.7649573325  0.4082482905 -0.4981702648
-0.8504298372  0.1691019787 -0.4981702648
-0.1459106924 -0.1691019787 -0.0854725047
-0.0604381877  0.4082482905  0.9108680249
-0.1459106924  0.9855985597 -0.0854725047
8 0 2 6 11 15 9 4 1 3
8 0 3 7 12 16 10 5 2 3
3 0 1 3 
8 1 4 8 14 19 13 7 3 3
3 2 5 6 
3 4 9 8 
8 5 10 17 21 22 18 11 6 3
3 7 13 12 
8 8 9 15 18 22 23 20 14 3
3 10 16 17 
3 11 18 15 
8 12 13 19 20 23 21 17 16 3
3 14 20 19 
3 21 23 22 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 3 2 
3 3 5 0 
3 4 6 1 
3 0 6 4 
3 1 7 3 
3 3 8 5 
3 8 0 5 
3 6 9 1 
3 0 10 6 
3 1 11 7 
3 11 3 7 
3 3 12 8 
3 8 10 0 
3 9 11 1 
3 6 11 9 
3 8 6 10 
3 11 12 3 
3 11 8 12 
3 6 13 11 
3 8 13 6 
3 11 8 13 
great truncated cuboctahedron
great disdyakisdodecahedron
4/3 2 3|
(8/3.4.6)
octahedral group
S4
8{6}+12{4}+6{8/3}
24 48 72 26 48 1 0 0 2 3 3 48 4 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8305094692  0.0000000000  0.5570045077
 0.5180497550  0.6491305182  0.5570045077
-0.7696968212  0.3119499667  0.5570045077
 0.1740414692  0.6491305182  0.7404992487
 0.8913221171  0.3119499667 -0.3289864768
-0.2516470662  0.9610804849  0.1140090155
 0.6159262346 -0.2688786644  0.7404992487
-0.7088841733  0.6238999334 -0.3289864768
 0.2348541172  0.9610804849 -0.1454917358
 0.2719179488 -0.2688786644  0.9239939897
 0.1216252958  0.6238999334 -0.7719819690
-0.9234674078  0.3550212690 -0.1454917358
-0.0405417653  0.3802518538  0.9239939897
-0.0558941070 -0.8749378802  0.4809984974
-0.2768364897  0.8318665779  0.4809984974
 0.3935432447  0.3550212690 -0.8479879793
 0.7899677039  0.3802518538  0.4809984974
 0.4306070763 -0.8749378802  0.2214977461
 0.5536729794  0.8318665779  0.0380030052
-0.4914197242  0.5629879135  0.6644932384
-0.8255909283 -0.5629879135  0.0380030052
-0.7123621069 -0.2258073621  0.6644932384
-0.9486568314  0.2258073621  0.2214977461
 0.8255909283  0.5629879135 -0.0380030052
 0.4914197242 -0.5629879135 -0.6644932384
 0.9486568314 -0.2258073621 -0.2214977461
 0.7123621069  0.2258073621 -0.6644932384
-0.3935432447 -0.3550212690  0.8479879793
-0.4306070763  0.8749378802 -0.2214977461
-0.5536729794 -0.8318665779 -0.0380030052
-0.7899677039 -0.3802518538 -0.4809984974
 0.9234674078 -0.3550212690  0.1454917358
 0.0558941070  0.8749378802 -0.4809984974
 0.2768364897 -0.8318665779 -0.4809984974
 0.0405417653 -0.3802518538 -0.9239939897
-0.2348541172 -0.9610804849  0.1454917358
-0.2719179488  0.2688786644 -0.9239939897
-0.1216252958 -0.6238999334  0.7719819690
 0.2516470662 -0.9610804849 -0.1140090155
-0.6159262346  0.2688786644 -0.7404992487
 0.7088841733 -0.6238999334  0.3289864768
-0.8913221171 -0.3119499667  0.3289864768
-0.1740414692 -0.6491305182 -0.7404992487
 0.7696968212 -0.3119499667 -0.5570045077
-0.5180497550 -0.6491305182 -0.5570045077
-0.8305094692  0.0000000000 -0.5570045077
 0.0000000000  0.0000000000 -1.0000000000
 0.1801043973  0.0866934567  0.3376522109
-0.0762733399  0.2913001116  0.3376522109
 0.1801043973  0.9238795325  0.3376522109
 0.3229079525  0.2913001116  0.1247280725
-0.4554111647  0.1275611441  0.8810952421
-0.2736567697  0.2705980501  0.0764920424
 0.9854240134  0.1275611441  0.1125507370
 0.2159554198  0.2705980501 -0.1846681261
-0.0292293734 -0.1499375931  0.4258482767
-0.0470439665  0.4412377047 -0.0881960659
 0.3699519190 -0.1499375931  0.2129241384
-0.3991812924  0.0000000000  0.2129241384
 0.3499084514 -0.6687572443  0.6559937682
-0.2159554198 -0.2705980501  0.1846681261
-0.3499084514  0.6687572443 -0.6559937682
 0.3991812924  0.0000000000 -0.2129241384
 0.2736567697 -0.2705980501 -0.0764920424
-0.9854240134 -0.1275611441 -0.1125507370
-0.3699519190  0.1499375931 -0.2129241384
 0.4554111647 -0.1275611441 -0.8810952421
 0.0292293734  0.1499375931 -0.4258482767
 0.0470439665 -0.4412377047  0.0881960659
-0.1801043973 -0.0866934567 -0.3376522109
-0.3229079525 -0.2913001116 -0.1247280725
-0.1801043973 -0.9238795325 -0.3376522109
 0.0762733399 -0.2913001116 -0.3376522109
8 0 2 7 13 17 10 4 1 3
4 0 3 6 2 
6 0 1 5 11 8 3 
4 1 4 9 5 
6 2 6 12 21 14 7 
8 3 8 15 23 29 20 12 6 3
6 4 10 18 25 16 9 
8 5 9 16 24 33 27 19 11 3
4 7 14 22 13 
4 8 11 19 15 
4 10 17 26 18 
4 12 20 28 21 
6 13 22 30 34 26 17 
8 14 21 28 36 42 38 30 22 3
6 15 19 27 35 31 23 
4 16 25 32 24 
8 18 26 34 41 44 39 32 25 3
6 20 29 37 43 36 28 
4 23 31 37 29 
6 24 32 39 45 40 33 
4 27 33 40 35 
4 30 38 41 34 
8 31 35 40 45 47 46 43 37 3
4 36 43 46 42 
6 38 42 46 47 44 41 
4 39 44 47 45 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 6 0 
3 2 7 3 
3 4 5 1 
3 0 8 4 
3 5 9 2 
3 7 6 3 
3 6 10 0 
3 9 7 2 
3 4 11 5 
3 0 12 8 
3 8 13 4 
3 5 14 9 
3 7 15 6 
3 10 12 0 
3 6 16 10 
3 14 7 9 
3 11 17 5 
3 13 11 4 
3 12 13 8 
3 5 18 14 
3 7 19 15 
3 15 16 6 
3 16 12 10 
3 14 20 7 
3 13 17 11 
3 17 18 5 
3 12 21 13 
3 18 22 14 
3 19 16 15 
3 20 19 7 
3 16 21 12 
3 22 20 14 
3 13 23 17 
3 17 22 18 
3 21 24 13 
3 19 25 16 
3 22 19 20 
3 16 24 21 
3 24 23 13 
3 23 22 17 
3 25 24 16 
3 22 25 19 
3 24 22 23 
3 25 24 22 
great rhombihexahedron
great rhombihexacron
4/3 3/2 2|
(4.8/3.4/3.8/5)
octahedral group
S4
6{4}+3{8/3}+3{8/5}+6{4/3}
25 24 48 18 24 0 0 1 -6 4 4 48 4 0 1
 0.0000000000  0.0000000000  1.0000000000
 0.9968739365  0.0000000000  0.0790085736
-0.8508851285 -0.5193766874  0.0790085736
 0.0729944040 -0.9941978990  0.0790085736
 0.4556778364  0.8866314650  0.0790085736
 0.1459888080 -0.5193766874 -0.8419828529
 0.0427591319  0.8866314650  0.4604957132
 0.4254425643 -0.7790650311  0.4604957132
-0.3952072921  0.3672547776 -0.8419828529
 0.5286722404 -0.1075664339 -0.8419828529
-0.8811204006 -0.1075664339  0.4604957132
 0.8081259966 -0.3672547776  0.4604957132
-0.8081259966  0.3672547776 -0.4604957132
 0.3952072921 -0.3672547776  0.8419828529
 0.8811204006  0.1075664339 -0.4604957132
-0.5286722404  0.1075664339  0.8419828529
-0.0427591319 -0.8866314650 -0.4604957132
-0.4254425643  0.7790650311 -0.4604957132
-0.1459888080  0.5193766874  0.8419828529
-0.4556778364 -0.8866314650 -0.0790085736
 0.8508851285  0.5193766874 -0.0790085736
-0.0729944040  0.9941978990 -0.0790085736
-0.9968739365  0.0000000000 -0.0790085736
 0.0000000000  0.0000000000 -1.0000000000
 0.2596883437 -0.9238795325  0.2810846377
-0.1390719130 -0.2705980501  0.2810846377
 0.9404146820 -0.1913417162  0.2810846377
 0.2596883437  0.1585126678  0.2810846377
 0.2059051267 -0.1913417162  0.9596829823
 0.2911938228 -0.2705980501 -0.1164290691
-0.2596883437 -0.1585126678 -0.2810846377
 0.0537832170 -0.7325378163 -0.6785983445
 0.1390719130  0.2705980501 -0.2810846377
 0.7345095553 -0.0000000000 -0.6785983445
-0.6807263383 -0.7325378163 -0.0000000000
-0.7345095553 -0.0000000000  0.6785983445
-0.2911938228  0.2705980501  0.1164290691
 0.6807263383  0.7325378163 -0.0000000000
-0.0537832170  0.7325378163  0.6785983445
-0.2059051267  0.1913417162 -0.9596829823
-0.9404146820  0.1913417162 -0.2810846377
-0.2596883437  0.9238795325 -0.2810846377
4 0 2 5 1 
8 0 3 10 13 19 15 7 2 3
4 0 4 9 3 3
8 0 1 6 13 20 18 11 4 5
4 1 3 10 6 3
8 1 5 7 14 16 11 9 3 3
8 2 8 16 22 23 19 12 5 5
4 2 7 14 8 3
8 4 8 14 21 23 20 17 9 3
4 4 11 16 8 
4 5 12 15 7 3
4 6 12 19 13 
8 6 10 17 18 22 21 15 12 3
4 9 17 18 11 
4 10 17 20 13 3
4 14 16 22 21 
4 15 19 23 21 3
4 18 20 23 22 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 1 4 5 2 
4 2 8 9 3 
4 5 10 6 0 
4 3 11 12 4 
4 7 5 10 1 
4 6 9 8 7 
4 5 13 8 2 
4 1 14 12 4 
4 9 5 13 3 
4 10 12 11 6 
4 3 14 1 11 
4 8 15 5 7 
4 12 16 1 10 
4 6 15 5 9 
4 13 12 14 8 
4 12 17 3 13 
4 16 6 11 1 
4 17 8 14 3 
4 8 16 12 15 
4 6 17 12 15 
4 16 6 17 8 
icosahedron
dodecahedron
5|2 3
(3.3.3.3.3)
icosahedral group
A5
20{3}
26 12 30 20 12 1 0 0 2 1 5 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8944271910  0.0000000000  0.4472135955
 0.2763932023  0.8506508084  0.4472135955
-0.7236067977  0.5257311121  0.4472135955
-0.7236067977 -0.5257311121  0.4472135955
 0.2763932023 -0.8506508084  0.4472135955
 0.7236067977  0.5257311121 -0.4472135955
 0.7236067977 -0.5257311121 -0.4472135955
-0.2763932023  0.8506508084 -0.4472135955
-0.8944271910 -0.0000000000 -0.4472135955
-0.2763932023 -0.8506508084 -0.4472135955
 0.0000000000  0.0000000000 -1.0000000000
 0.4911234732  0.3568220898  0.7946544723
-0.1875924741  0.5773502692  0.7946544723
-0.6070619982 -0.0000000000  0.7946544723
-0.1875924741 -0.5773502692  0.7946544723
 0.4911234732 -0.3568220898  0.7946544723
 0.7946544723 -0.5773502692  0.1875924741
 0.9822469464  0.0000000000 -0.1875924741
 0.7946544723  0.5773502692  0.1875924741
 0.3035309991  0.9341723590 -0.1875924741
-0.3035309991  0.9341723590  0.1875924741
-0.7946544723  0.5773502692 -0.1875924741
-0.9822469464 -0.0000000000  0.1875924741
-0.7946544723 -0.5773502692 -0.1875924741
-0.3035309991 -0.9341723590  0.1875924741
 0.3035309991 -0.9341723590 -0.1875924741
 0.6070619982  0.0000000000 -0.7946544723
 0.1875924741  0.5773502692 -0.7946544723
 0.1875924741 -0.5773502692 -0.7946544723
-0.4911234732  0.3568220898 -0.7946544723
-0.4911234732 -0.3568220898 -0.7946544723
3 0 2 1 
3 0 3 2 
3 0 4 3 
3 0 5 4 
3 0 1 5 
3 1 7 5 
3 1 6 7 
3 1 2 6 
3 2 8 6 
3 2 3 8 
3 3 9 8 
3 3 4 9 
3 4 10 9 
3 4 5 10 
3 5 7 10 
3 6 11 7 
3 6 8 11 
3 7 11 10 
3 8 9 11 
3 9 10 11 
5 4 0 1 2 3 
5 4 5 6 7 0 
5 7 8 9 1 0 
5 9 10 11 2 1 
5 11 12 13 3 2 
5 13 14 5 4 3 
5 6 15 16 8 7 
5 14 17 15 6 5 
5 16 18 10 9 8 
5 18 19 12 11 10 
5 19 17 14 13 12 
5 15 16 18 19 17 
dodecahedron
icosahedron
3|2 5
(5.5.5)
icosahedral group
A5
12{5}
27 20 30 12 20 1 0 0 2 1 3 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.6666666667  0.0000000000  0.7453559925
-0.3333333333  0.5773502692  0.7453559925
-0.3333333333 -0.5773502692  0.7453559925
 0.7453559925  0.5773502692  0.3333333333
 0.7453559925 -0.5773502692  0.3333333333
-0.8726779962  0.3568220898  0.3333333333
 0.1273220038  0.9341723590  0.3333333333
 0.1273220038 -0.9341723590  0.3333333333
-0.8726779962 -0.3568220898  0.3333333333
 0.8726779962  0.3568220898 -0.3333333333
 0.8726779962 -0.3568220898 -0.3333333333
-0.7453559925  0.5773502692 -0.3333333333
-0.1273220038  0.9341723590 -0.3333333333
-0.1273220038 -0.9341723590 -0.3333333333
-0.7453559925 -0.5773502692 -0.3333333333
 0.3333333333  0.5773502692 -0.7453559925
 0.3333333333 -0.5773502692 -0.7453559925
-0.6666666667  0.0000000000 -0.7453559925
 0.0000000000  0.0000000000 -1.0000000000
 0.3035309991  0.5257311121  0.7946544723
-0.6070619982  0.0000000000  0.7946544723
 0.3035309991 -0.5257311121  0.7946544723
 0.9822469464  0.0000000000  0.1875924741
-0.4911234732  0.8506508084  0.1875924741
-0.4911234732 -0.8506508084  0.1875924741
 0.4911234732  0.8506508084 -0.1875924741
 0.4911234732 -0.8506508084 -0.1875924741
-0.9822469464 -0.0000000000 -0.1875924741
 0.6070619982  0.0000000000 -0.7946544723
-0.3035309991  0.5257311121 -0.7946544723
-0.3035309991 -0.5257311121 -0.7946544723
5 0 2 7 4 1 
5 0 3 9 6 2 
5 0 1 5 8 3 
5 1 4 10 11 5 
5 2 6 12 13 7 
5 3 8 14 15 9 
5 4 7 13 16 10 
5 5 11 17 14 8 
5 6 9 15 18 12 
5 10 16 19 17 11 
5 12 18 19 16 13 
5 14 17 19 18 15 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 6 0 
3 2 7 3 
3 4 8 1 
3 6 4 0 
3 5 7 2 
3 8 5 1 
3 3 9 6 
3 7 9 3 
3 4 10 8 
3 6 10 4 
3 5 11 7 
3 8 11 5 
3 9 10 6 
3 11 9 7 
3 10 11 8 
3 9 10 11 
icosidodecahedron
rhombic triacontahedron
2|3 5
(3.5.3.5)
icosahedral group
A5
12{5}+20{3}
28 30 60 32 30 1 0 0 2 2 4 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.5877852523  0.0000000000  0.8090169944
 0.2628655561  0.5257311121  0.8090169944
-0.5877852523 -0.0000000000  0.8090169944
-0.2628655561 -0.5257311121  0.8090169944
 0.9510565163  0.0000000000  0.3090169944
 0.6881909602 -0.5257311121  0.5000000000
-0.1624598481  0.8506508084  0.5000000000
 0.4253254042  0.8506508084  0.3090169944
-0.9510565163 -0.0000000000  0.3090169944
-0.6881909602  0.5257311121  0.5000000000
 0.1624598481 -0.8506508084  0.5000000000
-0.4253254042 -0.8506508084  0.3090169944
 0.9510565163 -0.0000000000 -0.3090169944
 0.8506508084  0.5257311121  0.0000000000
 0.5257311121 -0.8506508084  0.0000000000
-0.5257311121  0.8506508084  0.0000000000
 0.4253254042  0.8506508084 -0.3090169944
-0.9510565163 -0.0000000000 -0.3090169944
-0.8506508084 -0.5257311121  0.0000000000
-0.4253254042 -0.8506508084 -0.3090169944
 0.5877852523 -0.0000000000 -0.8090169944
 0.6881909602 -0.5257311121 -0.5000000000
 0.1624598481 -0.8506508084 -0.5000000000
-0.6881909602  0.5257311121 -0.5000000000
-0.1624598481  0.8506508084 -0.5000000000
 0.2628655561  0.5257311121 -0.8090169944
-0.5877852523 -0.0000000000 -0.8090169944
-0.2628655561 -0.5257311121 -0.8090169944
 0.0000000000  0.0000000000 -1.0000000000
 0.2763932023  0.1708203932  0.8506508084
-0.2763932023  0.4472135955  0.8506508084
-0.2763932023 -0.1708203932  0.8506508084
 0.2763932023 -0.4472135955  0.8506508084
 0.7236067977 -0.1708203932  0.5257311121
 0.7236067977  0.4472135955  0.5257311121
 0.1708203932  0.7236067977  0.5257311121
-0.7236067977  0.1708203932  0.5257311121
-0.7236067977 -0.4472135955  0.5257311121
-0.1708203932 -0.7236067977  0.5257311121
 0.8944271910 -0.4472135955  0.0000000000
 0.8944271910  0.1708203932  0.0000000000
 0.4472135955 -0.7236067977  0.3249196962
 0.0000000000  1.0000000000  0.0000000000
-0.4472135955  0.7236067977  0.3249196962
 0.5527864045  0.7236067977 -0.0000000000
-0.8944271910  0.4472135955 -0.0000000000
-0.8944271910 -0.1708203932  0.0000000000
-0.0000000000 -1.0000000000  0.0000000000
-0.5527864045 -0.7236067977 -0.0000000000
 0.7236067977 -0.1708203932 -0.5257311121
 0.7236067977  0.4472135955 -0.5257311121
 0.4472135955 -0.7236067977 -0.3249196962
-0.4472135955  0.7236067977 -0.3249196962
 0.1708203932  0.7236067977 -0.5257311121
-0.7236067977  0.1708203932 -0.5257311121
-0.7236067977 -0.4472135955 -0.5257311121
-0.1708203932 -0.7236067977 -0.5257311121
 0.2763932023 -0.4472135955 -0.8506508084
 0.2763932023  0.1708203932 -0.8506508084
-0.2763932023  0.4472135955 -0.8506508084
-0.2763932023 -0.1708203932 -0.8506508084
3 0 2 1 
5 0 3 10 7 2 
3 0 4 3 
5 0 1 6 11 4 
3 1 5 6 
5 1 2 8 14 5 
3 2 7 8 
3 3 9 10 
5 3 4 12 19 9 
3 4 11 12 
5 5 13 22 15 6 
3 5 14 13 
3 6 15 11 
5 7 16 25 17 8 
3 7 10 16 
3 8 17 14 
5 9 18 24 16 10 
3 9 19 18 
5 11 15 23 20 12 
3 12 20 19 
3 13 21 22 
5 13 14 17 26 21 
3 15 22 23 
3 16 24 25 
3 17 25 26 
3 18 27 24 
5 18 19 20 28 27 
3 20 23 28 
5 21 29 28 23 22 
3 21 26 29 
5 24 27 29 26 25 
3 27 28 29 
4 3 0 1 2 
4 3 4 5 0 
4 5 6 1 0 
4 1 7 8 2 
4 8 9 3 2 
4 4 10 11 5 
4 3 12 10 4 
4 6 13 14 1 
4 5 15 13 6 
4 7 16 17 8 
4 14 16 7 1 
4 9 18 12 3 
4 8 19 18 9 
4 10 20 21 11 
4 21 15 5 11 
4 18 22 10 12 
4 13 23 16 14 
4 21 24 13 15 
4 16 25 26 17 
4 26 19 8 17 
4 26 27 18 19 
4 20 28 29 21 
4 22 28 20 10 
4 27 28 22 18 
4 23 30 25 16 
4 24 30 23 13 
4 29 30 24 21 
4 30 31 26 25 
4 31 28 27 26 
4 28 29 30 31 
truncated icosahedron
pentakisdodecahedron
2 5|3
(6.6.5)
icosahedral group
A5
20{6}+12{5}
29 60 90 32 60 1 0 0 2 2 3 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.3952480672  0.0000000000  0.9185744202
-0.2227859215  0.3264773618  0.9185744202
-0.1440965957 -0.3680451137  0.9185744202
 0.5677102129  0.3264773618  0.7557232605
 0.4954282110 -0.3680451137  0.7868250644
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 0.8403525023  0.2849096099  0.4611227451
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 0.7680705005 -0.4096128656  0.4922245490
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-0.8319652063 -0.5184386529  0.1976240336
 0.8319652063  0.5184386529 -0.1976240336
 0.9864290700 -0.1503935392 -0.0658746779
 0.2195822596  0.9733674322  0.0658746779
 0.8423324743 -0.5184386529 -0.1473002577
-0.7073794566  0.6786450072 -0.1976240336
-0.9864290700  0.1503935392  0.0658746779
-0.3740461233  0.9061093968 -0.1976240336
 0.1756658076 -0.9733674322 -0.1473002577
-0.2195822596 -0.9733674322 -0.0658746779
-0.7860687824 -0.5856966883 -0.1976240336
 0.5716701569  0.6786450072 -0.4611227451
 0.9321453501  0.1503935392 -0.3293733893
 0.2654786835  0.9061093968 -0.3293733893
 0.6439521587 -0.5856966883 -0.4922245490
-0.7680705005  0.4096128656 -0.4922245490
-0.9405326461  0.0831355038 -0.3293733893
-0.1014038338  0.8645416449 -0.4922245490
 0.3106188254 -0.8131610779 -0.4922245490
-0.4798773090 -0.8131610779 -0.3293733893
-0.8403525023 -0.2849096099 -0.4611227451
 0.5109791130  0.4096128656 -0.7557232605
 0.7337650345  0.0831355038 -0.6742976806
 0.5896684388 -0.2849096099 -0.7557232605
-0.4954282110  0.3680451137 -0.7868250644
-0.1620948777  0.5955095034 -0.7868250644
 0.0503237759 -0.6529547237 -0.7557232605
-0.3449242913 -0.6529547237 -0.6742976806
-0.5677102129 -0.3264773618 -0.7557232605
 0.1440965957  0.3680451137 -0.9185744202
 0.2227859215 -0.3264773618 -0.9185744202
-0.3952480672 -0.0000000000 -0.9185744202
-0.0000000000 -0.0000000000 -1.0000000000
 0.1884917927  0.3568220898  0.9149583817
-0.4009827382 -0.0454313035  0.9149583817
 0.1884917927 -0.2762216876  0.9149583817
 0.7299680182 -0.0454313035  0.6819697127
-0.3769835855  0.5524433752  0.7082839194
-0.2238218084 -0.6962909658  0.6819697127
 0.6262353286  0.5524433752  0.5016094570
 0.4751441987 -0.6962909658  0.5379747963
-0.8612946448  0.2378813932  0.4489810437
 0.0924951818  0.8887410555  0.4489810437
-0.7427296631 -0.3817289838  0.5016094570
 0.9686221187  0.2378813932  0.0719974582
 0.8805126380 -0.3817289838  0.1672031523
-0.5563085176  0.8152316624  0.1609912108
 0.0344457437 -0.9590792530  0.1672031523
-0.5746422389 -0.8152316624  0.0719974582
 0.5746422389  0.8152316624 -0.0719974582
 0.5563085176 -0.8152316624 -0.1609912108
-0.8805126380  0.3817289838 -0.1672031523
-0.9686221187 -0.2378813932 -0.0719974582
-0.0344457437  0.9590792530 -0.1672031523
 0.7427296631  0.3817289838 -0.5016094570
 0.8612946448 -0.2378813932 -0.4489810437
-0.4751441987  0.6962909658 -0.5379747963
-0.0924951818 -0.8887410555 -0.4489810437
-0.6262353286 -0.5524433752 -0.5016094570
 0.2238218084  0.6962909658 -0.6819697127
 0.3769835855 -0.5524433752 -0.7082839194
-0.7299680182  0.0454313035 -0.6819697127
 0.4009827382  0.0454313035 -0.9149583817
-0.1884917927  0.2762216876 -0.9149583817
-0.1884917927 -0.3568220898 -0.9149583817
6 0 2 7 11 4 1 
6 0 3 9 14 6 2 
5 0 1 5 8 3 
6 1 4 10 19 12 5 
5 2 6 13 15 7 
6 3 8 16 26 17 9 
5 4 11 20 18 10 
6 5 12 21 25 16 8 
6 6 14 23 33 22 13 
6 7 15 24 30 20 11 
5 9 17 27 23 14 
6 10 18 28 39 29 19 
5 12 19 29 31 21 
6 13 22 32 34 24 15 
5 16 25 35 36 26 
6 17 26 36 46 37 27 
6 18 20 30 40 38 28 
6 21 31 41 45 35 25 
5 22 33 43 42 32 
6 23 27 37 47 43 33 
5 24 34 44 40 30 
5 28 38 48 49 39 
6 29 39 49 50 41 31 
6 32 42 51 52 44 34 
6 35 45 53 54 46 36 
5 37 46 54 55 47 
6 38 40 44 52 56 48 
5 41 50 57 53 45 
6 42 43 47 55 58 51 
6 48 56 59 57 50 49 
5 51 58 59 56 52 
6 53 57 59 58 55 54 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 6 0 
3 2 7 3 
3 4 8 1 
3 0 9 4 
3 5 7 2 
3 1 10 5 
3 3 11 6 
3 6 9 0 
3 7 12 3 
3 4 13 8 
3 8 10 1 
3 9 13 4 
3 5 14 7 
3 10 15 5 
3 11 16 6 
3 12 11 3 
3 16 9 6 
3 7 17 12 
3 13 18 8 
3 8 19 10 
3 9 20 13 
3 14 17 7 
3 15 14 5 
3 19 15 10 
3 11 21 16 
3 12 22 11 
3 16 20 9 
3 17 22 12 
3 13 23 18 
3 18 19 8 
3 20 23 13 
3 14 24 17 
3 15 24 14 
3 19 25 15 
3 21 26 16 
3 22 21 11 
3 26 20 16 
3 17 27 22 
3 23 28 18 
3 28 19 18 
3 26 23 20 
3 24 27 17 
3 25 24 15 
3 28 25 19 
3 21 29 26 
3 22 29 21 
3 27 29 22 
3 23 30 28 
3 26 30 23 
3 24 31 27 
3 25 31 24 
3 28 31 25 
3 29 30 26 
3 31 29 27 
3 30 31 28 
3 29 30 31 
truncated dodecahedron
triakisicosahedron
2 3|5
(10.10.3)
icosahedral group
A5
12{10}+20{3}
30 60 90 32 60 1 0 0 2 2 3 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.3319544852  0.0000000000  0.9432954043
-0.2860795036  0.1683814059  0.9432954043
 0.1611340919 -0.2902233358  0.9432954043
 0.5829886213  0.1683814059  0.7948408455
-0.5878317720  0.1506049079  0.7948408455
-0.4170113787  0.4408282437  0.7948408455
 0.1357750258 -0.5914331516  0.7948408455
 0.8183499926  0.1506049079  0.5546363234
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-0.7899976948 -0.0465394760  0.6113409191
-0.3427840993  0.7132750815  0.6113409191
-0.0663908970 -0.7885775354  0.6113409191
 0.2655635881 -0.7885775354  0.5546363234
 0.9481385550 -0.0465394760  0.3144318014
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-0.8153567609 -0.3477492917  0.4628863603
-0.9462886360 -0.0753024539  0.3144318014
-0.3935022315  0.8638799894  0.3144318014
-0.0917499632  0.8816564874  0.4628863603
-0.3681431654 -0.8063540334  0.4628863603
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 0.9227794888 -0.3477492917  0.1659772426
 0.9970067683 -0.0753024539 -0.0175226837
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-0.6542226690 -0.6379726275  0.4061817646
-0.9970067683  0.0753024539  0.0175226837
-0.5497931728  0.8351170114  0.0175226837
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-0.9481385550  0.0465394760 -0.3144318014
-0.9227794888  0.3477492917 -0.1659772426
-0.7519590956  0.6379726275 -0.1659772426
-0.5009249595  0.8063540334 -0.3144318014
-0.4755658933 -0.8638799894 -0.1659772426
 0.3935022315 -0.8638799894 -0.3144318014
 0.7899976948  0.0465394760 -0.6113409191
 0.8153567609  0.3477492917 -0.4628863603
 0.6542226690  0.6379726275 -0.4061817646
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-0.8183499926 -0.1506049079 -0.5546363234
-0.2655635881  0.7885775354 -0.5546363234
-0.5262840256 -0.7132750815 -0.4628863603
-0.2402045220 -0.8816564874 -0.4061817646
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 0.5878317720 -0.1506049079 -0.7948408455
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-0.6572159007 -0.4408282437 -0.6113409191
-0.5829886213 -0.1683814059 -0.7948408455
-0.1357750258  0.5914331516 -0.7948408455
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 0.2860795036 -0.1683814059 -0.9432954043
-0.3319544852  0.0000000000 -0.9432954043
-0.1611340919  0.2902233358 -0.9432954043
-0.0000000000  0.0000000000 -1.0000000000
 0.1432337790  0.5257311121  0.8385051474
-0.3901124942 -0.3804226065  0.8385051474
 0.1432337790 -0.0843049040  0.8385051474
 0.6463368675 -0.3804226065  0.6614584599
-0.3749909018  0.2207131041  0.7357864254
 0.5979747984  0.2207131041  0.5695840419
-0.7989163046  0.4702282018  0.3749909018
 0.0972965700 -0.6299377043  0.5695840419
 0.8780939903  0.4702282018  0.0885233438
-0.7412085774 -0.1364082001  0.4033816583
-0.2405303491  0.7142426083  0.4033816583
 0.0151215924 -0.9959593140  0.0885233438
 0.8330829954 -0.1364082001  0.1344605528
 0.3607955236  0.7142426083  0.3006629363
-0.8780939903 -0.4702282018 -0.0885233438
-0.0151215924  0.9959593140 -0.0885233438
-0.4493188674 -0.6621393122  0.3006629363
 0.5236468329 -0.6621393122  0.1344605528
 0.7989163046 -0.4702282018 -0.3749909018
-0.8330829954  0.1364082001 -0.1344605528
-0.5236468329  0.6621393122 -0.1344605528
 0.7412085774  0.1364082001 -0.4033816583
 0.4493188674  0.6621393122 -0.3006629363
-0.6463368675  0.3804226065 -0.6614584599
-0.3607955236 -0.7142426083 -0.3006629363
 0.2405303491 -0.7142426083 -0.4033816583
 0.3901124942  0.3804226065 -0.8385051474
-0.5979747984 -0.2207131041 -0.5695840419
-0.0972965700  0.6299377043 -0.5695840419
-0.1432337790 -0.5257311121 -0.8385051474
 0.3749909018 -0.2207131041 -0.7357864254
-0.1432337790  0.0843049040 -0.8385051475
10 0 2 6 11 19 25 15 9 4 1 
10 0 3 7 12 20 26 16 10 5 2 
3 0 1 3 
10 1 4 8 14 22 31 21 13 7 3 
3 2 5 6 
3 4 9 8 
10 5 10 17 27 35 36 28 18 11 6 
3 7 13 12 
10 8 9 15 24 33 42 41 32 23 14 
3 10 16 17 
3 11 18 19 
10 12 13 21 30 39 48 47 38 29 20 
3 14 23 22 
3 15 25 24 
10 16 26 29 38 46 52 44 34 27 17 
10 18 28 37 45 51 43 33 24 25 19 
3 20 29 26 
3 21 31 30 
10 22 23 32 40 50 55 49 39 30 31 
3 27 34 35 
3 28 36 37 
3 32 41 40 
3 33 43 42 
10 34 44 53 57 58 54 45 37 36 35 
3 38 47 46 
3 39 49 48 
10 40 41 42 43 51 54 58 59 56 50 
3 44 52 53 
3 45 54 51 
10 46 47 48 49 55 56 59 57 53 52 
3 50 56 55 
3 57 59 58 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 3 2 
3 3 5 0 
3 4 6 1 
3 0 6 4 
3 1 7 3 
3 3 8 5 
3 8 0 5 
3 6 9 1 
3 0 10 6 
3 1 11 7 
3 11 3 7 
3 3 12 8 
3 8 13 0 
3 9 14 1 
3 6 14 9 
3 10 15 6 
3 0 15 10 
3 1 16 11 
3 11 17 3 
3 3 18 12 
3 18 8 12 
3 8 15 13 
3 13 0 15 
3 14 16 1 
3 6 19 14 
3 15 20 6 
3 14 11 16 
3 11 18 17 
3 17 3 18 
3 18 21 8 
3 8 22 15 
3 19 23 14 
3 6 23 19 
3 20 23 6 
3 15 23 20 
3 14 24 11 
3 11 25 18 
3 18 26 21 
3 26 8 21 
3 26 22 8 
3 26 15 22 
3 23 27 14 
3 15 28 23 
3 14 29 24 
3 29 11 24 
3 29 25 11 
3 29 18 25 
3 18 30 26 
3 26 28 15 
3 27 29 14 
3 23 29 27 
3 26 23 28 
3 29 30 18 
3 29 26 30 
3 23 31 29 
3 26 31 23 
3 29 26 31 
rhombicosidodecahedron
deltoidal hexecontahedron
3 5|2
(4.3.4.5)
icosahedral group
A5
12{5}+30{4}+20{3}
31 60 120 62 60 1 0 0 2 3 4 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.4364663517  0.0000000000  0.8997205810
-0.0230394894  0.4358578416  0.8997205810
-0.3947875239  0.1861335198  0.8997205810
-0.1650346033 -0.4040624406  0.8997205810
 0.4134268623  0.4358578416  0.7994411620
 0.7478962199  0.1861335198  0.6371856536
 0.5411827887 -0.4040624406  0.7374650726
-0.2253527696  0.7370282030  0.6371856536
-0.5598221272 -0.2179289208  0.7994411620
-0.5971008041  0.4873038812  0.6371856536
 0.1694347542 -0.6537867624  0.7374650726
-0.4551056902 -0.6219913614  0.6371856536
 0.4808646224  0.7370282030  0.4749301452
 0.8526126568 -0.2179289208  0.4749301452
 0.8153339799  0.4873038812  0.3126746369
 0.6875780535 -0.6219913614  0.3746507262
 0.0860770985  0.9231617228  0.3746507262
-0.5296630440  0.7884742426  0.3126746369
-0.8641324015 -0.1664828812  0.4749301452
-0.8871718909  0.2693749604  0.3746507262
-0.1206363326 -0.8717156832  0.4749301452
 0.3158300191 -0.8717156832  0.3746507262
-0.7594159645 -0.5705453218  0.3126746369
 0.6130206997  0.7884742426  0.0501397095
 0.9847687342 -0.1664828812  0.0501397095
 0.9617292448  0.2693749604 -0.0501397095
 0.8197341309 -0.5705453218 -0.0501397095
-0.2182331759  0.9746077624  0.0501397095
 0.2182331759  0.9746077624 -0.0501397095
-0.8197341309  0.5705453218  0.0501397095
-0.9617292448 -0.2693749604  0.0501397095
-0.9847687342  0.1664828812 -0.0501397095
-0.2182331759 -0.9746077624  0.0501397095
 0.2182331759 -0.9746077624 -0.0501397095
-0.6130206997 -0.7884742426 -0.0501397095
 0.7594159645  0.5705453218 -0.3126746369
 0.8871718909 -0.2693749604 -0.3746507262
 0.8641324015  0.1664828812 -0.4749301452
 0.5296630440 -0.7884742426 -0.3126746369
-0.3158300191  0.8717156832 -0.3746507262
 0.1206363326  0.8717156832 -0.4749301452
-0.6875780535  0.6219913614 -0.3746507262
-0.8153339799 -0.4873038812 -0.3126746369
-0.8526126568  0.2179289208 -0.4749301452
-0.0860770985 -0.9231617228 -0.3746507262
-0.4808646224 -0.7370282030 -0.4749301452
 0.4551056902  0.6219913614 -0.6371856536
 0.5971008041 -0.4873038812 -0.6371856536
 0.5598221272  0.2179289208 -0.7994411620
 0.2253527696 -0.7370282030 -0.6371856536
-0.1694347542  0.6537867624 -0.7374650726
-0.5411827887  0.4040624406 -0.7374650726
-0.7478962199 -0.1861335198 -0.6371856536
-0.4134268623 -0.4358578416 -0.7994411620
 0.1650346033  0.4040624406 -0.8997205810
 0.3947875239 -0.1861335198 -0.8997205810
 0.0230394894 -0.4358578416 -0.8997205810
-0.4364663517 -0.0000000000 -0.8997205810
-0.0000000000 -0.0000000000 -1.0000000000
 0.2124281962  0.2239537475  0.9245941063
-0.1379991118  0.2054301247  0.9245941063
-0.2876494382 -0.1119768737  0.9245941063
 0.2124281962 -0.3162277660  0.9245941063
 0.6623583361 -0.1119768737  0.7063270456
 0.5277148574  0.2054301247  0.7716443776
 0.1583346290  0.7071067812  0.6891517578
-0.3186422944  0.4743416490  0.7896976442
-0.7144788670  0.1207882584  0.6891517578
-0.3897157456 -0.4108602493  0.7716443776
-0.1467842735 -0.6555240367  0.7063270456
 0.6313654799  0.4743416490  0.5714305835
 0.9436228948  0.1207882584  0.3081980354
 0.4403528206 -0.6555240367  0.5714305835
 0.6874320834 -0.4108602493  0.5241665181
-0.2279246243  0.8794777841  0.3531635228
-0.4465745066  0.6647858481  0.5241665181
-0.6778547641 -0.4051361351  0.5714305835
-0.7280022588  0.5435471629  0.3531635228
 0.1204287884 -0.7917486474  0.5241665181
-0.4686190076 -0.8278950396  0.3081980354
 0.6305733224  0.6647858481  0.2766886585
 0.3592124698  0.8794777841  0.2182670607
 0.8592901042 -0.4051361351  0.2182670607
 0.8091426096  0.5435471629 -0.0000000000
 0.5561442379 -0.8278950396  0.0727556869
 0.0284293805  0.9486832981  0.1237389298
-0.5561442379  0.8278950396 -0.0727556869
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 0.4686190076  0.8278950396 -0.3081980354
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 0.7280022588 -0.5435471629 -0.3531635228
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-0.3592124698 -0.8794777841 -0.2182670607
-0.0284293805 -0.9486832981 -0.1237389298
 0.2279246243 -0.8794777841 -0.3531635228
-0.6305733224 -0.6647858481 -0.2766886585
 0.6778547641  0.4051361351 -0.5714305835
 0.7144788670 -0.1207882584 -0.6891517578
 0.4465745066 -0.6647858481 -0.5241665181
-0.1204287884  0.7917486474 -0.5241665181
-0.4403528206  0.6555240367 -0.5714305835
 0.1467842735  0.6555240367 -0.7063270456
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-0.1583346290 -0.7071067812 -0.6891517578
 0.3897157456  0.4108602493 -0.7716443776
 0.3186422944 -0.4743416490 -0.7896976442
 0.2876494382  0.1119768737 -0.9245941063
-0.2124281962  0.3162277660 -0.9245941063
-0.5277148574 -0.2054301247 -0.7716443776
-0.2124281962 -0.2239537475 -0.9245941063
 0.1379991118 -0.2054301247 -0.9245941063
4 0 2 5 1 
3 0 3 2 
4 0 4 9 3 
5 0 1 7 11 4 
4 1 6 14 7 
3 1 5 6 
5 2 8 17 13 5 
4 2 3 10 8 
5 3 9 19 20 10 
3 4 12 9 
4 4 11 21 12 
4 5 13 15 6 
5 6 15 26 25 14 
4 7 16 22 11 
3 7 14 16 
4 8 18 28 17 
3 8 10 18 
4 9 12 23 19 
4 10 20 30 18 
3 11 22 21 
5 12 21 33 35 23 
3 13 24 15 
4 13 17 29 24 
4 14 25 27 16 
4 15 24 36 26 
5 16 27 39 34 22 
3 17 28 29 
5 18 30 42 40 28 
4 19 31 32 20 
3 19 23 31 
3 20 32 30 
4 21 22 34 33 
4 23 35 43 31 
5 24 29 41 47 36 
3 25 37 27 
4 25 26 38 37 
3 26 36 38 
4 27 37 48 39 
4 28 40 41 29 
4 30 32 44 42 
5 31 43 53 44 32 
4 33 45 46 35 
3 33 34 45 
4 34 39 50 45 
3 35 46 43 
4 36 47 49 38 
5 37 38 49 56 48 
3 39 48 50 
3 40 51 41 
4 40 42 52 51 
4 41 51 55 47 
3 42 44 52 
4 43 46 54 53 
4 44 53 58 52 
5 45 50 57 54 46 
3 47 55 49 
4 48 56 57 50 
4 49 55 59 56 
5 51 52 58 59 55 
3 53 54 58 
4 54 57 59 58 
3 56 59 57 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 7 8 2 1 
4 2 9 10 3 
4 5 11 6 0 
4 4 12 11 5 
4 3 13 14 4 
4 6 15 16 7 
4 8 17 9 2 
4 16 18 8 7 
4 10 19 13 3 
4 17 20 10 9 
4 11 21 22 6 
4 14 23 12 4 
4 12 24 21 11 
4 13 25 23 14 
4 22 26 15 6 
4 15 27 18 16 
4 8 28 29 17 
4 18 30 28 8 
4 20 31 19 10 
4 31 25 13 19 
4 29 32 20 17 
4 24 33 22 21 
4 23 34 35 12 
4 35 36 24 12 
4 25 37 34 23 
4 26 38 27 15 
4 33 38 26 22 
4 27 39 30 18 
4 28 40 32 29 
4 39 40 28 30 
4 20 41 42 31 
4 42 43 25 31 
4 32 44 41 20 
4 36 45 33 24 
4 37 46 35 34 
4 46 45 36 35 
4 43 47 37 25 
4 38 48 49 27 
4 33 50 48 38 
4 49 51 39 27 
4 40 52 44 32 
4 51 53 40 39 
4 41 54 43 42 
4 52 54 41 44 
4 45 55 50 33 
4 47 56 46 37 
4 46 57 55 45 
4 54 56 47 43 
4 50 58 49 48 
4 58 53 51 49 
4 53 59 52 40 
4 59 60 54 52 
4 57 58 50 55 
4 56 61 57 46 
4 60 61 56 54 
4 58 60 59 53 
4 57 58 60 61 
truncated icosidodecahedron
disdyakistriacontahedron
2 3 5|
(4.6.10)
icosahedral group
A5
12{10}+20{6}+30{4}
32 120 180 62 120 1 0 0 2 3 3 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.2607080006  0.0000000000  0.9654177015
-0.0045873783  0.2606676380  0.9654177015
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 0.2561208549  0.2606676380  0.9308353722
 0.4633267724 -0.1411140222  0.8748800687
-0.2283903908  0.3802212538  0.8962531046
-0.3132059807 -0.3694413065  0.8748800687
-0.4430186467 -0.0215604065  0.8962531046
 0.4541524811  0.3802212538  0.8057154101
 0.5304628314 -0.3694413065  0.7629694001
 0.6613583986 -0.0215604065  0.7497601066
-0.3298032754  0.5736633003  0.7497601066
-0.4476060250  0.2391072316  0.8616708061
-0.5370090771 -0.2498878945  0.8057153910
-0.2460699217 -0.5977685908  0.7629694001
 0.5138663784  0.5736633003  0.6378493263
 0.6567712529  0.2391072316  0.7151777773
 0.7284945175 -0.2498878945  0.6378493381
 0.4364724850 -0.5977685908  0.6724317673
-0.5490190001  0.4325494506  0.7151776775
-0.2700897570  0.7671054904  0.5818940537
-0.6936761144 -0.3586617667  0.6246400447
-0.0434511498 -0.7388826131  0.6724317673
-0.4027369590 -0.7065424630  0.5818940537
 0.7164852035  0.4325494506  0.5473115438
 0.4124538677  0.7671054904  0.4913562594
 0.8325358571 -0.3586617667  0.4221916434
 0.2172568508 -0.7388826131  0.6378494688
 0.5405138246 -0.7065424630  0.4567740725
-0.7085212064  0.4848777911  0.5127291954
-0.0720583700  0.8866594825  0.4567740725
-0.4295919633  0.8194338309  0.3794455716
-0.8531785590 -0.3063341981  0.4221915508
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 0.8176915179  0.4848777911  0.3102806942
 0.1886510811  0.8866594825  0.4221915817
 0.5136601821  0.8194338309  0.2543254098
 0.9337423985 -0.3063341981  0.1851607203
 0.7385455107 -0.5869890510  0.3316540106
 0.3212979948 -0.8476566112  0.4221917432
-0.8651885085  0.3761046523  0.3316536375
-0.6488076880  0.6783199813  0.3448631425
-0.2315603996  0.9389879297  0.2543254788
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 0.9217330580  0.3761046523  0.0946227263
 0.7162790072  0.6783199813  0.1637876273
 0.2898571959  0.9389879297  0.1851606704
 0.8397521423 -0.5346614357  0.0946228761
 0.9934566827 -0.1128925413  0.0172943252
 0.1646311382 -0.9564306093  0.2411163161
-0.8054751299  0.5695467454  0.1637874231
-0.9591793219  0.1477776761  0.2411157125
-0.1303544328  0.9913166095  0.0172945558
-0.8203200648 -0.5695470165  0.0518766546
-0.9888693637 -0.1477781439  0.0172916663
-0.1303536668 -0.9913167102  0.0172945558
 0.8203206401  0.5695467454 -0.0518705331
 0.9888694917  0.1477776761 -0.0172883463
 0.1303553059  0.9913166095 -0.0172879732
 0.8054761704 -0.5695470165 -0.1637813633
 0.9591800640 -0.1477781439 -0.2411124739
 0.1303545664 -0.9913167102 -0.0172877735
-0.8397525647  0.5346618623 -0.0946167165
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-0.2898558028 -0.9389895580 -0.1851545936
 0.7860446559  0.5346618623 -0.3102748651
 0.9545928720  0.1128921245 -0.2756951522
 0.0960787036  0.9564322465 -0.2756922934
 0.6488098576 -0.6783208443 -0.3448573632
 0.8651904546 -0.3761053597 -0.3316477584
 0.2315606390 -0.9389895580 -0.2543192490
-0.7385472639  0.5869902473 -0.3316479890
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-0.3212992842  0.8476584134 -0.4221871436
-0.8176928415 -0.4848792845 -0.3102748723
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-0.1886494644 -0.8866613987 -0.4221882798
 0.6265433179  0.5869902473 -0.5127240198
 0.8531810896  0.3063348862 -0.4221859376
 0.2001204504  0.8476584134 -0.4913522358
 0.7085240020 -0.4848792845 -0.5127239199
 0.4295944105 -0.8194350139 -0.3794402462
 0.0720576700 -0.8866613987 -0.4567704634
-0.8325379870  0.3586633178 -0.4221861255
-0.5405162125  0.7065442357 -0.4567685048
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-0.7164876491 -0.4325518944 -0.5473064108
-0.4124548660 -0.7671068289 -0.4913533317
 0.6936796092  0.3586633178 -0.6246352729
 0.4027407159  0.7065442357 -0.5818893011
 0.0434540643  0.7388844270 -0.6724295858
 0.5490226993 -0.4325518944 -0.7151733596
 0.2700914841 -0.7671068289 -0.5818914876
-0.7284976588  0.2498903768 -0.6378447779
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-0.6567747682 -0.2391103983 -0.7151734903
-0.5138692103 -0.5736660641 -0.6378445591
 0.5370132986  0.2498903768 -0.8057118075
 0.2460744543  0.5977701626 -0.7629667067
 0.4476105365 -0.2391103983 -0.8616675839
 0.3298072522 -0.5736660641 -0.7497562426
-0.6613622562  0.0215634725 -0.7497566156
-0.5304666075  0.3694443652 -0.7629652937
-0.4541562762 -0.3802243954 -0.8057117884
 0.4430232811  0.0215634725 -0.8962507401
 0.3132106967  0.3694443652 -0.8748770888
 0.2283949989 -0.3802243954 -0.8962505976
-0.4633311450  0.1411172572 -0.8748772313
-0.2561255056 -0.2606708670 -0.9308331883
 0.2192205953  0.1411172572 -0.9654161022
 0.0045924376 -0.2606708671 -0.9654168058
-0.2607129987  0.0000032913 -0.9654163518
 0.0000051772  0.0000032913 -1.0000000002
 0.1200387571  0.1221698550  0.9049446030
-0.2175780247  0.1162282816  0.9049446030
 0.1200387571 -0.4082474279  0.9049446030
 0.4459799746  0.1162282816  0.8169252068
 0.1016985225  0.6339220449  0.7666817889
-0.3544276914 -0.1832548434  0.8300952867
 0.5585832497 -0.1832548434  0.7089865490
-0.3643565320  0.3809295903  0.7552459704
-0.4568036952 -0.4649138222  0.6745068322
-0.7747432361  0.0697368203  0.6284189748
 0.5486549126  0.3809295903  0.6341371659
 0.6168557011 -0.4649138222  0.5320884576
 0.9117846887  0.0697368203  0.4047050422
-0.4756956529  0.6085799433  0.5320883790
-0.2091195905 -0.6774423865  0.5878778112
 0.5979647013  0.6085799433  0.3896698773
 0.3551522032 -0.6774423865  0.5130284950
-0.2351136470  0.7996124516  0.3919196492
-0.6935150612 -0.4186830921  0.4381790039
 0.0589047087 -0.8240793946  0.4440690614
-0.5063278658 -0.8431340489  0.1809911096
 0.3291594648  0.7996124516  0.3170701581
 0.7837684883 -0.4186830921  0.2422208418
 0.5360037147 -0.8431340489  0.0427282955
-0.7095802914  0.4941881267  0.3170700500
 0.0283375922  0.9128709077  0.2136305953
-0.5360037809  0.8431342740 -0.0427230226
-0.8627717620 -0.3317288924  0.1592318224
 0.7677040727  0.4941881267  0.1211117799
 0.5063293044  0.8431342740 -0.1809860363
 0.8744481415 -0.3317288924 -0.0712062810
-0.8744476717  0.3317288831  0.0712120936
-0.9130127824 -0.0000002089  0.1211105323
 0.0160652247 -0.9128709077  0.1211120373
 0.8627728239  0.3317288831 -0.1592260883
 0.9130131866 -0.0000002089 -0.1211074853
-0.0160644264  0.9128718312 -0.1211060185
-0.7677045094 -0.4941888273 -0.1211061534
-0.9117856757 -0.0697383469 -0.4047106460
-0.0283368549 -0.9128720729 -0.2136250368
 0.7095821798 -0.4941888273 -0.3170647319
 0.7747427279 -0.0697383469 -0.6284246421
-0.7837697662  0.4186839017 -0.2422153076
-0.0589041897  0.8240821079 -0.4440651491
-0.5979663637 -0.6085817063 -0.3896645730
-0.3291594183 -0.7996144008 -0.3170661961
 0.6935177376  0.4186839017 -0.4381739941
 0.4756986407 -0.6085817062 -0.5320836915
 0.2351146351 -0.7996144008 -0.3919158120
-0.6168583888  0.4649158905 -0.5320835344
-0.3551545140  0.6774441676 -0.5130247732
-0.1016986410 -0.6339226751 -0.7666826828
 0.4568075735  0.4649158905 -0.6745027800
 0.2091227917  0.6774441676 -0.5878748206
-0.1200394925  0.4082445693 -0.9049501464
-0.5486577777 -0.3809323480 -0.6341330304
 0.3643603763 -0.3809323480 -0.7552427249
-0.5585867166  0.1832576685 -0.7089830873
-0.4459830958 -0.1162285368 -0.8169244453
 0.3544319410  0.1832576685 -0.8300928485
 0.2175812366 -0.1162285368 -0.9049446814
-0.1200388933 -0.1221699931 -0.9049456264
4 0 2 4 1 
6 0 3 8 13 6 2 
10 0 1 5 10 19 28 23 15 7 3 
6 1 4 9 17 11 5 
10 2 6 12 21 31 37 26 16 9 4 
4 3 7 14 8 
4 5 11 18 10 
4 6 13 20 12 
6 7 15 24 34 22 14 
10 8 14 22 33 46 55 42 30 20 13 
4 9 16 25 17 
6 10 18 27 40 29 19 
10 11 17 25 36 48 61 52 39 27 18 
6 12 20 30 43 32 21 
4 15 23 35 24 
6 16 26 38 49 36 25 
4 19 29 41 28 
4 21 32 44 31 
4 22 34 45 33 
6 23 28 41 53 47 35 
10 24 35 47 59 71 82 69 57 45 34 
4 26 37 50 38 
4 27 39 51 40 
10 29 40 51 63 75 88 77 65 53 41 
4 30 42 54 43 
6 31 44 56 62 50 37 
10 32 43 54 66 78 91 80 68 56 44 
6 33 45 57 70 58 46 
4 36 49 60 48 
10 38 50 62 74 86 96 84 72 60 49 
6 39 52 64 76 63 51 
6 42 55 67 79 66 54 
4 46 58 67 55 
4 47 53 65 59 
6 48 60 72 85 73 61 
4 52 61 73 64 
4 56 68 74 62 
4 57 69 81 70 
10 58 70 81 93 102 108 100 90 79 67 
6 59 65 77 89 83 71 
4 63 76 87 75 
10 64 73 85 95 104 111 106 98 87 76 
4 66 79 90 78 
6 68 80 92 97 86 74 
6 69 82 94 103 93 81 
4 71 83 94 82 
4 72 84 95 85 
6 75 87 98 107 99 88 
4 77 88 99 89 
6 78 90 100 109 101 91 
4 80 91 101 92 
10 83 89 99 107 113 117 115 110 103 94 
6 84 96 105 112 104 95 
4 86 97 105 96 
10 92 101 109 114 118 119 116 112 105 97 
4 93 103 110 102 
4 98 106 113 107 
4 100 108 114 109 
6 102 110 115 118 114 108 
4 104 112 116 111 
6 106 111 116 119 117 113 
4 115 117 119 118 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 4 0 
3 2 6 3 
3 4 7 1 
3 5 8 2 
3 1 9 5 
3 3 10 4 
3 2 11 6 
3 6 12 3 
3 4 13 7 
3 7 9 1 
3 9 8 5 
3 8 14 2 
3 10 15 4 
3 12 10 3 
3 11 12 6 
3 2 16 11 
3 13 9 7 
3 4 17 13 
3 9 18 8 
3 14 19 2 
3 8 20 14 
3 12 15 10 
3 15 21 4 
3 11 22 12 
3 19 16 2 
3 16 23 11 
3 13 24 9 
3 4 25 17 
3 17 26 13 
3 9 27 18 
3 18 20 8 
3 20 19 14 
3 12 28 15 
3 21 25 4 
3 15 29 21 
3 22 30 12 
3 23 22 11 
3 19 23 16 
3 24 31 9 
3 26 24 13 
3 25 26 17 
3 27 20 18 
3 9 32 27 
3 20 33 19 
3 12 34 28 
3 28 29 15 
3 29 25 21 
3 23 30 22 
3 30 35 12 
3 33 23 19 
3 26 31 24 
3 31 32 9 
3 25 36 26 
3 27 37 20 
3 32 38 27 
3 20 39 33 
3 34 29 28 
3 35 34 12 
3 29 36 25 
3 23 40 30 
3 30 41 35 
3 39 23 33 
3 26 42 31 
3 31 38 32 
3 36 43 26 
3 37 44 20 
3 38 37 27 
3 20 45 39 
3 34 46 29 
3 41 34 35 
3 29 43 36 
3 23 47 40 
3 40 41 30 
3 39 48 23 
3 26 49 42 
3 42 38 31 
3 43 50 26 
3 38 44 37 
3 44 45 20 
3 45 51 39 
3 46 52 29 
3 41 46 34 
3 29 53 43 
3 47 41 40 
3 48 47 23 
3 51 48 39 
3 49 38 42 
3 50 49 26 
3 43 54 50 
3 38 55 44 
3 44 51 45 
3 41 52 46 
3 52 53 29 
3 53 54 43 
3 47 56 41 
3 51 47 48 
3 49 57 38 
3 54 49 50 
3 38 58 55 
3 55 51 44 
3 41 59 52 
3 52 54 53 
3 56 60 41 
3 51 56 47 
3 57 58 38 
3 54 57 49 
3 58 51 55 
3 60 59 41 
3 59 54 52 
3 51 60 56 
3 54 58 57 
3 58 61 51 
3 60 54 59 
3 61 60 51 
3 54 61 58 
3 60 54 61 
snub dodecahedron
pentagonal hexecontahedron
|2 3 5
(3.3.3.3.5)
icosahedral group
A5
12{5}+80{3}
33 60 150 92 60 1 0 0 2 2 5 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.4512088258  0.0000000000  0.8924183971
 0.2127790861  0.3978875029  0.8924183971
-0.2505259628  0.3752680994  0.8924183971
-0.4490629634 -0.0439529224  0.8924183971
-0.1730083366 -0.4167223535  0.8924183971
 0.5570628795 -0.4167223535  0.7183477071
 0.8034191070 -0.0439529224  0.5937894232
 0.6262410352  0.3752680994  0.6833710701
 0.3401140582  0.7292026799  0.5937894232
-0.4095292581  0.6926037162  0.5937894232
-0.6598181766  0.3124803264  0.6833710701
-0.5867073299 -0.4344864666  0.6833710701
-0.2674638242 -0.7588657481  0.5937894232
 0.1712754568 -0.6742709318  0.7183477071
 0.5066126656 -0.7588657481  0.4092265672
 0.8319314730 -0.4344864666  0.3451253896
 0.9853200794 -0.0345183587  0.1671909808
 0.6986399371  0.6437955034  0.3121371303
 0.3534611035  0.9196768661  0.1710546996
-0.0444936500  0.9113473168  0.4092265672
-0.4413672010  0.8808718883  0.1710546996
-0.7580304168  0.5726781810  0.3121371303
-0.9277164283  0.1422346447  0.3451253896
-0.8825314401 -0.3194162218  0.3451253896
-0.6326042630 -0.7087892905  0.3121371303
 0.0822881568 -0.9349423109  0.3451253896
 0.3841470954 -0.9232462719 -0.0068797092
 0.9105239830 -0.3983895691 -0.1105975932
 0.9561362417  0.0261888093 -0.2917492648
 0.9205629910  0.3905335442 -0.0068797092
 0.6521763631  0.7453882542 -0.1380664403
-0.0487110154  0.9977300839 -0.0464964156
-0.4177242369  0.8604584989 -0.2917492648
-0.9300960831  0.3617906055 -0.0634730968
-0.9941677927 -0.0973061317 -0.0464964156
-0.8422948163 -0.5352668572 -0.0634730968
-0.5085214838 -0.8539169004 -0.1105975932
-0.0666936701 -0.9936871537 -0.0902097278
 0.2171184410 -0.8730158634 -0.4366954143
 0.6337780180 -0.7004597412 -0.3281487085
 0.7752228621 -0.3165232566 -0.5466649267
 0.7846911652  0.4275505711 -0.4488432737
 0.4346204276  0.7157251860 -0.5466649267
 0.0014482055  0.8716810135 -0.4900715391
-0.3439002478  0.6359394784 -0.6908788601
-0.7197752973  0.5396486232 -0.4366954143
-0.8871554693  0.1072142198 -0.4488432737
-0.6414198315 -0.6014211198 -0.4763121208
-0.2422737833 -0.8373370292 -0.4900715391
 0.4183769714 -0.5607792259 -0.7144839884
 0.4919671680 -0.1269691999 -0.8613054788
 0.4978189011  0.3328937158 -0.8008483725
 0.0947401619  0.5614556665 -0.8220655912
-0.5854826930  0.2482988995 -0.7717238319
-0.6691452398 -0.2043459771 -0.7144839884
-0.3249352618 -0.5030496595 -0.8008483725
 0.0833693593 -0.3321275372 -0.9395428936
 0.1242523988  0.1277815601 -0.9839884218
-0.2961484454 -0.0657599657 -0.9528755035
 0.2190839064  0.1312836377  0.9188614921
-0.0124546442  0.2551039658  0.9188614921
-0.2308305197  0.1093179889  0.9188614921
-0.2052534511 -0.1520005669  0.9188614921
 0.2190839064 -0.3281703830  0.9188614921
 0.5977703708 -0.1520005669  0.7273967313
 0.6205958173  0.1093179889  0.7158561322
 0.4257131685  0.2551039658  0.8143892546
 0.3890572668  0.4957055924  0.7158561322
-0.0330094857  0.6761213397  0.7360504792
-0.4354944038  0.4554494653  0.7158561322
-0.4485386151  0.2124213879  0.8143892546
-0.7630826557 -0.0746882186  0.6419708175
-0.3988385021 -0.2953600929  0.8143892546
-0.3389195666 -0.5312467586  0.7158561322
-0.0888218963 -0.6103640383  0.7273967313
 0.4074741194 -0.6103640383  0.6090650015
 0.6254586613 -0.5312467586  0.4859196824
 0.7233904360 -0.2953600929  0.5468165011
 0.8646946053 -0.1692512546  0.3649614304
 0.8780829721  0.2897337362  0.3808210291
 0.5493678557  0.5768433427  0.5243913714
 0.4593636674  0.7564719129  0.3553517403
 0.2141655150  0.8447510749  0.3873865601
-0.2954354429  0.8198714201  0.3873865601
-0.5308680756  0.7081269803  0.3553517403
-0.6029463352  0.5205852472  0.5243913714
-0.7739230465  0.3389900646  0.4423442636
-0.6935065744 -0.4826176302  0.4423442636
-0.4905640004 -0.6276147261  0.5243913714
-0.3032002312 -0.9251016481  0.2285969389
-0.0045863974 -0.7813515677  0.5468165011
 0.2508214168 -0.7813515677  0.4859196824
 0.3210587649 -0.8635013917  0.2466297006
 0.7110959079 -0.6998764938  0.0671974935
 0.9000340357 -0.2861982107  0.1325477729
 0.9410156039 -0.1341976438 -0.0775900694
 0.9443279912  0.1261088383 -0.0433681826
 0.7494453424  0.5872206583  0.0551649398
 0.5623291395  0.7618123698  0.1138746914
 0.3032002312  0.9251016481 -0.2285969389
 0.0858720409  0.9333521346  0.1761231918
-0.1763828687  0.9205483682  0.1761231918
-0.2995309163  0.9037575188 -0.0551649398
-0.7110959079  0.6998764938 -0.0671974935
-0.8631016874  0.3552600725  0.1959217993
-0.9410156039  0.1341976438  0.0775900694
-0.9253215715 -0.0905676721  0.2124078137
-0.8971365698 -0.3141104098  0.0775900694
-0.7778380870 -0.5158702863  0.1959217993
-0.6544328852 -0.6922296665  0.0455552496
 0.1318953941 -0.9409811017  0.0818398716
 0.1763828687 -0.9205483682 -0.1761231918
 0.4075046572 -0.8237974999 -0.2546315508
 0.7653310532 -0.4670045122 -0.3251380596
 0.8716936806 -0.2272456248 -0.3131280032
 0.7630826557  0.0746882186 -0.6419708175
 0.8781301501  0.2785692436 -0.2466297006
 0.7778380870  0.5158702863 -0.1959217993
 0.6175005369  0.6231678047 -0.3740248218
-0.1534232428  0.9007249745 -0.2733046324
-0.2508214168  0.7813515677 -0.4859196824
-0.4887903007  0.6717969331 -0.4683081420
-0.8370961923  0.3328068685 -0.3131280032
-0.9276324486  0.1226425968 -0.1843812002
-0.8780829721 -0.2897337362 -0.3808210291
-0.6573415966 -0.6568033615 -0.2145948808
-0.4593636674 -0.7564719129 -0.3553517403
-0.2697318228 -0.8859007376 -0.2279566191
-0.0303057331 -0.8922024719 -0.3355531328
 0.0330094857 -0.6761213397 -0.7360504792
 0.4187988612 -0.7042009004 -0.4881067495
 0.6029463352 -0.5205852472 -0.5243913714
 0.5561556114 -0.3313610975 -0.7003073269
 0.5665700378  0.4870645516 -0.5927108132
 0.3389195666  0.5312467586 -0.7158561322
 0.1751412372  0.7090205159 -0.6133148036
-0.0817329434  0.6826950901 -0.6608984288
-0.2190839064  0.3281703830 -0.9188614921
-0.5441424799  0.4698138638 -0.6266765419
-0.7233904360  0.2953600929 -0.5468165011
-0.7066849651  0.0498778478 -0.6384732991
-0.5396360317 -0.4318462468 -0.6571463807
-0.3987890908 -0.6407026882 -0.5831011230
 0.3278774074 -0.3365097556 -0.8299380599
 0.2308305197 -0.1093179889 -0.9188614921
 0.3675788294  0.1101068700 -0.8730990062
 0.2365131238  0.3372537898 -0.8601517406
-0.5116812230 -0.0071952699 -0.8047795644
-0.4257131685 -0.2551039658 -0.8143892546
-0.1774197357 -0.2972657023 -0.8886478115
-0.0292095264 -0.0891219012 -0.9490751728
3 0 2 1 
3 0 3 2 
3 0 4 3 
3 0 5 4 
5 0 1 6 14 5 
3 1 7 6 
3 1 8 7 
3 1 2 8 
3 2 9 8 
5 2 3 10 20 9 
3 3 11 10 
3 3 4 11 
5 4 12 24 23 11 
3 4 5 12 
3 5 13 12 
3 5 14 13 
3 6 15 14 
3 6 16 15 
3 6 7 16 
3 7 17 16 
5 7 8 18 30 17 
3 8 9 18 
3 9 19 18 
3 9 20 19 
3 10 21 20 
3 10 22 21 
3 10 11 22 
3 11 23 22 
3 12 25 24 
3 12 13 25 
5 13 26 38 37 25 
3 13 14 26 
3 14 15 26 
3 15 27 26 
5 15 16 28 40 27 
3 16 17 28 
3 17 29 28 
3 17 30 29 
3 18 31 30 
3 18 19 31 
5 19 32 44 43 31 
3 19 20 32 
3 20 21 32 
3 21 33 32 
5 21 22 34 46 33 
3 22 23 34 
3 23 35 34 
3 23 24 35 
3 24 36 35 
3 24 25 36 
3 25 37 36 
3 26 27 38 
3 27 39 38 
3 27 40 39 
3 28 41 40 
3 28 29 41 
5 29 42 52 51 41 
3 29 30 42 
3 30 31 42 
3 31 43 42 
3 32 33 44 
3 33 45 44 
3 33 46 45 
3 34 47 46 
3 34 35 47 
5 35 36 48 55 47 
3 36 37 48 
3 37 49 48 
3 37 38 49 
3 38 39 49 
5 39 50 57 56 49 
3 39 40 50 
3 40 41 50 
3 41 51 50 
3 42 43 52 
3 43 53 52 
3 43 44 53 
3 44 45 53 
5 45 54 59 58 53 
3 45 46 54 
3 46 47 54 
3 47 55 54 
3 48 56 55 
3 48 49 56 
3 50 51 57 
3 51 58 57 
3 51 52 58 
3 52 53 58 
3 54 55 59 
3 55 56 59 
3 56 57 59 
3 57 58 59 
5 4 0 1 2 3 
5 4 5 6 7 0 
5 7 8 9 1 0 
5 9 10 11 2 1 
5 11 12 13 3 2 
5 13 14 15 4 3 
5 4 16 17 18 5 
5 18 19 20 6 5 
5 20 21 8 7 6 
5 21 22 23 9 8 
5 9 24 25 26 10 
5 26 27 12 11 10 
5 12 28 29 14 13 
5 29 30 31 15 14 
5 31 32 16 4 15 
5 32 33 34 17 16 
5 34 35 19 18 17 
5 35 36 37 20 19 
5 20 38 39 22 21 
5 39 40 41 23 22 
5 41 42 24 9 23 
5 42 43 44 25 24 
5 44 45 27 26 25 
5 45 46 47 12 27 
5 47 48 49 28 12 
5 49 50 30 29 28 
5 30 51 33 32 31 
5 51 52 53 34 33 
5 34 54 55 36 35 
5 55 56 57 37 36 
5 57 58 38 20 37 
5 58 59 40 39 38 
5 40 60 43 42 41 
5 60 61 62 44 43 
5 44 63 64 46 45 
5 64 65 48 47 46 
5 65 66 50 49 48 
5 66 67 68 30 50 
5 68 69 52 51 30 
5 69 70 71 53 52 
5 71 72 54 34 53 
5 72 73 56 55 54 
5 56 74 59 58 57 
5 74 75 76 40 59 
5 76 77 61 60 40 
5 77 78 79 62 61 
5 79 80 63 44 62 
5 80 81 65 64 63 
5 65 82 83 67 66 
5 83 70 69 68 67 
5 70 84 73 72 71 
5 84 85 86 56 73 
5 86 87 75 74 56 
5 87 78 77 76 75 
5 78 88 81 80 79 
5 88 89 82 65 81 
5 89 90 70 83 82 
5 90 91 85 84 70 
5 91 78 87 86 85 
5 78 88 89 90 91 
small ditrigonal icosidodecahedron
small triambic icosahedron
3|5/2 3
(5/2.3.5/2.3.5/2.3)
icosahedral group
A5
20{3}+12{5/2}
34 20 60 32 20 2 0 0 -8 2 6 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9428090416  0.0000000000  0.3333333333
 0.6727182848  0.6605596098  0.3333333333
-0.4714045208  0.8164965809  0.3333333333
-0.9084205452  0.2523113194  0.3333333333
-0.4714045208 -0.8164965809  0.3333333333
 0.2357022604 -0.9128709292  0.3333333333
 0.0900302522  0.6605596098  0.7453559925
 0.4714045208  0.8164965809 -0.3333333333
 0.6170765289  0.2523113194 -0.7453559925
 0.4714045208 -0.8164965809 -0.3333333333
-0.2357022604  0.9128709292 -0.3333333333
 0.9084205452 -0.2523113194 -0.3333333333
 0.5270462767 -0.4082482905  0.7453559925
-0.6170765289 -0.2523113194  0.7453559925
-0.9428090416  0.0000000000 -0.3333333333
-0.5270462767  0.4082482905 -0.7453559925
-0.6727182848 -0.6605596098 -0.3333333333
-0.0900302522 -0.6605596098 -0.7453559925
 0.0000000000  0.0000000000 -1.0000000000
 0.5270462767  0.2154995940  0.7453559925
 0.0900302522  0.6605596098  0.7453559925
-0.4501512612  0.3486856676  0.7453559925
-0.6170765289 -0.2523113194  0.7453559925
-0.0768950155 -0.5641852616  0.7453559925
 0.5270462767 -0.4082482905  0.7453559925
 0.7283600407 -0.5641852616  0.1759546817
 0.9084205452 -0.2523113194 -0.3333333333
 0.8527787893  0.3486856676 -0.1759546817
 0.6727182848  0.6605596098  0.3333333333
 0.9428090416 -0.0000000000  0.3333333333
 0.4714045208  0.8164965809 -0.3333333333
 0.1244187486  0.9128709292  0.1759546817
-0.2357022604  0.9128709292 -0.3333333333
-0.7283600407  0.5641852616 -0.1759546817
-0.9084205452  0.2523113194  0.3333333333
-0.4714045208  0.8164965809  0.3333333333
-0.9428090416 -0.0000000000 -0.3333333333
-0.8527787893 -0.3486856676  0.1759546817
-0.6727182848 -0.6605596098 -0.3333333333
-0.1244187486 -0.9128709292 -0.1759546817
 0.2357022604 -0.9128709292  0.3333333333
-0.4714045208 -0.8164965809  0.3333333333
 0.4714045208 -0.8164965809 -0.3333333333
 0.0000000000 -0.0000000000  1.0000000000
 0.6170765289  0.2523113194 -0.7453559925
 0.0768950155  0.5641852616 -0.7453559925
 0.4501512612 -0.3486856676 -0.7453559925
-0.0000000000  0.0000000000 -1.0000000000
-0.0900302522 -0.6605596098 -0.7453559925
-0.5270462767  0.4082482905 -0.7453559925
-0.5270462767 -0.2154995940 -0.7453559925
5 0 2 13 7 1 2
3 0 3 2 
5 0 4 7 14 3 2
3 0 5 4 
5 0 6 14 13 5 2
3 0 1 6 
5 1 10 13 12 6 2
3 1 9 10 
5 1 8 12 2 9 2
3 1 7 8 
3 2 12 13 
3 2 11 9 
5 2 3 8 7 11 2
3 3 16 8 
5 3 15 11 4 16 2
3 3 14 15 
3 4 11 7 
3 4 17 16 
5 4 5 15 14 17 2
3 5 18 15 
5 5 10 17 6 18 2
3 5 13 10 
3 6 17 14 
3 6 12 18 
3 7 13 14 
3 8 19 12 
5 8 16 9 11 19 2
5 9 18 12 19 10 2
3 9 16 18 
3 10 19 17 
3 11 15 19 
5 15 18 16 17 19 2
6 5 0 1 2 3 4 
6 5 6 7 8 9 0 
6 0 10 8 11 12 1 
6 12 13 14 15 2 1 
6 2 16 14 17 18 3 
6 18 19 20 21 4 3 
6 4 22 20 23 6 5 
6 9 12 16 2 24 0 
6 8 25 26 13 12 9 
6 7 27 28 26 11 8 
6 6 21 20 29 27 7 
6 26 30 14 16 12 11 
6 10 6 23 27 25 8 
6 24 4 21 6 10 0 
6 15 18 22 4 24 2 
6 30 31 19 18 15 14 
6 28 31 17 14 13 26 
6 31 29 20 22 18 17 
6 19 20 23 27 28 31 
6 25 26 30 31 29 27 
small icosicosidodecahedron
small icosacronic hexecontahedron
5/2 3|3
(6.5/2.6.3)
icosahedral group
A5
20{6}+20{3}+12{5/2}
35 60 120 52 60 2 0 0 -8 3 4 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.5558508647  0.0000000000  0.8312820317
-0.3547421326  0.4279348118  0.8312820317
-0.5423346067  0.1218333214  0.8312820317
 0.2523198656 -0.4952826155  0.8312820317
 0.7569595968  0.4279348118  0.4938460950
 0.9129018498  0.1218333214  0.3895726561
-0.3230919115 -0.1426449373  0.9355554706
-0.6764070948  0.6250652668  0.3895726561
-0.1536334005  0.8558696236  0.4938460950
-0.8323493477 -0.2516159727  0.4938460950
-0.8639995688  0.3189637764  0.3895726561
-0.0195609124  0.3526376782  0.9355554706
 0.3058398516 -0.8687319096  0.3895726561
-0.0376948755 -0.8687319096  0.4938460950
 0.7886098179 -0.1426449373  0.5981195340
 0.7788293617  0.6250652668 -0.0521367195
 0.4022174642  0.8558696236  0.3251281267
 0.9664218358 -0.2516159727 -0.0521367195
 0.9347716147  0.3189637764 -0.1564101584
 0.5362899523  0.3526376782  0.7668375023
-0.6131066526 -0.5160942314  0.5981195340
-0.0707720459 -0.6379275528  0.7668375023
-0.8421298039  0.5160942314 -0.1564101584
-0.9664218358  0.2516159727  0.0521367195
 0.2034175846  0.9777029450  0.0521367195
-0.7788293617 -0.6250652668  0.0521367195
-0.5800294821 -0.7468985882  0.3251281267
-0.6628908367  0.7468985882  0.0521367195
 0.1815478197  0.7805724901  0.5981195340
 0.1401171424 -0.9777029450 -0.1564101584
 0.6628908367 -0.7468985882 -0.0521367195
-0.2034175846 -0.9777029450 -0.0521367195
 0.4850788188 -0.6379275528  0.5981195340
 0.8421298039 -0.5160942314  0.1564101584
 0.6131066526  0.5160942314 -0.5981195340
 0.8323493477  0.2516159727 -0.4938460950
-0.1401171424  0.9777029450  0.1564101584
 0.6764070948 -0.6250652668 -0.3895726561
 0.5800294821  0.7468985882 -0.3251281267
-0.9347716147 -0.3189637764  0.1564101584
-0.7886098179  0.1426449373 -0.5981195340
-0.4850788188  0.6379275528 -0.5981195340
-0.9129018498 -0.1218333214 -0.3895726561
 0.0376948755  0.8687319096 -0.4938460950
-0.4022174642 -0.8558696236 -0.3251281267
-0.7569595968 -0.4279348118 -0.4938460950
-0.3058398516  0.8687319096 -0.3895726561
-0.1815478197 -0.7805724901 -0.5981195340
 0.8639995688 -0.3189637764 -0.3895726561
 0.1536334005 -0.8558696236 -0.4938460950
 0.3230919115  0.1426449373 -0.9355554706
 0.0707720459  0.6379275528 -0.7668375023
 0.5423346067 -0.1218333214 -0.8312820317
 0.3547421326 -0.4279348118 -0.8312820317
-0.5362899523 -0.3526376782 -0.7668375023
-0.5558508647 -0.0000000000 -0.8312820317
-0.2523198656  0.4952826155 -0.8312820317
 0.0195609124 -0.3526376782 -0.9355554706
-0.0000000000 -0.0000000000 -1.0000000000
 0.2470682788  0.5257311121  0.8139803827
-0.2225822414  0.1364082001  0.8139803827
-0.3562920523 -0.4587939735  0.8139803827
 0.2470682788 -0.1514143222  0.8139803827
 0.7486308807 -0.4587939735  0.4786020209
 0.6374803174  0.1364082001  0.5529247349
-0.3622034226  0.5835662368  0.5242062787
-0.7921037010  0.0669371386  0.6067051560
-0.4192065089  0.6754071043  0.6067051560
-0.6843946014  0.0578351247  0.5242062787
 0.1678297972 -0.6299377043  0.5529247349
 0.9956991595  0.0669371386  0.0640515676
 0.5924737103  0.5835662368  0.2344321747
 0.8603054480  0.0578351247  0.0553419293
 0.6857164240  0.6754071043  0.2713267942
-0.3078439816 -0.3964078418  0.7032965240
 0.2859515514 -0.1752437040  0.9420835178
-0.3923388284  0.9175879470 -0.0640515676
-0.7202912637  0.4414262081  0.1305278239
 0.0885913156  0.7985475123  0.2918690871
-0.9956991595 -0.0669371386 -0.0640515676
-0.6713191889 -0.4414262081  0.2918690871
 0.2134722966  0.4542429665  0.7032965240
-0.2905410991 -0.9175879470  0.2713267942
 0.3389891699 -0.7928156837  0.0553419293
-0.2510337466 -0.7928156837  0.2344321747
 0.3923388284 -0.9175879470  0.0640515676
 0.6468331514 -0.3964078418  0.4135224200
 0.6713191889  0.4414262081 -0.2918690871
 0.2905410991  0.9175879470 -0.2713267942
 0.7202912637 -0.4414262081 -0.1305278239
 0.7921037010 -0.0669371386 -0.6067051560
-0.6468331514  0.3964078418 -0.4135224200
-0.7486308807  0.4587939735 -0.4786020209
-0.8603054480 -0.0578351247 -0.0553419293
 0.2510337466  0.7928156837 -0.2344321747
-0.5924737103 -0.5835662368 -0.2344321747
-0.6857164240 -0.6754071043 -0.2713267942
-0.3389891699  0.7928156837 -0.0553419293
-0.0885913156 -0.7985475123 -0.2918690871
 0.4192065089 -0.6754071043 -0.6067051560
 0.3078439816  0.3964078418 -0.7032965240
 0.6843946014 -0.0578351247 -0.5242062787
 0.3562920523  0.4587939735 -0.8139803827
 0.3622034226 -0.5835662368 -0.5242062787
-0.2859515514  0.1752437040 -0.9420835178
-0.6374803174 -0.1364082001 -0.5529247349
-0.1678297972  0.6299377043 -0.5529247349
-0.2470682788 -0.5257311121 -0.8139803827
-0.2134722966 -0.4542429665 -0.7032965240
 0.2225822414 -0.1364082001 -0.8139803827
-0.2470682788  0.1514143222 -0.8139803827
6 0 2 9 17 5 1 
5 0 3 12 7 2 2
6 0 4 14 27 10 3 
3 0 1 4 
6 1 6 18 31 13 4 
5 1 5 15 20 6 2
3 2 8 9 
6 2 7 21 40 24 8 
6 3 11 28 37 29 12 
3 3 10 11 
5 4 13 22 33 14 2
6 5 16 36 49 34 15 
3 5 17 16 
3 6 19 18 
6 6 20 29 25 39 19 
3 7 22 21 
6 7 12 20 15 33 22 
6 8 23 42 44 25 9 
5 8 24 28 11 23 2
5 9 25 29 37 17 2
6 10 26 46 41 23 11 
5 10 27 40 21 26 2
3 12 29 20 
6 13 30 45 26 21 22 
3 13 31 30 
3 14 32 27 
6 14 33 34 38 50 32 
3 15 34 33 
5 16 35 19 39 36 2
6 16 17 37 47 52 35 
5 18 38 34 49 31 2
6 18 19 35 51 54 38 
3 23 41 42 
6 24 43 56 57 47 28 
3 24 40 43 
3 25 44 39 
3 26 45 46 
6 27 32 48 55 43 40 
3 28 47 37 
5 30 48 32 50 45 2
6 30 31 49 53 58 48 
3 35 52 51 
3 36 53 49 
6 36 39 44 57 59 53 
3 38 54 50 
6 41 55 58 51 52 42 
5 41 46 56 43 55 2
5 42 52 47 57 44 2
6 45 50 54 59 56 46 
3 48 58 55 
5 51 58 53 59 54 2
3 56 59 57 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 1 8 9 2 
4 2 10 4 3 
4 5 11 12 0 
4 4 13 14 5 
4 7 15 16 1 
4 6 17 18 7 
4 0 19 17 6 
4 9 20 21 2 
4 8 18 20 9 
4 16 22 8 1 
4 10 23 24 4 
4 2 25 26 10 
4 5 16 27 11 
4 11 28 29 12 
4 29 19 0 12 
4 4 30 31 13 
4 31 28 14 13 
4 14 22 16 5 
4 7 21 23 15 
4 10 16 15 23 
4 17 32 20 18 
4 18 33 34 7 
4 19 14 35 17 
4 20 36 23 21 
4 21 37 25 2 
4 8 38 33 18 
4 19 8 22 14 
4 23 39 40 24 
4 40 30 4 24 
4 37 39 26 25 
4 26 27 16 10 
4 26 30 11 27 
4 31 41 29 28 
4 11 42 43 28 
4 29 38 8 19 
4 26 44 31 30 
4 43 35 14 28 
4 34 37 21 7 
4 32 45 46 20 
4 17 47 45 32 
4 33 46 37 34 
4 43 47 17 35 
4 36 48 39 23 
4 46 48 36 20 
4 29 47 33 38 
4 37 49 40 39 
4 40 42 11 30 
4 48 44 26 39 
4 31 50 45 41 
4 41 29 47 45 
4 40 50 43 42 
4 48 50 31 44 
4 45 49 37 46 
4 33 51 48 46 
4 43 51 33 47 
4 49 40 50 45 
4 50 43 51 48 
small snub icosicosidodecahedron
small hexagonal hexecontahedron
|5/2 3 3
(3.5/2.3.3.3.3)
icosahedral group
A5
100{3}+12{5/2}
36 60 180 112 60 2 0 0 -8 2 6 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.6442062214  0.0000000000  0.7648518447
 0.2791862208  0.5805658531  0.7648518447
-0.1419451564  0.6283734783  0.7648518447
-0.6278134281  0.1444020607  0.7648518447
-0.4022186612 -0.5032114906  0.7648518447
 0.2791862208 -0.5805658531  0.7648518447
 0.8003600018 -0.5032114906  0.3258865804
 0.9729065754 -0.1444020607  0.1805570281
 0.8003600018  0.5032114906  0.3258865804
 0.2915016934  0.9393752830  0.1805570281
-0.3057103174  0.8142132953  0.4935563915
-0.3144917300  0.2695640484  0.9101813971
 0.3669131520  0.1922096859  0.9101813971
 0.4804410603  0.7249679138  0.4935563915
-0.0735183072  0.9808130393  0.1805570281
-0.6671962580  0.6698112346  0.3258865804
-0.9805179561  0.0773543625  0.1805570281
-0.8927910249 -0.3110018047  0.3258865804
-0.4946496843 -0.8501299015  0.1805570281
 0.1154210597 -0.8620209205  0.4935563915
-0.3057103174 -0.8142132953  0.4935563915
 0.2915016934 -0.9393752830  0.1805570281
 0.6671962580 -0.6698112346 -0.3258865804
 0.9805179561 -0.0773543625 -0.1805570281
 0.8763982317  0.1665997441  0.4518524813
 0.5972120109 -0.4139661090  0.6870006366
 0.6584148454 -0.7471655971  0.0907384251
 0.8167527950 -0.3588094299 -0.4518524813
 0.8927910249  0.3110018047 -0.3258865804
 0.4946496843  0.8501299015 -0.1805570281
 0.8091414144  0.5805658531 -0.0907384251
 0.3057103174  0.8142132953 -0.4935563915
-0.2915016934  0.9393752830 -0.1805570281
-0.6584148454  0.7471655971 -0.0907384251
-0.8167527950  0.3588094299  0.4518524813
-0.6748076386 -0.2695640484  0.6870006366
-0.0407327207 -0.3588094299  0.9325216558
-0.1154210597  0.8620209205 -0.4935563915
-0.8003600018  0.5032114906 -0.3258865804
-0.8763982317 -0.1665997441 -0.4518524813
-0.8091414144 -0.5805658531  0.0907384251
-0.9729065754  0.1444020607 -0.1805570281
-0.8003600018 -0.5032114906 -0.3258865804
-0.4804410603 -0.7249679138 -0.4935563915
 0.0735183072 -0.9808130393 -0.1805570281
-0.2915016934 -0.9393752830 -0.1805570281
 0.3057103174 -0.8142132953 -0.4935563915
 0.1419451564 -0.6283734783 -0.7648518447
 0.6278134281 -0.1444020607 -0.7648518447
 0.6748076386  0.2695640484 -0.6870006366
 0.3144917300 -0.2695640484 -0.9101813971
 0.4022186612  0.5032114906 -0.7648518447
 0.0407327207  0.3588094299 -0.9325216558
-0.2791862208  0.5805658531 -0.7648518447
-0.5972120109  0.4139661090 -0.6870006366
-0.6442062214 -0.0000000000 -0.7648518447
-0.3669131520 -0.1922096859 -0.9101813971
-0.2791862208 -0.5805658531 -0.7648518447
-0.0000000000 -0.0000000000 -1.0000000000
 0.3351898516  0.2107443956  0.9182780424
 0.0400368356  0.3526794657  0.9182780424
-0.2794210283  0.2805161775  0.9182780424
-0.3738998581 -0.1302471994  0.9182780424
-0.0446605620 -0.3934092920  0.9182780424
 0.3351898516 -0.2107443956  0.9182780424
 0.6257191411 -0.3934092920  0.6735760428
 0.8213888526 -0.1889259414  0.5087707326
 0.8775384241  0.1302471994  0.4614780399
 0.6257191411  0.3934092920  0.6735760428
 0.4976880105  0.7344008871  0.4614780399
 0.0961864071  0.8472940016  0.5223418899
-0.1237881524  0.6041536876  0.7871942677
 0.2560622612  0.5610323550  0.7871942677
 0.0961864071  0.8472940016  0.5223418899
-0.3204039448  0.8272722230  0.4614780399
-0.5216121103  0.5236564915  0.6735760428
-0.8260125790  0.3236375102  0.4614780399
-0.8428360805  0.0000000000  0.5087707326
-0.6979814484 -0.2431403140  0.6735760428
-0.6496432409 -0.6041536876  0.4614780399
-0.2836640065 -0.8041726690  0.5223418899
-0.0747391792 -0.6583680602  0.7281386332
 0.0961864071 -0.8472940016  0.5223418899
 0.4976880105 -0.7344008871  0.4614780399
 0.6385349796 -0.7667968054  0.0655418874
 0.8886466854 -0.4538847096 -0.0655418874
 0.9645866382 -0.1502689781  0.2167760402
 0.8089537623 -0.4739064882  0.3478598150
 0.8886466854 -0.4538847096 -0.0655418874
 0.9737248312 -0.0697717819 -0.2167760402
 0.9677742757  0.2431403140  0.0655418874
 0.7941678555  0.6041536876 -0.0655418874
 0.6071295333  0.7595733041  0.1538260133
 0.5105038490  0.8472940016 -0.1465561155
 0.1109723139  0.9775412010 -0.1791601123
-0.1109723139  0.9775412010  0.1791601123
-0.4214180402  0.8763359572  0.1538260133
-0.6464556034  0.6970250235  0.3102438870
-0.5216121103  0.5236564915  0.6735760428
-0.6555937963  0.1302471994  0.7437959675
-0.3738998581 -0.1302471994  0.9182780424
 0.0042429783  0.0373758635  0.9992922705
 0.3351898516 -0.2107443956  0.9182780424
 0.6681067932 -0.0200217787  0.7437959675
 0.6257191411  0.3934092920  0.6735760428
 0.7862472317  0.5343819058  0.3102438870
 0.3272692278  0.9277911978  0.1791601123
 0.1109723139  0.9775412010 -0.1791601123
-0.3075881063  0.9401653375 -0.1465561155
-0.6385349796  0.7667968054 -0.0655418874
-0.8886466854  0.4538847096  0.0655418874
-0.9645866382  0.1502689781 -0.2167760402
-0.9677742757 -0.2431403140 -0.0655418874
-0.8945972408 -0.2805161775  0.3478598150
-0.9737248312  0.0697717819  0.2167760402
-0.9677742757 -0.2431403140 -0.0655418874
-0.7941678555 -0.6041536876  0.0655418874
-0.6071295333 -0.7595733041 -0.1538260133
-0.3272692278 -0.9277911978 -0.1791601123
-0.1109723139 -0.9775412010  0.1791601123
 0.3075881063 -0.9401653375  0.1465561155
 0.4976880105 -0.7344008871  0.4614780399
 0.2438986592 -0.5934282734  0.7670438895
-0.3707122206 -0.5236564915  0.7670438895
-0.6496432409 -0.6041536876  0.4614780399
-0.5105038490 -0.8472940016  0.1465561155
-0.1109723139 -0.9775412010  0.1791601123
 0.1109723139 -0.9775412010 -0.1791601123
 0.4214180402 -0.8763359572 -0.1538260133
 0.3204039448 -0.8272722230 -0.4614780399
 0.5216121103 -0.5236564915 -0.6735760428
 0.8260125790 -0.3236375102 -0.4614780399
 0.8428360805  0.0000000000 -0.5087707326
 0.8945972408  0.2805161775 -0.3478598150
 0.9677742757  0.2431403140  0.0655418874
 0.6464556034 -0.6970250235 -0.3102438870
 0.5216121103 -0.5236564915 -0.6735760428
 0.6555937963 -0.1302471994 -0.7437959675
 0.6979814484  0.2431403140 -0.6735760428
 0.6496432409  0.6041536876 -0.4614780399
 0.2836640065  0.8041726690 -0.5223418899
 0.6496432409  0.6041536876 -0.4614780399
 0.3707122206  0.5236564915 -0.7670438895
 0.0747391792  0.6583680602 -0.7281386332
-0.0961864071  0.8472940016 -0.5223418899
-0.4976880105  0.7344008871 -0.4614780399
-0.4976880105  0.7344008871 -0.4614780399
-0.8089537623  0.4739064882 -0.3478598150
-0.8886466854  0.4538847096  0.0655418874
-0.2438986592  0.5934282734 -0.7670438895
-0.6257191411  0.3934092920 -0.6735760428
-0.8213888526  0.1889259414 -0.5087707326
-0.6681067932  0.0200217787 -0.7437959675
-0.6257191411 -0.3934092920 -0.6735760428
-0.7862472317 -0.5343819058 -0.3102438870
-0.8775384241 -0.1302471994 -0.4614780399
-0.6257191411 -0.3934092920 -0.6735760428
-0.4976880105 -0.7344008871 -0.4614780399
-0.2560622612 -0.5610323550 -0.7871942677
-0.0961864071 -0.8472940016 -0.5223418899
-0.0961864071 -0.8472940016 -0.5223418899
 0.1237881524 -0.6041536876 -0.7871942677
-0.0400368356 -0.3526794657 -0.9182780424
 0.2794210283 -0.2805161775 -0.9182780424
 0.3738998581  0.1302471994 -0.9182780424
 0.3738998581  0.1302471994 -0.9182780424
-0.0042429783 -0.0373758635 -0.9992922705
 0.0446605620  0.3934092920 -0.9182780424
-0.3351898516  0.2107443956 -0.9182780424
-0.3351898516  0.2107443956 -0.9182780424
-0.3351898516 -0.2107443956 -0.9182780424
3 0 2 1 
5 0 3 13 12 2 2
3 0 4 3 
3 0 5 4 
3 0 6 5 
3 0 1 6 
3 1 7 6 
5 1 8 26 25 7 2
3 1 9 8 
3 1 2 9 
3 2 10 9 
3 2 11 10 
3 2 12 11 
3 3 14 13 
3 3 15 14 
3 3 16 15 
3 3 4 16 
3 4 17 16 
5 4 18 35 36 17 2
3 4 5 18 
3 5 19 18 
3 5 20 19 
5 5 6 21 37 20 2
3 6 22 21 
3 6 7 22 
3 7 23 22 
3 7 24 23 
3 7 25 24 
3 8 27 26 
3 8 28 27 
3 8 29 28 
3 8 9 29 
3 9 30 29 
5 9 10 31 14 30 2
3 10 32 31 
3 10 33 32 
3 10 11 33 
5 11 34 15 16 33 2
3 11 35 34 
3 11 12 35 
3 12 36 35 
3 12 37 36 
3 12 13 37 
3 13 26 37 
3 13 25 26 
3 13 14 25 
3 14 31 25 
3 14 15 30 
3 15 38 30 
3 15 34 38 
3 16 39 33 
3 16 17 39 
3 17 40 39 
3 17 41 40 
3 17 36 41 
3 18 42 35 
3 18 43 42 
3 18 19 43 
5 19 44 41 46 43 2
3 19 45 44 
3 19 20 45 
3 20 27 45 
3 20 26 27 
3 20 37 26 
3 21 36 37 
3 21 41 36 
3 21 46 41 
3 21 22 46 
3 22 47 46 
5 22 23 45 27 47 2
3 23 48 45 
3 23 49 48 
3 23 24 49 
5 24 50 28 29 49 2
3 24 31 50 
3 24 25 31 
3 27 28 47 
3 28 51 47 
3 28 50 51 
3 29 52 49 
3 29 30 52 
3 30 38 52 
3 31 32 50 
3 32 53 50 
5 32 54 52 38 53 2
3 32 33 54 
3 33 39 54 
3 34 55 38 
3 34 42 55 
3 34 35 42 
3 38 55 53 
3 39 56 54 
5 39 40 55 42 56 2
3 40 57 55 
3 40 44 57 
3 40 41 44 
3 42 43 56 
3 43 58 56 
3 43 46 58 
3 44 48 57 
3 44 45 48 
3 46 47 58 
3 47 51 58 
5 48 59 58 51 57 2
3 48 49 59 
3 49 52 59 
3 50 53 51 
3 51 53 57 
3 52 54 59 
3 53 55 57 
3 54 56 59 
3 56 58 59 
6 5 0 1 2 3 4 
6 5 6 7 8 9 0 
6 9 10 11 12 1 0 
6 1 13 14 15 16 2 
6 16 17 18 19 3 2 
6 19 20 21 22 4 3 
6 22 23 24 6 5 4 
6 24 25 26 27 7 6 
6 7 28 29 30 31 8 
6 31 32 33 10 9 8 
6 33 34 35 36 11 10 
6 36 37 38 39 12 11 
6 39 40 41 42 1 12 
6 42 43 44 45 13 1 
6 45 46 33 47 14 13 
6 47 48 49 37 15 14 
6 37 50 51 17 16 15 
6 51 52 53 54 18 17 
6 18 55 56 57 20 19 
6 57 58 59 60 21 20 
6 60 61 62 63 22 21 
6 22 64 65 66 67 23 
6 67 68 69 25 24 23 
6 69 70 71 72 26 25 
6 72 73 74 75 27 26 
6 75 46 45 44 7 27 
6 43 63 62 28 7 44 
6 61 69 76 29 28 62 
6 76 77 78 73 30 29 
6 73 79 80 32 31 30 
6 80 81 48 47 33 32 
6 74 82 34 33 46 75 
6 82 83 84 85 35 34 
6 85 86 50 37 36 35 
6 49 87 88 89 38 37 
6 89 55 18 40 39 38 
6 54 65 64 41 40 18 
6 41 42 43 63 22 64 
6 81 84 90 87 49 48 
6 86 91 92 52 51 50 
6 92 93 94 95 53 52 
6 95 58 66 65 54 53 
6 88 92 96 56 55 89 
6 96 97 98 58 57 56 
6 94 99 100 59 58 95 
6 100 70 69 61 60 59 
6 98 101 68 67 66 58 
6 101 102 77 76 69 68 
6 99 103 104 71 70 100 
6 104 105 79 73 72 71 
6 78 106 83 82 74 73 
6 102 103 107 106 78 77 
6 105 108 84 81 80 79 
6 107 109 90 84 83 106 
6 108 110 91 86 85 84 
6 109 93 92 88 87 90 
6 110 111 97 96 92 91 
6 93 94 99 103 107 109 
6 111 103 102 101 98 97 
6 103 104 105 108 110 111 
small dodecicosidodecahedron
small dodecacronic hexecontahedron
3/2 5|5
(10.3/2.10.5)
icosahedral group
A5
12{10}+12{5}+20{3/2}
37 60 120 44 60 2 0 0 -16 3 4 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.4364663517  0.0000000000  0.8997205810
-0.3947875239  0.1861335198  0.8997205810
-0.0230394894  0.4358578416  0.8997205810
-0.1650346033 -0.4040624406  0.8997205810
 0.7478962199  0.1861335198  0.6371856536
 0.4134268623  0.4358578416  0.7994411620
 0.5411827887 -0.4040624406  0.7374650726
-0.5598221272 -0.2179289208  0.7994411620
-0.5971008041  0.4873038812  0.6371856536
-0.2253527696  0.7370282030  0.6371856536
 0.1694347542 -0.6537867624  0.7374650726
-0.4551056902 -0.6219913614  0.6371856536
 0.8526126568 -0.2179289208  0.4749301452
 0.8153339799  0.4873038812  0.3126746369
 0.4808646224  0.7370282030  0.4749301452
 0.6875780535 -0.6219913614  0.3746507262
-0.8641324015 -0.1664828812  0.4749301452
-0.5296630440  0.7884742426  0.3126746369
-0.8871718909  0.2693749604  0.3746507262
 0.0860770985  0.9231617228  0.3746507262
 0.3158300191 -0.8717156832  0.3746507262
-0.1206363326 -0.8717156832  0.4749301452
-0.7594159645 -0.5705453218  0.3126746369
 0.9847687342 -0.1664828812  0.0501397095
 0.6130206997  0.7884742426  0.0501397095
 0.9617292448  0.2693749604 -0.0501397095
 0.8197341309 -0.5705453218 -0.0501397095
-0.9617292448 -0.2693749604  0.0501397095
-0.8197341309  0.5705453218  0.0501397095
-0.2182331759  0.9746077624  0.0501397095
-0.9847687342  0.1664828812 -0.0501397095
 0.2182331759  0.9746077624 -0.0501397095
 0.2182331759 -0.9746077624 -0.0501397095
-0.2182331759 -0.9746077624  0.0501397095
-0.6130206997 -0.7884742426 -0.0501397095
 0.8871718909 -0.2693749604 -0.3746507262
 0.7594159645  0.5705453218 -0.3126746369
 0.8641324015  0.1664828812 -0.4749301452
 0.5296630440 -0.7884742426 -0.3126746369
-0.8153339799 -0.4873038812 -0.3126746369
-0.6875780535  0.6219913614 -0.3746507262
-0.3158300191  0.8717156832 -0.3746507262
-0.8526126568  0.2179289208 -0.4749301452
 0.1206363326  0.8717156832 -0.4749301452
-0.0860770985 -0.9231617228 -0.3746507262
-0.4808646224 -0.7370282030 -0.4749301452
 0.5971008041 -0.4873038812 -0.6371856536
 0.4551056902  0.6219913614 -0.6371856536
 0.5598221272  0.2179289208 -0.7994411620
 0.2253527696 -0.7370282030 -0.6371856536
-0.7478962199 -0.1861335198 -0.6371856536
-0.5411827887  0.4040624406 -0.7374650726
-0.1694347542  0.6537867624 -0.7374650726
-0.4134268623 -0.4358578416 -0.7994411620
 0.3947875239 -0.1861335198 -0.8997205810
 0.1650346033  0.4040624406 -0.8997205810
 0.0230394894 -0.4358578416 -0.8997205810
-0.4364663517  0.0000000000 -0.8997205810
-0.0000000000  0.0000000000 -1.0000000000
 0.1583346290  0.7071067812  0.6891517578
-0.1028584649  0.1531185745  0.6891517578
-0.7144788670  0.1207882584  0.6891517578
 0.1583346290 -0.2357022604  0.6891517578
 0.9436228948  0.1207882584  0.3081980354
 0.3933354313  0.1531185745  0.5751497609
-0.5325411050  0.0900302522  0.5136633924
 0.2124281962 -0.3162277660  0.9245941063
 0.1180156646  0.5270462767  0.5136633924
-0.2904769664 -0.3062371489  0.5751497609
-0.4686190076 -0.8278950396  0.3081980354
 0.7033349793  0.0900302522  0.2297172526
 0.5561442379 -0.8278950396  0.0727556869
 0.5123816228 -0.3062371489  0.3906906553
-0.3328569846  0.4955021156  0.3906906553
-0.5561442379  0.8278950396 -0.0727556869
 0.0897623191 -0.5901345989  0.3906906553
-0.3492879855 -0.6170765289  0.2297172526
 0.4686190076  0.8278950396 -0.3081980354
 0.4700016046  0.4955021156  0.2062315497
 0.4145254404 -0.6170765289  0.0542288872
-0.9436228948 -0.1207882584 -0.3081980354
-0.6364300969 -0.2477510578  0.2062315497
-0.4145254404  0.6170765289 -0.0542288872
-0.6626223886  0.2477510578  0.0922295528
 0.0211900091  0.7071067812  0.0922295528
 0.6626223886 -0.2477510578 -0.0922295528
 0.7144788670 -0.1207882584 -0.6891517578
 0.3492879855  0.6170765289 -0.2297172526
 0.6364300969  0.2477510578 -0.2062315497
-0.7033349793 -0.0900302522 -0.2297172526
-0.0211900091 -0.7071067812 -0.0922295528
-0.1583346290 -0.7071067812 -0.6891517578
-0.4700016046 -0.4955021156 -0.2062315497
 0.5325411050 -0.0900302522 -0.5136633924
 0.3328569846 -0.4955021156 -0.3906906553
-0.2124281962  0.3162277660 -0.9245941063
-0.5123816228  0.3062371489 -0.3906906553
-0.0897623191  0.5901345989 -0.3906906553
-0.1180156646 -0.5270462767 -0.5136633924
 0.2904769664  0.3062371489 -0.5751497609
-0.3933354313 -0.1531185745 -0.5751497609
-0.1583346290  0.2357022604 -0.6891517578
 0.1028584649 -0.1531185745 -0.6891517578
10 0 2 9 18 30 32 25 14 5 1 
3 0 3 2 2
10 0 4 12 23 28 31 29 18 10 3 
5 0 1 7 11 4 
10 1 6 15 25 37 38 36 27 16 7 
3 1 5 6 2
5 2 8 17 19 9 
10 2 3 6 5 13 16 21 22 12 8 
5 3 10 20 15 6 
3 4 8 12 2
10 4 11 21 33 45 46 40 28 17 8 
5 5 14 26 24 13 
10 7 13 24 36 47 50 45 34 22 11 
3 7 16 13 2
3 9 10 18 2
10 9 19 31 43 52 53 44 32 20 10 
3 11 22 21 2
5 12 22 34 35 23 
10 14 15 20 30 42 53 56 49 38 26 
3 14 25 15 2
5 16 27 39 33 21 
10 17 23 35 46 54 58 52 41 29 19 
3 17 28 23 2
5 18 29 41 42 30 
3 19 29 31 2
3 20 32 30 2
3 24 27 36 2
10 24 26 37 48 56 59 57 50 39 27 
5 25 32 44 48 37 
3 26 38 37 2
5 28 40 51 43 31 
3 33 34 45 2
10 33 39 47 55 59 58 51 40 35 34 
3 35 40 46 2
5 36 38 49 55 47 
3 39 50 47 2
10 41 43 51 54 57 55 49 48 44 42 
3 41 52 43 2
3 42 44 53 2
5 45 50 57 54 46 
3 48 49 56 2
3 51 58 54 2
5 52 58 59 56 53 
3 55 57 59 2
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 7 8 2 1 
4 2 9 10 3 
4 5 7 11 0 
4 4 8 7 5 
4 3 12 13 4 
4 6 10 9 7 
4 0 14 15 6 
4 8 15 14 2 
4 10 16 12 3 
4 2 17 7 9 
4 7 13 12 11 
4 11 18 19 0 
4 4 19 18 8 
4 7 20 4 13 
4 6 21 22 10 
4 0 23 2 14 
4 15 24 21 6 
4 18 25 15 8 
4 10 20 7 16 
4 17 12 16 7 
4 2 22 21 17 
4 12 26 27 11 
4 4 28 0 19 
4 27 29 18 11 
4 20 27 26 4 
4 2 30 10 22 
4 23 21 24 2 
4 0 25 18 23 
4 15 30 2 24 
4 28 15 25 0 
4 10 31 32 20 
4 17 32 31 12 
4 21 33 32 17 
4 12 34 4 26 
4 4 29 27 28 
4 34 18 29 4 
4 32 35 27 20 
4 30 32 33 10 
4 23 36 37 21 
4 18 38 36 23 
4 15 37 36 30 
4 28 36 38 15 
4 10 39 12 31 
4 21 39 10 33 
4 12 35 32 34 
4 27 40 36 28 
4 34 36 40 18 
4 39 27 35 12 
4 36 41 32 30 
4 15 42 21 37 
4 18 42 15 38 
4 21 41 36 39 
4 32 43 36 34 
4 27 42 18 40 
4 43 27 39 36 
4 42 32 41 21 
4 32 43 27 42 
small stellated dodecahedron
great dodecahedron
5|2 5/2
(5/2.5/2.5/2.5/2.5/2)
icosahedral group
A5
12{5/2}
38 12 30 12 12 3 0 0 -6 1 5 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8944271910  0.0000000000 -0.4472135955
 0.2763932023  0.8506508084 -0.4472135955
-0.7236067977  0.5257311121 -0.4472135955
-0.7236067977 -0.5257311121 -0.4472135955
 0.2763932023 -0.8506508084 -0.4472135955
-0.2763932023  0.8506508084  0.4472135955
-0.2763932023 -0.8506508084  0.4472135955
-0.8944271910 -0.0000000000  0.4472135955
 0.7236067977 -0.5257311121  0.4472135955
 0.7236067977  0.5257311121  0.4472135955
 0.0000000000 -0.0000000000 -1.0000000000
 0.7236067977  0.5257311121  0.4472135955
-0.2763932023  0.8506508084  0.4472135955
-0.8944271910 -0.0000000000  0.4472135955
-0.2763932023 -0.8506508084  0.4472135955
 0.7236067977 -0.5257311121  0.4472135955
 0.2763932023 -0.8506508084 -0.4472135955
-0.0000000000  0.0000000000 -1.0000000000
 0.2763932023  0.8506508084 -0.4472135955
 0.8944271910  0.0000000000 -0.4472135955
-0.7236067977  0.5257311121 -0.4472135955
-0.7236067977 -0.5257311121 -0.4472135955
 0.0000000000 -0.0000000000  1.0000000000
5 0 2 9 6 1 2
5 0 3 10 8 2 2
5 0 4 6 7 3 2
5 0 5 8 9 4 2
5 0 1 7 10 5 2
5 1 4 9 11 7 2
5 1 3 5 2 4 2
5 1 6 11 10 3 2
5 2 5 10 11 9 2
5 2 8 11 6 4 2
5 3 7 11 8 5 2
5 6 9 8 10 7 2
5 4 0 1 2 3 
5 4 5 6 7 0 
5 0 8 6 9 1 
5 1 7 6 10 2 
5 2 9 6 5 3 
5 3 10 6 8 4 
5 7 9 2 11 0 
5 4 11 2 10 5 
5 9 10 3 11 1 
5 5 8 0 11 3 
5 8 7 1 11 4 
5 7 9 10 5 8 
great dodecahedron
small stellated dodecahedron
5/2|2 5
(5.5.5.5.5)/2
icosahedral group
A5
12{5}
39 12 30 12 12 3 0 0 -6 1 5 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8944271910  0.0000000000  0.4472135955
-0.7236067977  0.5257311121  0.4472135955
 0.2763932023 -0.8506508084  0.4472135955
 0.2763932023  0.8506508084  0.4472135955
-0.7236067977 -0.5257311121  0.4472135955
 0.7236067977  0.5257311121 -0.4472135955
 0.7236067977 -0.5257311121 -0.4472135955
-0.8944271910 -0.0000000000 -0.4472135955
-0.2763932023  0.8506508084 -0.4472135955
-0.2763932023 -0.8506508084 -0.4472135955
-0.0000000000 -0.0000000000 -1.0000000000
 0.2763932023  0.8506508084  0.4472135955
-0.7236067977 -0.5257311121  0.4472135955
 0.8944271910  0.0000000000  0.4472135955
-0.7236067977  0.5257311121  0.4472135955
 0.2763932023 -0.8506508084  0.4472135955
 0.7236067977  0.5257311121 -0.4472135955
 0.0000000000  0.0000000000  1.0000000000
 0.7236067977 -0.5257311121 -0.4472135955
-0.8944271910 -0.0000000000 -0.4472135955
-0.2763932023  0.8506508084 -0.4472135955
-0.2763932023 -0.8506508084 -0.4472135955
-0.0000000000 -0.0000000000 -1.0000000000
5 0 2 9 6 1 
5 0 3 10 8 2 
5 0 4 6 7 3 
5 0 5 8 9 4 
5 0 1 7 10 5 
5 1 4 9 11 7 
5 1 3 5 2 4 
5 1 6 11 10 3 
5 2 5 10 11 9 
5 2 8 11 6 4 
5 3 7 11 8 5 
5 6 9 8 10 7 
5 4 0 1 2 3 
5 4 5 6 7 0 
5 0 8 6 9 1 
5 1 7 6 10 2 
5 2 9 6 5 3 
5 3 10 6 8 4 
5 7 9 2 11 0 
5 4 11 2 10 5 
5 9 10 3 11 1 
5 5 8 0 11 3 
5 8 7 1 11 4 
5 7 9 10 5 8 
great dodecadodecahedron
medial rhombic triacontahedron
2|5/2 5
(5/2.5.5/2.5)
icosahedral group
A5
12{5}+12{5/2}
40 30 60 24 30 3 0 0 -6 2 4 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8660254038  0.0000000000  0.5000000000
 0.6454972244  0.5773502692  0.5000000000
-0.8660254038 -0.0000000000  0.5000000000
-0.6454972244 -0.5773502692  0.5000000000
 0.1102640897  0.5773502692  0.8090169944
 0.8660254038 -0.0000000000 -0.5000000000
 0.7557613141 -0.5773502692 -0.3090169944
 0.1784110449  0.9341723590 -0.3090169944
 0.6454972244  0.5773502692 -0.5000000000
 0.4670861795 -0.3568220898  0.8090169944
-0.1102640897 -0.5773502692  0.8090169944
-0.8660254038  0.0000000000 -0.5000000000
-0.7557613141  0.5773502692 -0.3090169944
-0.1784110449 -0.9341723590 -0.3090169944
-0.6454972244 -0.5773502692 -0.5000000000
-0.4670861795  0.3568220898  0.8090169944
-0.3568220898  0.9341723590 -0.0000000000
-0.7557613141  0.5773502692  0.3090169944
 0.7557613141 -0.5773502692  0.3090169944
-0.0000000000  0.0000000000 -1.0000000000
 0.1102640897  0.5773502692 -0.8090169944
-0.1102640897 -0.5773502692 -0.8090169944
 0.9341723590  0.3568220898  0.0000000000
-0.4670861795  0.3568220898 -0.8090169944
 0.4670861795 -0.3568220898 -0.8090169944
 0.1784110449  0.9341723590  0.3090169944
-0.1784110449 -0.9341723590  0.3090169944
 0.3568220898 -0.9341723590 -0.0000000000
-0.9341723590 -0.3568220898  0.0000000000
 0.3035309991  0.1159385250  0.5257311121
-0.3035309991  0.7946544723  0.5257311121
-0.3035309991 -0.1159385250  0.5257311121
 0.3035309991 -0.7946544723  0.5257311121
 0.6070619982 -0.1159385250 -0.0000000000
 0.6070619982  0.7946544723 -0.0000000000
 0.9822469464 -0.1875924741 -0.0000000000
 0.3751849482  0.4911234732 -0.0000000000
-0.6070619982  0.1159385250 -0.0000000000
-0.6070619982 -0.7946544723 -0.0000000000
-0.9822469464  0.1875924741 -0.0000000000
-0.3751849482 -0.4911234732 -0.0000000000
-0.1875924741  0.4911234732  0.3249196962
-0.4911234732 -0.1875924741  0.8506508084
 0.3035309991 -0.7946544723 -0.5257311121
 0.3035309991  0.1159385250 -0.5257311121
 0.1875924741 -0.4911234732 -0.3249196962
 0.4911234732  0.1875924741 -0.8506508084
-0.1875924741  0.4911234732 -0.3249196962
-0.3035309991  0.7946544723 -0.5257311121
 0.1875924741 -0.4911234732  0.3249196962
 0.4911234732  0.1875924741  0.8506508084
-0.3035309991 -0.1159385250 -0.5257311121
-0.4911234732 -0.1875924741 -0.8506508084
5 0 2 10 5 1 2
5 0 3 13 8 2 
5 0 4 16 11 3 2
5 0 1 7 14 4 
5 1 6 19 23 7 2
5 1 5 17 21 6 
5 2 9 25 28 10 
5 2 8 23 26 9 2
5 3 12 18 29 13 2
5 3 11 28 22 12 
5 4 15 24 17 16 
5 4 14 29 27 15 2
5 5 18 26 16 17 2
5 5 10 27 29 18 
5 6 20 15 27 19 
5 6 21 25 9 20 2
5 7 22 28 25 14 2
5 7 23 8 24 22 
5 8 13 21 17 24 2
5 9 26 18 12 20 
5 10 28 11 19 27 2
5 11 16 26 23 19 
5 12 22 24 15 20 2
5 13 29 14 25 21 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 1 8 9 2 
4 2 10 11 3 
4 5 12 13 0 
4 4 14 15 5 
4 3 16 17 4 
4 7 17 18 1 
4 6 15 19 7 
4 13 20 6 0 
4 9 20 21 2 
4 8 19 22 9 
4 18 23 8 1 
4 11 23 16 3 
4 10 22 14 11 
4 21 12 10 2 
4 5 18 10 12 
4 12 19 8 13 
4 4 21 20 14 
4 14 15 19 22 
4 15 23 18 5 
4 16 9 22 17 
4 7 21 4 17 
4 17 18 10 22 
4 6 16 23 15 
4 19 7 21 12 
4 13 11 14 20 
4 20 6 16 9 
4 23 8 13 11 
truncated great dodecahedron
small stellapentakisdodecahedron
2 5/2|5
(10.10.5/2)
icosahedral group
A5
12{10}+12{5/2}
41 60 90 24 60 3 0 0 -6 2 3 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.5135543437  0.0000000000  0.8580570704
-0.4864456563  0.1646471601  0.8580570704
 0.4079815347 -0.3119120569  0.8580570704
 0.8580570704  0.1646471601  0.4864456563
 0.0905874952 -0.3119120569  0.9457826254
-0.8655497273  0.1191398043  0.4864456563
-0.7599769183  0.4310518612  0.4864456563
 0.2614078885  0.1927722527  0.9457826254
 0.5816638682 -0.6519492065  0.4864456563
 0.9925073431  0.1191398043 -0.0271086873
 0.9019198479  0.4310518612  0.0271086873
-0.2492845149 -0.6519492065  0.7161141409
-0.5256777172  0.4591769538  0.7161141409
-0.9925073431 -0.1191398043  0.0271086873
-0.7161141409  0.6974565623  0.0271086873
-0.6964981104 -0.0455073558  0.7161141409
 0.1979290806  0.6693314697  0.7161141409
 0.4547062524 -0.8902288150  0.0271086873
 0.7161141409 -0.6974565623 -0.0271086873
 0.8188250096  0.4591769538  0.3445027268
 0.8655497273 -0.1191398043 -0.4864456563
 0.6283885859  0.6974565623 -0.3445027268
 0.9653986558 -0.0455073558  0.2567771718
-0.3762421307 -0.8902288150  0.2567771718
-0.6283885859 -0.6974565623  0.3445027268
-0.1027108687  0.7710890108  0.6283885859
-0.8188250096 -0.4591769538 -0.3445027268
-0.8580570704 -0.1646471601 -0.4864456563
-0.5816638682  0.6519492065 -0.4864456563
-0.3716114141  0.8621037224 -0.3445027268
-0.5499244642 -0.5501916655  0.6283885859
-0.0756021814  0.9357361708  0.3445027268
 0.2417918580  0.9357361708  0.2567771718
 0.7945782625 -0.5501916655  0.2567771718
 0.0756021814 -0.9357361708 -0.3445027268
 0.7599769183 -0.4310518612 -0.4864456563
 0.3716114141 -0.8621037224  0.3445027268
 0.4108434749  0.7710890108  0.4864456563
 0.5256777172 -0.4591769538 -0.7161141409
 0.4864456563 -0.1646471601 -0.8580570704
 0.2492845149  0.6519492065 -0.7161141409
 0.1419429296  0.8621037224 -0.4864456563
-0.2417918580 -0.9357361708 -0.2567771718
-0.9019198479 -0.4310518612 -0.0271086873
-0.1419429296 -0.8621037224  0.4864456563
-0.9653986558  0.0455073558 -0.2567771718
-0.4108434749 -0.7710890108 -0.4864456563
-0.5135543437  0.0000000000 -0.8580570704
-0.4547062524  0.8902288150 -0.0271086873
-0.4079815347  0.3119120569 -0.8580570704
-0.7945782625  0.5501916655 -0.2567771718
 0.3762421307  0.8902288150 -0.2567771718
-0.1979290806 -0.6693314697 -0.7161141409
 0.6964981104  0.0455073558 -0.7161141409
 0.1027108687 -0.7710890108 -0.6283885859
 0.0000000000 -0.0000000000 -1.0000000000
-0.0905874952  0.3119120569 -0.9457826254
 0.5499244642  0.5501916655 -0.6283885859
-0.2614078885 -0.1927722527 -0.9457826254
 0.1400572398  0.8506508084  0.5067318540
-0.4053854832 -0.7608452130  0.5067318540
 0.1400572398 -0.0474051448  0.5067318540
 0.6080782248 -0.7608452130  0.2266173744
-0.3666746142  0.1241082803  0.3588694917
 0.9451803665  0.2351141009  0.2266173744
 0.4989267315  0.1241082803  0.1196231639
-0.6946383593  0.2351141009  0.6798521231
-0.6080782248  0.7608452130 -0.2266173744
-0.9451803665 -0.2351141009 -0.2266173744
 0.3209826314 -0.4016228318  0.1196231639
 0.4053854832  0.7608452130 -0.5067318540
 0.6946383593 -0.2351141009 -0.6798521231
-0.2139884209 -0.4016228318  0.2674855262
 0.2653282434 -0.0898055953  0.9599666027
-0.4989267315 -0.1241082803 -0.1196231639
-0.3209826314  0.4016228318 -0.1196231639
 0.0739311811  0.4490279766  0.2674855262
-0.1400572398 -0.8506508084 -0.5067318540
 0.3666746142 -0.1241082803 -0.3588694917
 0.2139884209  0.4016228318 -0.2674855262
-0.2653282434  0.0898055953 -0.9599666027
-0.0739311811 -0.4490279766 -0.2674855262
-0.1400572398  0.0474051448 -0.5067318540
10 0 2 7 15 30 42 22 11 4 1 
10 0 3 9 18 35 47 27 14 6 2 
5 0 1 5 8 3 2
10 1 4 10 21 39 55 43 24 12 5 
5 2 6 13 16 7 2
10 3 8 17 33 52 58 54 36 19 9 
5 4 11 23 20 10 2
10 5 12 25 44 46 51 49 32 17 8 
10 6 14 28 48 57 41 52 33 26 13 
10 7 16 31 24 43 53 59 50 29 15 
5 9 19 37 34 18 2
10 10 20 38 32 49 29 50 56 40 21 
10 11 22 41 57 59 53 35 18 34 23 
5 12 24 31 45 25 2
10 13 26 38 20 23 34 37 45 31 16 
5 14 27 46 44 28 2
5 15 29 49 51 30 2
5 17 32 38 26 33 2
10 19 36 40 56 48 28 44 25 45 37 
5 21 40 36 54 39 2
5 22 42 58 52 41 2
10 27 47 55 39 54 58 42 30 51 46 
5 35 53 43 55 47 2
5 48 56 50 59 57 2
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 6 0 
3 2 7 3 
3 4 8 1 
3 0 9 4 
3 5 7 2 
3 1 10 5 
3 3 11 6 
3 6 12 0 
3 7 13 3 
3 4 14 8 
3 8 15 1 
3 0 16 9 
3 9 14 4 
3 5 17 7 
3 1 12 10 
3 10 18 5 
3 11 14 6 
3 3 19 11 
3 12 20 0 
3 14 12 6 
3 13 9 3 
3 7 18 13 
3 14 17 8 
3 15 21 1 
3 8 18 15 
3 16 11 9 
3 0 21 16 
3 13 14 9 
3 17 11 7 
3 5 8 17 
3 14 10 12 
3 1 22 12 
3 18 19 5 
3 14 18 10 
3 11 14 17 
3 3 21 19 
3 18 11 19 
3 12 8 20 
3 20 21 0 
3 9 22 3 
3 7 15 18 
3 18 13 14 
3 7 21 15 
3 21 22 1 
3 8 23 18 
3 16 7 11 
3 11 23 9 
3 21 16 7 
3 5 20 8 
3 9 12 22 
3 21 5 19 
3 3 21 22 
3 18 11 23 
3 12 23 8 
3 20 21 5 
3 23 9 12 
rhombidodecadodecahedron
medial deltoidal hexecontahedron
5/2 5|2
(4.5/2.4.5)
icosahedral group
A5
12{5}+30{4}+12{5/2}
42 60 120 54 60 3 0 0 -6 3 4 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.6998542122  0.0000000000  0.7142857143
-0.1166423687  0.6900655593  0.7142857143
-0.5248906592  0.4629100499  0.7142857143
-0.3689536881 -0.5947008445  0.7142857143
 0.5832118435  0.6900655593  0.4285714286
 0.8748177653  0.4629100499  0.1428571429
 0.7634342145 -0.5947008445  0.2519902889
-0.4528017108  0.0364260797  0.8908668539
-0.6022384255  0.7854302742  0.1428571429
-0.8938443472 -0.1317907946  0.4285714286
-0.3499271061  0.9258200998  0.1428571429
 0.2077578990  0.4039714148  0.8908668539
 0.1028746047 -0.9622461795  0.2519902889
-0.8545497448 -0.4993361296  0.1428571429
 0.9469067137  0.0364260797  0.3194382825
 0.5301494771  0.7854302742 -0.3194382825
 0.9383977675 -0.1317907946 -0.3194382825
 0.3499271061  0.9258200998 -0.1428571429
 0.4750784209  0.4039714148  0.7817337079
 0.7103718480 -0.4993361296 -0.4960194221
-0.9383977675  0.1317907946  0.3194382825
-0.0891068406 -0.6172133998  0.7817337079
-0.2024990811  0.8443689093 -0.4960194221
-0.9711921135  0.1907294297 -0.1428571429
-0.9469067137 -0.0364260797 -0.3194382825
-0.5301494771 -0.7854302742  0.3194382825
 0.3827214521  0.8668814647  0.3194382825
-0.6107473716  0.6172133998 -0.4960194221
 0.5714527692 -0.2496680648  0.7817337079
-0.3827214521 -0.8668814647 -0.3194382825
 0.0498122382 -0.8668814647 -0.4960194221
-0.5937294793 -0.1907294297  0.7817337079
 0.8938443472  0.1317907946 -0.4285714286
 0.6107473716 -0.6172133998  0.4960194221
 0.5937294793  0.1907294297 -0.7817337079
 0.4528017108 -0.0364260797 -0.8908668539
 0.6022384255 -0.7854302742 -0.1428571429
-0.0498122382  0.8668814647  0.4960194221
 0.0891068406  0.6172133998 -0.7817337079
 0.1389190789 -0.2496680648  0.9583148475
 0.9711921135 -0.1907294297  0.1428571429
-0.8748177653 -0.4629100499 -0.1428571429
-0.7634342145  0.5947008445 -0.2519902889
-0.3499271061 -0.9258200998  0.1428571429
-0.5714527692  0.2496680648 -0.7817337079
-0.1389190789  0.2496680648 -0.9583148475
-0.7103718480  0.4993361296  0.4960194221
-0.5832118435 -0.6900655593 -0.4285714286
-0.4750784209 -0.4039714148 -0.7817337079
 0.2024990811 -0.8443689093  0.4960194221
-0.1028746047  0.9622461795 -0.2519902889
 0.8545497448  0.4993361296 -0.1428571429
 0.3499271061 -0.9258200998 -0.1428571429
-0.2077578990 -0.4039714148 -0.8908668539
 0.5248906592 -0.4629100499 -0.7142857143
 0.3689536881  0.5947008445 -0.7142857143
 0.1166423687 -0.6900655593 -0.7142857143
-0.6998542122  0.0000000000 -0.7142857143
-0.0000000000  0.0000000000 -1.0000000000
 0.3126527364  0.3699357065  0.7658396707
-0.1612652036  0.2898289539  0.7658396707
-0.4791790224 -0.0706514331  0.7658396707
 0.3126527364 -0.5619055661  0.7658396707
 0.8782468497 -0.0706514331  0.2116728790
 0.6511655506  0.2898289539  0.4341662042
 0.0501361976  0.9911632216  0.1228081018
-0.5655941134  0.4405871397  0.5541667917
-0.0762151731  0.7128849670  0.5541667917
-0.8686716880  0.4799246488  0.1228081018
-0.5895677240 -0.4005337633  0.4341662042
-0.4029638493 -0.7835364001  0.2116728790
 0.7918317588  0.4405871397 -0.0000000000
 0.7064275445  0.4799246488 -0.5202234672
 0.4422753728  0.7128849670  0.3424939127
 0.4359714769 -0.7835364001 -0.1308210337
 0.7249728497 -0.4005337633 -0.1024927377
-0.7064275445 -0.4799246488  0.5202234672
 0.0636073813 -0.1143164201  0.8966607045
-0.6292014946  0.5549035598 -0.3424939127
-0.7249728497  0.4005337633  0.1024927377
-0.7918317588 -0.4405871397 -0.0000000000
 0.0418424850  0.8272013871  0.1024927377
-0.1398225544  0.8272013871 -0.3424939127
 0.7802348436  0.3472767383  0.5202234672
-0.0418424850 -0.8272013871 -0.1024927377
-0.8389353262  0.0000000000  0.3424939127
-0.7802348436 -0.3472767383 -0.5202234672
 0.5820979272 -0.1143164201  0.6849878255
 0.8686716880 -0.4799246488 -0.1228081018
 0.5895677240  0.4005337633 -0.4341662042
 0.2097338315  0.5549035598 -0.6849878255
 0.5655941134 -0.4405871397 -0.5541667917
-0.1932300177  0.3472767383  0.9176388327
 0.1932300177 -0.3472767383 -0.9176388327
 0.8389353262 -0.0000000000 -0.3424939127
-0.8782468497  0.0706514331 -0.2116728790
 0.1398225544 -0.8272013871  0.3424939127
 0.2609325806 -0.4689530983  0.6391516797
-0.2609325806  0.4689530983 -0.6391516797
-0.5820979272  0.1143164201 -0.6849878255
-0.6511655506 -0.2898289539 -0.4341662042
-0.0501361976 -0.9911632216 -0.1228081018
-0.2097338315 -0.5549035598  0.6849878255
 0.4029638493  0.7835364001 -0.2116728790
 0.6292014946 -0.5549035598  0.3424939127
 0.0762151731 -0.7128849670 -0.5541667917
-0.4422753728 -0.7128849670 -0.3424939127
 0.4791790224  0.0706514331 -0.7658396707
 0.1612652036 -0.2898289539 -0.7658396707
-0.0636073813  0.1143164201 -0.8966607045
-0.4359714769  0.7835364001  0.1308210337
-0.3126527364  0.5619055661 -0.7658396707
-0.3126527364 -0.3699357065 -0.7658396707
4 0 2 5 1 
5 0 3 12 8 2 2
4 0 4 10 3 
5 0 1 7 13 4 
4 1 6 17 7 
5 1 5 15 19 6 2
5 2 9 23 16 5 
4 2 8 21 9 
4 3 11 27 12 
5 3 10 25 28 11 
5 4 14 32 26 10 2
4 4 13 30 14 
4 5 16 33 15 
5 6 18 39 36 17 
4 6 19 38 18 
4 7 20 31 13 
5 7 17 37 41 20 2
5 8 22 44 42 21 
4 8 12 29 22 
4 9 24 45 23 
5 9 21 43 47 24 2
4 10 26 48 25 
5 11 18 38 51 27 2
4 11 28 39 18 
5 12 27 52 41 29 
5 13 31 44 53 30 2
4 14 24 47 32 
5 14 30 54 45 24 
4 15 34 40 19 
5 15 33 55 53 34 
5 16 35 52 56 33 2
4 16 23 46 35 
4 17 36 57 37 
5 19 40 32 47 38 
5 20 35 46 49 31 
4 20 41 52 35 
4 21 42 58 43 
4 22 34 53 44 
5 22 29 50 40 34 2
5 23 45 39 28 46 2
4 25 49 46 28 
5 25 48 58 42 49 2
5 26 50 37 57 48 
4 26 32 40 50 
4 27 51 56 52 
4 29 41 37 50 
4 30 53 55 54 
4 31 49 42 44 
4 33 56 59 55 
5 36 54 55 59 57 2
4 36 39 45 54 
4 38 47 43 51 
5 43 58 59 56 51 
4 48 57 59 58 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 1 8 9 2 
4 2 10 11 3 
4 5 12 6 0 
4 4 13 14 5 
4 3 15 16 4 
4 7 17 18 1 
4 6 19 20 7 
4 9 21 10 2 
4 8 22 23 9 
4 18 24 8 1 
4 11 25 15 3 
4 10 26 27 11 
4 5 28 29 12 
4 12 30 31 6 
4 16 32 13 4 
4 13 23 22 14 
4 14 33 28 5 
4 15 34 35 16 
4 20 36 17 7 
4 17 37 38 18 
4 31 39 19 6 
4 19 27 26 20 
4 9 40 41 21 
4 21 42 43 10 
4 24 44 22 8 
4 23 39 40 9 
4 38 45 24 18 
4 27 46 25 11 
4 25 47 34 15 
4 43 33 26 10 
4 29 48 30 12 
4 28 38 37 29 
4 30 35 34 31 
4 32 49 50 13 
4 16 45 42 32 
4 22 51 33 14 
4 50 39 23 13 
4 43 38 28 33 
4 35 24 45 16 
4 36 41 47 17 
4 20 51 52 36 
4 25 37 17 47 
4 50 27 19 39 
4 34 40 39 31 
4 26 20 51 33 
4 41 53 42 21 
4 40 41 47 34 
4 42 43 38 45 
4 44 52 51 22 
4 30 44 24 35 
4 46 29 37 25 
4 49 46 27 50 
4 49 48 29 46 
4 48 52 44 30 
4 53 49 32 42 
4 52 53 41 36 
4 49 48 52 53 
small rhombidodecahedron
small rhombidodecacron
2 5/2 5|
(10.4.10/9.4/3)
icosahedral group
A5
6{10}+15{4}+15{4/3}+6{10/9}
43 60 120 42 60 0 0 1 -18 4 4 120 5 0 1
 0.0000000000  0.0000000000  1.0000000000
 0.4364663517  0.0000000000  0.8997205810
-0.3947875239  0.1861335198  0.8997205810
-0.1650346033 -0.4040624406  0.8997205810
-0.0230394894  0.4358578416  0.8997205810
 0.7478962199  0.1861335198  0.6371856536
 0.5411827887 -0.4040624406  0.7374650726
 0.4134268623  0.4358578416  0.7994411620
-0.5598221272 -0.2179289208  0.7994411620
-0.5971008041  0.4873038812  0.6371856536
-0.4551056902 -0.6219913614  0.6371856536
 0.1694347542 -0.6537867624  0.7374650726
-0.2253527696  0.7370282030  0.6371856536
 0.8526126568 -0.2179289208  0.4749301452
 0.8153339799  0.4873038812  0.3126746369
 0.6875780535 -0.6219913614  0.3746507262
 0.4808646224  0.7370282030  0.4749301452
-0.8641324015 -0.1664828812  0.4749301452
-0.5296630440  0.7884742426  0.3126746369
-0.8871718909  0.2693749604  0.3746507262
-0.1206363326 -0.8717156832  0.4749301452
-0.7594159645 -0.5705453218  0.3126746369
 0.3158300191 -0.8717156832  0.3746507262
 0.0860770985  0.9231617228  0.3746507262
 0.9847687342 -0.1664828812  0.0501397095
 0.6130206997  0.7884742426  0.0501397095
 0.9617292448  0.2693749604 -0.0501397095
 0.8197341309 -0.5705453218 -0.0501397095
-0.9617292448 -0.2693749604  0.0501397095
-0.8197341309  0.5705453218  0.0501397095
-0.2182331759  0.9746077624  0.0501397095
-0.9847687342  0.1664828812 -0.0501397095
-0.2182331759 -0.9746077624  0.0501397095
-0.6130206997 -0.7884742426 -0.0501397095
 0.2182331759 -0.9746077624 -0.0501397095
 0.2182331759  0.9746077624 -0.0501397095
 0.8871718909 -0.2693749604 -0.3746507262
 0.7594159645  0.5705453218 -0.3126746369
 0.8641324015  0.1664828812 -0.4749301452
 0.5296630440 -0.7884742426 -0.3126746369
-0.8153339799 -0.4873038812 -0.3126746369
-0.6875780535  0.6219913614 -0.3746507262
-0.3158300191  0.8717156832 -0.3746507262
-0.8526126568  0.2179289208 -0.4749301452
-0.0860770985 -0.9231617228 -0.3746507262
-0.4808646224 -0.7370282030 -0.4749301452
 0.1206363326  0.8717156832 -0.4749301452
 0.5971008041 -0.4873038812 -0.6371856536
 0.4551056902  0.6219913614 -0.6371856536
 0.5598221272  0.2179289208 -0.7994411620
 0.2253527696 -0.7370282030 -0.6371856536
-0.7478962199 -0.1861335198 -0.6371856536
-0.5411827887  0.4040624406 -0.7374650726
-0.1694347542  0.6537867624 -0.7374650726
-0.4134268623 -0.4358578416 -0.7994411620
 0.3947875239 -0.1861335198 -0.8997205810
 0.1650346033  0.4040624406 -0.8997205810
 0.0230394894 -0.4358578416 -0.8997205810
-0.4364663517  0.0000000000 -0.8997205810
 0.0000000000 -0.0000000000 -1.0000000000
 0.1583346290  0.7071067812  0.6891517578
-0.2144012325 -0.0834626339  0.6891517578
-0.7144788670  0.1207882584  0.6891517578
 0.1583346290  0.1669252677  0.6891517578
 0.9436228948  0.1207882584  0.3081980354
 0.4936927550 -0.0834626339  0.5264650961
-0.2375019436  0.3535533906  0.5886058714
 0.2124281962 -0.3162277660  0.9245941063
-0.4686190076 -0.8278950396  0.3081980354
-0.1094065379 -0.4885987690  0.5264650961
 0.4705920439  0.3535533906  0.4259192097
 0.3282196136 -0.4885987690  0.4259192097
 0.5561442379 -0.8278950396  0.0727556869
-0.5052431105 -0.3019706461  0.4259192097
-0.5426208461  0.4051361351  0.2632325481
-0.5561442379  0.8278950396 -0.0727556869
-0.1698849846  0.6555240367  0.2632325481
 0.6404770285 -0.3019706461  0.1626866616
 0.4686190076  0.8278950396 -0.3081980354
 0.6030992928  0.4051361351  0.0000000000
 0.2677411669  0.6555240367  0.1626866616
-0.9436228948 -0.1207882584 -0.3081980354
-0.7080939875  0.0000000000  0.1626866616
 0.0373777356 -0.7071067812  0.1626866616
-0.6030992928 -0.4051361351 -0.0000000000
 0.7080939875 -0.0000000000 -0.1626866616
 0.7144788670 -0.1207882584 -0.6891517578
 0.5426208461 -0.4051361351 -0.2632325481
-0.6404770285  0.3019706461 -0.1626866616
-0.0373777356  0.7071067812 -0.1626866616
-0.2677411669 -0.6555240367 -0.1626866616
-0.1583346290 -0.7071067812 -0.6891517578
 0.1698849846 -0.6555240367 -0.2632325481
 0.5052431105  0.3019706461 -0.4259192097
-0.4705920439 -0.3535533906 -0.4259192097
-0.2124281962  0.3162277660 -0.9245941063
-0.3282196136  0.4885987690 -0.4259192097
-0.4936927550  0.0834626339 -0.5264650961
 0.1094065379  0.4885987690 -0.5264650961
 0.2375019436 -0.3535533906 -0.5886058714
 0.2144012325  0.0834626339 -0.6891517578
-0.1583346290 -0.1669252677 -0.6891517578
10 0 2 9 18 30 35 25 14 5 1 
4 0 3 8 2 
10 0 4 12 18 29 31 28 21 10 3 9
4 0 1 7 4 3
10 1 6 15 27 36 38 37 25 16 7 9
4 1 5 13 6 
4 2 4 12 9 3
10 2 8 10 20 22 15 13 5 7 4 9
10 3 11 22 34 44 45 40 28 17 8 
4 3 10 20 11 3
4 5 14 16 7 3
4 6 11 22 15 3
10 6 13 24 36 47 50 44 32 20 11 
4 8 17 21 10 3
4 9 19 29 18 
10 9 12 23 35 46 53 52 43 31 19 9
4 12 23 30 18 3
4 13 15 27 24 3
10 14 26 38 49 56 53 42 30 23 16 9
4 14 25 37 26 
4 16 25 35 23 3
10 17 19 29 41 52 58 54 45 33 21 9
4 17 28 31 19 
4 20 22 34 32 
4 21 28 40 33 3
4 24 26 38 36 
10 24 27 39 50 57 59 56 48 37 26 9
4 27 39 47 36 3
4 29 41 43 31 3
4 30 42 46 35 
4 32 33 45 44 3
10 32 34 39 47 55 59 58 51 40 33 
4 34 39 50 44 
4 37 38 49 48 3
4 40 45 54 51 
10 41 42 46 48 49 55 57 54 51 43 9
4 41 52 53 42 
4 43 52 58 51 3
4 46 53 56 48 
4 47 55 57 50 
4 49 55 59 56 3
4 54 57 59 58 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 1 8 9 2 
4 2 6 7 3 
4 5 7 10 0 
4 4 11 12 5 
4 10 4 3 7 
4 7 13 8 1 
4 0 14 15 6 
4 9 7 13 2 
4 8 11 12 9 
4 2 16 15 6 
4 12 17 7 5 
4 10 18 19 0 
4 4 17 7 11 
4 18 20 4 10 
4 13 21 22 8 
4 0 16 2 14 
4 14 21 22 15 
4 12 23 7 9 
4 21 24 2 13 
4 8 23 7 11 
4 16 18 20 15 
4 12 25 26 17 
4 19 4 20 0 
4 18 25 26 19 
4 4 27 26 17 
4 22 2 24 8 
4 2 28 21 14 
4 0 29 18 16 
4 28 15 22 2 
4 12 30 31 23 
4 21 30 31 24 
4 8 32 31 23 
4 29 15 20 0 
4 12 27 4 25 
4 26 33 4 19 
4 18 33 4 25 
4 27 31 32 26 
4 31 34 8 24 
4 28 35 36 21 
4 29 35 36 18 
4 35 37 15 28 
4 12 32 8 30 
4 21 34 8 30 
4 35 38 15 29 
4 12 39 31 27 
4 26 38 35 33 
4 18 40 35 33 
4 39 26 32 12 
4 31 37 35 34 
4 36 15 37 21 
4 38 18 36 15 
4 21 41 35 34 
4 39 35 40 31 
4 26 40 18 38 
4 41 26 39 35 
4 31 41 21 37 
4 40 31 41 26 
snub dodecadodecahedron
medial pentagonal hexecontahedron
|2 5/2 5
(3.3.5/2.3.5)
icosahedral group
A5
12{5}+60{3}+12{5/2}
44 60 150 84 60 3 0 0 -6 3 5 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.7217483383  0.0000000000  0.6921555722
 0.2952223438  0.6586079498  0.6921555722
-0.4802341493  0.5387910779  0.6921555722
-0.7128072909  0.1132538291  0.6921555722
-0.3949112124 -0.6041239924  0.6921555722
 0.7729021303 -0.6041239924  0.1940528249
 0.9929356725  0.1132538291 -0.0353881415
 0.6298389795  0.6967741838  0.3432325693
 0.8934465412  0.2897320856  0.3432325693
 0.5094943059  0.8597460274 -0.0353881415
-0.7452206567  0.6658782563 -0.0353881415
-0.9392275176  0.0065630428  0.3432325693
-0.4160062641 -0.2197373699  0.8824138918
-0.0396950161  0.4687963622  0.8824138918
-0.5127015231  0.7869743017  0.3432325693
-0.9061974527 -0.4015688916  0.1324711369
-0.6380905382 -0.7691476741 -0.0353881415
 0.0827685741 -0.9774931531  0.1940528249
 0.4161165893 -0.7691476741 -0.4850348850
 0.8899385998 -0.1459468565 -0.4320981413
 0.7539503920 -0.5893107329 -0.2902958256
 0.6655112749  0.0439566123 -0.7450923159
 0.0780084845  0.9881123794 -0.1324711369
-0.1041736883  0.7897513117  0.6045169215
 0.3520254514  0.2279778217  0.9078018475
 0.6780508743 -0.4180984375  0.6045169215
 0.8524892978  0.2817520197 -0.4403155647
 0.5063993531  0.4753594049 -0.7194394563
-0.1335348318  0.8642393240 -0.4850348850
-0.6262555055  0.3003513119 -0.7194394563
-0.9884363197 -0.0737905134 -0.1324711369
-0.8685334856  0.3336886979 -0.3664716051
-0.8461505251 -0.4469425270 -0.2902958256
 0.0004392467 -0.8131042863  0.5821178804
 0.3680207594 -0.2011380776  0.9078018475
 0.2609051739  0.9140614801  0.3105158625
-0.5824195190  0.6885337320 -0.4320981413
-0.8256133779 -0.0460263585 -0.5623558700
-0.4967433944 -0.7479092215 -0.4403155647
-0.3220982637 -0.8943336110  0.3105158625
-0.7559043639 -0.2995786473  0.5821178804
-0.0593841233 -0.8247602084 -0.5623558700
-0.2654045267 -0.9535247958 -0.1426565840
-0.2602607645 -0.5330006997 -0.8050929068
 0.8544020838  0.5193160172 -0.0175486021
 0.9206031564 -0.1699152137  0.3515944377
 0.4508730059 -0.7963143545  0.4032331602
 0.1682912484 -0.5593947155 -0.8116376088
-0.0520696708 -0.1637734841 -0.9851228326
 0.1000551755  0.5846489317 -0.8050929068
-0.4001067482  0.9095681836 -0.1122511001
-0.7889119713  0.4637034829  0.4032331602
-0.0507662577 -0.4452651179  0.8939584788
 0.5039717878 -0.8635418251 -0.0175486021
 0.6117806625 -0.4310104555 -0.6632905911
 0.2552292055  0.2091181436 -0.9439955798
 0.2944167902  0.8325793470 -0.4691805458
-0.2044629478  0.2361469744 -0.9499628990
-0.4635135922 -0.0992132343 -0.8805179635
 0.3176067784  0.2056876888  0.7446363937
-0.0577804302  0.3739557632  0.7446363937
-0.2958960533  0.1617190385  0.7446363937
-0.3459479328 -0.1533020508  0.7446363937
 0.3176067784 -0.5870626674  0.7446363937
 0.7768898692 -0.1533020508  0.2657168836
 0.7322102858  0.2529771921  0.3123067203
 0.5190711176  0.3361595084  0.5345585472
 0.5303477767  0.5646774283  0.3123067203
-0.1488707758  0.9634937711  0.2225247069
-0.6760448370  0.3782760112  0.3123067203
-0.5732289698  0.1016922995  0.5989424632
-0.3951316587  0.4275555494  0.5989424632
-0.9507295624  0.3065030456  0.0465744808
-0.6289594872 -0.2787147143  0.4737012997
-0.5414902536 -0.5327952207  0.3018417444
-0.2967642069 -0.7341596510  0.2657168836
 0.3971877186 -0.7341596510 -0.0302716515
 0.6492723420 -0.4744621543 -0.2258228062
 0.7771543287 -0.2505446113 -0.0380713515
 0.7534079011 -0.1349478249 -0.3344106292
 0.6624305789  0.6517935348 -0.3692572492
 0.1885313770  0.7728460386  0.2546169088
 0.2741087173  0.5354509080  0.5795011528
 0.6007291180  0.0311093314  0.5795011528
 0.9507295624 -0.3065030456 -0.0465744808
 0.7043859914  0.4469827888 -0.0413716263
 0.5414902536  0.5327952207 -0.3018417444
 0.2755665915  0.6868701477 -0.3872173856
-0.4700250476  0.5716677363 -0.3872173856
-0.7370165274  0.2787147143 -0.2771093578
-0.7771543287  0.2505446113  0.0380713515
-0.8288344054 -0.0333202496 -0.0979190443
-0.6624305789 -0.6517935348  0.3692572492
-0.0148490159 -0.3853801636  0.7408957323
-0.0273832159  0.0149660237  0.8346801947
 0.6350041919  0.4112397892  0.6539506954
-0.0910347123  0.6776531605  0.4797538171
-0.1216913541  0.7875881686  0.1818982454
-0.3176510871  0.7694052113 -0.0691249417
-0.6959924610 -0.3733640806 -0.2717694010
-0.5387413071 -0.6382961364  0.0008343070
-0.7440492812 -0.3568156856  0.1293757453
-0.6350041919 -0.4112397892 -0.6539506954
-0.1919768421 -0.8030658240 -0.1260754705
 0.1216913541 -0.7875881686 -0.1818982454
-0.0342127958 -0.7044618897 -0.4474681893
 0.3619836047 -0.1978385309 -0.9109488381
 0.7029212391  0.2650636348 -0.3651134768
 0.8322798705  0.0635400349 -0.0306223940
 0.6637849964 -0.4858056897  0.1450763943
 0.1488707758 -0.9634937711 -0.2225247069
 0.4958659056 -0.3450204858 -0.5768385544
 0.2958960533 -0.1617190385 -0.7446363937
 0.2228298392  0.1451701761 -0.7917937437
-0.1262830522  0.7062176385 -0.4277547049
-0.4038726796  0.6755266122  0.2796703500
-0.3619836047  0.1978385309  0.9109488381
 0.3058451155 -0.1984352346  0.7514965554
 0.2596211293 -0.4798823043  0.6086877063
 0.3692908006 -0.6542027999  0.3651134768
 0.5370111450  0.0186945890 -0.6394797825
 0.4378962749  0.4133221760 -0.5788579109
 0.0525929431  0.4921159726 -0.6728452286
-0.2596211293  0.4798823043 -0.6086877063
-0.1805976074  0.2252439638 -0.7837821833
-0.7911518284  0.0282120159  0.2663601255
-0.6425873810  0.5330951931 -0.0235758922
-0.3176067784  0.5870626674 -0.7446363937
-0.6802657495 -0.0663548917 -0.4801045596
-0.5190711176 -0.3361595084 -0.5345585472
-0.4284272985 -0.6038350569 -0.3866498724
 0.0746433386 -0.8214200499  0.1317661698
 0.5432565786 -0.3645767609  0.5192503492
 0.4402662939  0.7076735504 -0.0550325933
 0.0484747550  0.8295519246 -0.0846088198
-0.5035932888  0.2744096577 -0.6072544682
-0.4029809447 -0.1070837544 -0.7237432401
-0.2473362223 -0.4392647648 -0.6659850669
 0.0243625739 -0.6670600099  0.5020978570
-0.3525221086 -0.5119261104  0.5579647573
 0.1562554434 -0.4433331772 -0.6904381075
 0.3299109277 -0.6618755327 -0.3882581729
-0.0124901259 -0.1403786872 -0.8232877205
3 0 2 1 
3 0 3 2 
5 0 4 14 13 3 2
3 0 5 4 
5 0 1 6 18 5 
3 1 7 6 
3 1 8 7 
5 1 2 9 25 8 2
3 2 10 9 
5 2 3 11 29 10 
3 3 12 11 
3 3 13 12 
3 4 15 14 
5 4 16 38 37 15 
3 4 5 16 
5 5 17 41 40 16 2
3 5 18 17 
3 6 19 18 
3 6 20 19 
5 6 7 21 46 20 2
3 7 22 21 
5 7 8 23 50 22 
3 8 24 23 
3 8 25 24 
3 9 26 25 
5 9 27 55 54 26 
3 9 10 27 
5 10 28 45 57 27 2
3 10 29 28 
3 11 30 29 
3 11 31 30 
5 11 12 32 52 31 2
3 12 33 32 
5 12 13 34 43 33 
3 13 35 34 
3 13 14 35 
5 14 36 45 46 35 
3 14 15 36 
5 15 23 24 51 36 2
3 15 37 23 
3 16 39 38 
3 16 40 39 
3 17 31 41 
5 17 42 49 30 31 
3 17 18 42 
5 18 19 43 54 42 2
3 19 44 43 
5 19 20 28 58 44 
3 20 45 28 
3 20 46 45 
3 21 47 46 
5 21 48 39 40 47 
3 21 22 48 
5 22 49 55 56 48 2
3 22 50 49 
3 23 37 50 
3 24 52 51 
5 24 25 53 41 52 
3 25 26 53 
5 26 34 35 47 53 2
3 26 54 34 
3 27 56 55 
3 27 57 56 
3 28 29 58 
5 29 30 50 37 58 2
3 30 49 50 
3 31 52 41 
3 32 51 52 
5 32 59 56 57 51 
3 32 33 59 
5 33 44 38 39 59 2
3 33 43 44 
3 34 54 43 
3 35 46 47 
3 36 57 45 
3 36 51 57 
3 37 38 58 
3 38 44 58 
3 39 48 59 
3 40 53 47 
3 40 41 53 
3 42 55 49 
3 42 54 55 
3 48 56 59 
5 4 0 1 2 3 
5 4 5 6 7 0 
5 7 8 9 1 0 
5 9 10 11 2 1 
5 2 12 13 14 3 
5 14 15 16 4 3 
5 4 17 18 19 5 
5 19 20 21 6 5 
5 21 22 23 7 6 
5 7 24 25 26 8 
5 26 27 28 9 8 
5 9 29 30 31 10 
5 31 32 33 11 10 
5 33 34 35 2 11 
5 35 36 37 12 2 
5 37 38 39 13 12 
5 13 40 41 15 14 
5 15 42 43 44 16 
5 44 45 17 4 16 
5 45 46 47 18 17 
5 47 48 49 19 18 
5 19 50 51 52 20 
5 52 53 54 21 20 
5 21 55 39 38 22 
5 38 56 57 23 22 
5 57 58 24 7 23 
5 58 59 60 25 24 
5 25 61 62 27 26 
5 27 48 47 63 28 
5 63 64 29 9 28 
5 64 65 43 30 29 
5 42 66 31 30 43 
5 31 67 68 69 32 
5 69 70 71 33 32 
5 33 72 60 59 34 
5 59 73 36 35 34 
5 36 74 75 38 37 
5 55 64 76 13 39 
5 76 77 70 40 13 
5 70 78 51 41 40 
5 51 79 80 15 41 
5 80 57 66 42 15 
5 43 81 82 45 44 
5 45 72 33 71 46 
5 77 47 46 71 70 
5 27 74 36 49 48 
5 73 50 19 49 36 
5 59 79 51 50 73 
5 78 83 53 52 51 
5 53 81 43 65 54 
5 54 21 55 64 65 
5 75 68 67 56 38 
5 56 57 66 31 67 
5 57 58 59 79 80 
5 82 25 60 72 45 
5 53 61 25 82 81 
5 83 68 62 61 53 
5 62 27 74 75 68 
5 47 63 64 76 77 
5 68 69 70 78 83 
ditrigonal dodecadodecahedron
medial triambic icosahedron
3|5/3 5
(5/3.5.5/3.5.5/3.5)
icosahedral group
A5
12{5}+12{5/3}
45 20 60 24 20 4 0 0 -16 2 6 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9428090416  0.0000000000  0.3333333333
 0.6727182848 -0.6605596098  0.3333333333
-0.4714045208  0.8164965809  0.3333333333
 0.2357022604  0.9128709292  0.3333333333
-0.4714045208 -0.8164965809  0.3333333333
-0.9084205452 -0.2523113194  0.3333333333
 0.0900302522 -0.6605596098  0.7453559925
 0.4714045208  0.8164965809 -0.3333333333
 0.4714045208 -0.8164965809 -0.3333333333
 0.6170765289 -0.2523113194 -0.7453559925
 0.9084205452  0.2523113194 -0.3333333333
-0.2357022604 -0.9128709292 -0.3333333333
 0.5270462767  0.4082482905  0.7453559925
-0.9428090416 -0.0000000000 -0.3333333333
-0.0900302522  0.6605596098 -0.7453559925
-0.6727182848  0.6605596098 -0.3333333333
-0.6170765289  0.2523113194  0.7453559925
-0.5270462767 -0.4082482905 -0.7453559925
 0.0000000000  0.0000000000 -1.0000000000
 0.1326479105 -0.0542373073  0.1875924741
 0.7765343938  0.6015009550  0.1875924741
-0.0193530693  0.1419951139  0.1875924741
-0.9091823043  0.3717480345  0.1875924741
-0.1132948412 -0.0877578066  0.1875924741
 0.1326479105 -0.9732489895  0.1875924741
 0.2146288278 -0.0877578066 -0.0442845760
 0.4799246488  0.3717480345 -0.7946544723
 0.1833149038  0.1419951139  0.0442845760
-0.0819809172  0.6015009550  0.7946544723
-0.4799246488 -0.3717480345  0.7946544723
 0.0313139240 -0.2297529205  0.0442845760
 0.0819809172 -0.6015009550 -0.7946544723
-0.0313139240  0.2297529205 -0.0442845760
-0.5619055661  0.2297529205 -0.7946544723
-0.2146288278  0.0877578066  0.0442845760
 0.5619055661 -0.2297529205  0.7946544723
-0.1833149038 -0.1419951139 -0.0442845760
-0.7765343938 -0.6015009550 -0.1875924741
 0.9091823043 -0.3717480345 -0.1875924741
 0.1132948412  0.0877578066 -0.1875924741
 0.0193530693 -0.1419951139 -0.1875924741
-0.1326479105  0.9732489895 -0.1875924741
-0.1326479105  0.0542373073 -0.1875924741
5 0 2 13 7 1 3
5 0 3 15 10 2 
5 0 4 17 13 3 3
5 0 5 18 15 4 
5 0 6 7 17 5 3
5 0 1 10 18 6 
5 1 9 11 2 10 3
5 1 4 16 18 9 
5 1 8 13 11 4 3
5 1 7 6 16 8 
5 2 12 14 3 13 
5 2 5 9 7 12 3
5 2 11 15 14 5 
5 3 8 16 4 15 3
5 3 6 12 10 8 
5 3 14 17 16 6 3
5 4 11 9 5 17 
5 5 14 12 6 18 3
5 7 9 19 16 17 
5 7 13 8 19 12 
5 8 10 15 11 19 3
5 9 18 10 12 19 3
5 11 13 17 14 19 
5 14 15 18 16 19 3
6 5 0 1 2 3 4 
6 5 6 7 8 9 0 
6 0 10 11 12 6 1 
6 1 13 14 15 10 2 
6 2 16 8 7 13 3 
6 3 17 12 11 16 4 
6 4 9 15 14 17 5 
6 4 18 11 19 0 9 
6 8 19 20 14 13 9 
6 6 16 11 18 21 7 
6 5 21 14 20 1 6 
6 12 20 22 8 16 6 
6 10 17 14 21 19 11 
6 22 2 10 0 19 8 
6 15 22 23 12 17 10 
6 23 3 13 1 20 12 
6 7 23 18 15 9 13 
6 2 16 4 18 15 22 
6 3 17 5 21 7 23 
6 19 20 22 23 18 21 
great ditrigonal dodecicosidodecahedron
great ditrigonal dodecacronic hexecontahedron
3 5|5/3
(10/3.3.10/3.5)
icosahedral group
A5
12{5}+12{10/3}+20{3}
46 60 120 44 60 4 0 0 -16 3 4 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.7913673487  0.0000000000  0.6113409191
 0.1126514014  0.7833083316  0.6113409191
-0.6820030709  0.4014151117  0.6113409191
-0.4944105968 -0.6179162098  0.6113409191
 0.4149268310  0.7833083316  0.4628863603
 0.9007316265  0.4014151117 -0.1659772426
 0.7860486710 -0.6179162098 -0.0175226837
-0.2691077939  0.9487004534 -0.1659772426
 0.8343963552  0.2991971590  0.4628863603
-0.7549125894 -0.4645892808  0.4628863603
-0.5726387930  0.8028302234 -0.1659772426
-0.0086058013 -0.9998094297 -0.0175226837
-0.8761697921 -0.4525240881 -0.1659772426
-0.8708511144  0.1653921218  0.4628863603
 0.0331676357  0.9487004534 -0.3144318014
-0.1437874830  0.2991971590  0.9432954043
 0.8278221080 -0.4645892808 -0.3144318014
 0.2187285557  0.8028302234 -0.5546363234
 0.4042894756 -0.4525240881 -0.7948408455
 0.8987000724  0.1653921218 -0.4061817646
 0.2166970016  0.5668072335 -0.7948408455
-0.7635183907  0.3307842435 -0.5546363234
-0.8278221080  0.4645892808  0.3144318014
 0.2756820411 -0.1849140136  0.9432954043
 0.7614868366 -0.5668072335  0.3144318014
-0.6906088722 -0.5983943180 -0.4061817646
-0.0331676357 -0.9487004534  0.3144318014
-0.0278489580 -0.3307842435  0.9432954043
 0.1544248384  0.9366352607  0.3144318014
-0.5779574707  0.1849140136 -0.7948408455
 0.1007584765 -0.5983943180 -0.7948408455
-0.1544248384 -0.9366352607 -0.3144318014
-0.7614868366  0.5668072335 -0.3144318014
 0.0278489580  0.3307842435 -0.9432954043
 0.7549125894  0.4645892808 -0.4628863603
 0.5779574707 -0.1849140136  0.7948408455
-0.2166970016 -0.5668072335  0.7948408455
 0.2691077939 -0.9487004534  0.1659772426
 0.7635183907 -0.3307842435  0.5546363234
-0.2756820411  0.1849140136 -0.9432954043
 0.1437874830 -0.2991971590 -0.9432954043
-0.1007584765  0.5983943180  0.7948408455
-0.9007316265 -0.4014151117  0.1659772426
-0.2187285557 -0.8028302234  0.5546363234
 0.8708511144 -0.1653921218 -0.4628863603
-0.4149268310 -0.7833083316 -0.4628863603
-0.4042894756  0.4525240881  0.7948408455
 0.8761697921  0.4525240881  0.1659772426
 0.5726387930 -0.8028302234  0.1659772426
-0.8343963552 -0.2991971590 -0.4628863603
 0.6906088722  0.5983943180  0.4061817646
 0.6820030709 -0.4014151117 -0.6113409191
-0.8987000724 -0.1653921218  0.4061817646
-0.1126514014 -0.7833083316 -0.6113409191
 0.0086058013  0.9998094297  0.0175226837
-0.7913673487  0.0000000000 -0.6113409191
 0.4944105968  0.6179162098 -0.6113409191
-0.7860486710  0.6179162098  0.0175226837
-0.0000000000  0.0000000000 -1.0000000000
 0.3248577762  0.2814806691  0.6614584599
-0.1694360713  0.3525674843  0.6614584599
-0.4227424795 -0.0777993435  0.6614584599
 0.3248577762 -0.6759734692  0.6614584599
 0.7818964037 -0.0777993435  0.0698320276
 0.6270398312  0.3525674843  0.2702904483
 0.5422372365  0.8355491589 -0.0885233438
-0.3167615539  0.6591266154  0.2958132161
-0.9911796417  0.0986232000 -0.0885233438
-0.6670382619 -0.2693375914  0.2702904483
-0.4277462201 -0.6591266154  0.0698320276
 0.4277462201  0.6591266154 -0.0698320276
-0.4015462944  0.8355491589  0.3749909018
 0.5358941893  0.0986232000 -0.8385051474
 0.3167615539 -0.6591266154 -0.2958132161
 0.6216868196 -0.2693375914 -0.3626326897
-0.2562654803  0.5332446333 -0.5217944046
-0.5536596562  0.5190272703 -0.1208775632
 0.5569679993 -0.1346687957  0.5120455748
-0.2428162464 -0.5190272703  0.5120455748
-0.0593658087  0.7565738714 -0.1208775632
-0.1780974260 -0.6536960660 -0.3626326897
-0.7818964037  0.0777993435 -0.0698320276
-0.4118095603 -0.3568220898 -0.8385051474
 0.2428162464  0.5190272703 -0.5120455748
 0.0647188203 -0.1346687957  0.7538007012
 0.5536596562 -0.5190272703  0.1208775632
 0.4227424795  0.0777993435 -0.6614584599
-0.0647188203  0.1346687957 -0.7538007012
-0.5358941893 -0.0986232000  0.8385051474
 0.2562654803 -0.5332446333  0.5217944046
 0.4015462944 -0.8355491589 -0.3749909018
-0.3248577762 -0.2814806691 -0.6614584599
 0.4118095603  0.3568220898  0.8385051474
 0.0593658087 -0.7565738714  0.1208775632
-0.5569679993  0.1346687957 -0.5120455748
 0.9911796417 -0.0986232000  0.0885233438
-0.5422372365 -0.8355491589  0.0885233438
 0.1780974260  0.6536960660  0.3626326897
-0.6270398312 -0.3525674843 -0.2702904483
 0.6670382619  0.2693375914 -0.2702904483
-0.6216868196  0.2693375914  0.3626326897
 0.1694360713 -0.3525674843 -0.6614584599
-0.3248577762  0.6759734692 -0.6614584599
10 0 2 9 24 42 51 36 16 5 1 3
3 0 3 2 
10 0 4 14 16 37 53 47 28 10 3 3
5 0 1 7 12 4 
10 1 6 17 39 48 45 25 9 20 7 3
3 1 5 6 
5 2 8 21 20 9 
10 2 3 11 29 47 58 55 42 23 8 3
5 3 10 26 30 11 
3 4 13 14 
10 4 12 26 10 27 46 43 44 32 13 3
10 5 15 35 51 55 57 48 29 18 6 3
5 5 16 14 33 15 
5 6 18 40 31 17 
10 7 19 32 49 52 54 38 17 31 12 3
3 7 20 19 
10 8 22 34 15 33 40 18 11 30 21 3
3 8 23 22 
3 9 25 24 
3 10 28 27 
3 11 18 29 
3 12 31 26 
10 13 22 23 43 56 58 53 50 33 14 3
5 13 32 19 34 22 
3 15 34 35 
3 16 36 37 
3 17 38 39 
10 19 20 21 41 45 57 59 52 35 34 3
3 21 30 41 
5 23 42 24 44 43 
10 24 25 27 28 39 38 37 36 49 44 3
5 25 45 41 46 27 
10 26 31 40 50 54 59 56 46 41 30 3
5 28 47 29 48 39 
3 32 44 49 
3 33 50 40 
5 35 52 49 36 51 
5 37 38 54 50 53 
3 42 55 51 
3 43 46 56 
3 45 48 57 
3 47 53 58 
3 52 59 54 
5 55 58 56 59 57 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 7 8 2 1 
4 2 9 10 3 
4 5 11 12 0 
4 4 13 11 5 
4 3 14 15 4 
4 6 16 17 7 
4 0 18 4 6 
4 8 10 19 2 
4 7 20 16 8 
4 10 21 14 3 
4 9 22 23 10 
4 2 12 22 9 
4 11 24 16 12 
4 2 25 0 12 
4 4 26 14 13 
4 13 16 20 11 
4 14 23 27 15 
4 27 6 4 15 
4 27 28 16 6 
4 16 23 22 17 
4 22 29 7 17 
4 0 29 30 18 
4 30 31 4 18 
4 8 32 21 10 
4 10 31 30 19 
4 30 33 2 19 
4 7 33 11 20 
4 28 32 8 16 
4 32 13 14 21 
4 14 34 10 23 
4 16 35 22 12 
4 24 27 23 16 
4 11 36 27 24 
4 25 30 36 0 
4 2 37 30 25 
4 26 30 37 14 
4 4 33 30 26 
4 32 35 16 13 
4 27 31 32 28 
4 0 38 7 29 
4 22 39 10 29 
4 34 30 29 10 
4 27 40 4 31 
4 39 32 31 10 
4 7 41 2 33 
4 40 11 33 4 
4 14 36 30 34 
4 32 37 22 35 
4 11 38 0 36 
4 14 42 27 36 
4 41 22 37 2 
4 32 42 14 37 
4 11 43 7 38 
4 22 43 32 39 
4 27 43 11 40 
4 7 41 22 43 
4 42 27 43 32 
small ditrigonal dodecicosidodecahedron
small ditrigonal dodecacronic hexecontahedron
5/3 3|5
(10.5/3.10.3)
icosahedral group
A5
12{10}+20{3}+12{5/3}
47 60 120 44 60 4 0 0 -16 3 4 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.5558508647  0.0000000000  0.8312820317
-0.5423346067  0.1218333214  0.8312820317
-0.3547421326  0.4279348118  0.8312820317
 0.2523198656 -0.4952826155  0.8312820317
 0.9129018498  0.1218333214  0.3895726561
 0.7569595968  0.4279348118  0.4938460950
-0.0195609124  0.3526376782  0.9355554706
-0.8323493477 -0.2516159727  0.4938460950
-0.8639995688  0.3189637764  0.3895726561
-0.6764070948  0.6250652668  0.3895726561
-0.1536334005  0.8558696236  0.4938460950
-0.3230919115 -0.1426449373  0.9355554706
-0.0376948755 -0.8687319096  0.4938460950
 0.3058398516 -0.8687319096  0.3895726561
 0.5362899523  0.3526376782  0.7668375023
 0.9664218358 -0.2516159727 -0.0521367195
 0.9347716147  0.3189637764 -0.1564101584
 0.7788293617  0.6250652668 -0.0521367195
 0.4022174642  0.8558696236  0.3251281267
 0.7886098179 -0.1426449373  0.5981195340
 0.1815478197  0.7805724901  0.5981195340
-0.5800294821 -0.7468985882  0.3251281267
-0.7788293617 -0.6250652668  0.0521367195
-0.8421298039  0.5160942314 -0.1564101584
-0.6628908367  0.7468985882  0.0521367195
-0.9664218358  0.2516159727  0.0521367195
 0.2034175846  0.9777029450  0.0521367195
-0.6131066526 -0.5160942314  0.5981195340
-0.0707720459 -0.6379275528  0.7668375023
 0.4850788188 -0.6379275528  0.5981195340
-0.2034175846 -0.9777029450 -0.0521367195
 0.1401171424 -0.9777029450 -0.1564101584
 0.6628908367 -0.7468985882 -0.0521367195
 0.6764070948 -0.6250652668 -0.3895726561
 0.6131066526  0.5160942314 -0.5981195340
 0.5800294821  0.7468985882 -0.3251281267
 0.8323493477  0.2516159727 -0.4938460950
-0.1401171424  0.9777029450  0.1564101584
 0.8421298039 -0.5160942314  0.1564101584
-0.9347716147 -0.3189637764  0.1564101584
-0.4022174642 -0.8558696236 -0.3251281267
-0.7569595968 -0.4279348118 -0.4938460950
-0.7886098179  0.1426449373 -0.5981195340
-0.4850788188  0.6379275528 -0.5981195340
-0.3058398516  0.8687319096 -0.3895726561
-0.9129018498 -0.1218333214 -0.3895726561
 0.0376948755  0.8687319096 -0.4938460950
-0.1815478197 -0.7805724901 -0.5981195340
 0.1536334005 -0.8558696236 -0.4938460950
 0.8639995688 -0.3189637764 -0.3895726561
 0.3547421326 -0.4279348118 -0.8312820317
 0.3230919115  0.1426449373 -0.9355554706
 0.0707720459  0.6379275528 -0.7668375023
 0.5423346067 -0.1218333214 -0.8312820317
-0.5558508647  0.0000000000 -0.8312820317
-0.5362899523 -0.3526376782 -0.7668375023
-0.2523198656  0.4952826155 -0.8312820317
 0.0195609124 -0.3526376782 -0.9355554706
-0.0000000000  0.0000000000 -1.0000000000
 0.1036376133  0.9341723590  0.3414399638
-0.0933664669  0.0572190828  0.3414399638
-0.7853356508 -0.5163977795  0.3414399638
 0.1036376133 -0.0635136937  0.3414399638
 0.8426251145 -0.5163977795 -0.1526965938
 0.2674035654  0.0572190828  0.2319350754
-0.2870826778  0.0242600722  0.2198885583
 0.1963339127 -0.7369259589  0.6468331514
 0.7457496051  0.1595756897  0.6468331514
-0.1519332973  0.2447882516  0.2198885583
 0.0703994852 -0.2642396690  0.2319350754
 0.3608719169  0.0242600722  0.0232142528
 0.2485246653  0.2447882516  0.0983371527
-0.2603854803  0.1595756897  0.9522263391
 0.0895451227  0.1905410810  0.2950114582
-0.8426251145  0.5163977795  0.1526965938
-0.7457496051 -0.1595756897 -0.6468331514
-0.2815979407 -0.1851648415  0.1224301871
-0.3021402336  0.1851648415  0.0547524442
-0.1963339127  0.7369259589 -0.6468331514
 0.0371613570  0.3349663450  0.1224301871
-0.1291311684 -0.1662810088  0.2950114582
-0.1053010062 -0.3325620175  0.0983371527
 0.1421956258 -0.3325620175  0.0232142528
 0.7853356508  0.5163977795 -0.3414399638
 0.3021402336 -0.1851648415 -0.0547524442
 0.2603854803 -0.1595756897 -0.9522263391
 0.2815979407  0.1851648415 -0.1224301871
 0.2713267942 -0.1662810088  0.1734600527
-0.2485246653 -0.2447882516 -0.0983371527
-0.2713267942  0.1662810088 -0.1734600527
-0.1421956258  0.3325620175 -0.0232142528
-0.3608719169 -0.0242600722 -0.0232142528
 0.1053010062  0.3325620175 -0.0983371527
-0.1036376133 -0.9341723590 -0.3414399638
-0.0371613570 -0.3349663450 -0.1224301871
 0.1519332973 -0.2447882516 -0.2198885583
 0.1291311684  0.1662810088 -0.2950114582
 0.2870826778 -0.0242600722 -0.2198885583
-0.2674035654 -0.0572190828 -0.2319350754
-0.0703994852  0.2642396690 -0.2319350754
-0.0895451227 -0.1905410810 -0.2950114582
 0.0933664669 -0.0572190828 -0.3414399638
-0.1036376133  0.0635136937 -0.3414399638
10 0 2 9 24 44 53 35 17 5 1 
5 0 3 12 7 2 3
10 0 4 14 32 48 56 43 24 10 3 
3 0 1 4 
10 1 6 18 35 52 58 48 31 13 4 
5 1 5 15 20 6 3
3 2 8 9 
10 2 7 15 5 16 34 49 41 23 8 
10 3 11 27 36 37 50 33 14 29 12 
3 3 10 11 
5 4 13 30 29 14 3
3 5 17 16 
3 6 19 18 
10 6 20 30 13 22 40 26 25 38 19 
3 7 21 15 
10 7 12 28 23 42 55 57 47 27 21 
10 8 22 31 49 51 52 53 45 25 9 
5 8 23 28 40 22 3
5 9 25 26 10 24 3
10 10 26 46 56 58 54 37 18 19 11 
5 11 19 38 21 27 3
3 12 29 28 
3 13 31 22 
3 14 33 32 
10 15 21 38 45 57 59 51 34 39 20 
5 16 33 50 39 34 3
10 16 17 36 47 44 43 42 41 32 33 
5 17 35 18 37 36 3
3 20 39 30 
3 23 41 42 
3 24 43 44 
3 25 45 38 
3 26 40 46 
3 27 47 36 
10 28 29 30 39 50 54 59 55 46 40 
5 31 48 32 41 49 3
3 34 51 49 
3 35 53 52 
3 37 54 50 
5 42 43 56 46 55 3
5 44 47 57 45 53 3
3 48 58 56 
5 51 59 54 58 52 3
3 55 59 57 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 1 8 9 2 
4 2 10 4 3 
4 5 7 11 0 
4 4 12 13 5 
4 7 14 15 1 
4 6 16 17 7 
4 0 18 16 6 
4 9 19 18 2 
4 8 20 19 9 
4 15 21 8 1 
4 10 13 22 4 
4 2 23 8 10 
4 5 24 14 7 
4 7 25 26 11 
4 26 27 0 11 
4 4 27 19 12 
4 20 13 12 19 
4 13 28 24 5 
4 24 20 15 14 
4 16 22 13 17 
4 17 15 29 7 
4 0 30 2 18 
4 18 13 31 16 
4 19 32 13 18 
4 8 33 15 20 
4 17 34 21 15 
4 34 10 8 21 
4 34 28 13 10 
4 16 35 4 22 
4 2 35 26 23 
4 25 8 23 26 
4 7 36 24 25 
4 4 37 0 27 
4 26 33 8 27 
4 8 38 19 27 
4 24 31 13 20 
4 34 25 24 28 
4 32 34 17 13 
4 29 26 35 7 
4 15 39 26 29 
4 30 26 39 2 
4 0 40 26 30 
4 24 40 16 31 
4 19 39 34 32 
4 40 15 33 26 
4 2 41 4 35 
4 16 36 7 35 
4 34 38 8 25 
4 16 42 24 36 
4 4 42 16 37 
4 37 0 40 16 
4 34 42 19 38 
4 15 43 34 39 
4 19 41 2 39 
4 24 43 15 40 
4 41 4 42 19 
4 42 24 43 34 
icosidodecadodecahedron
medial icosacronic hexecontahedron
5/3 5|3
(6.5/3.6.5)
icosahedral group
A5
20{6}+12{5}+12{5/3}
48 60 120 44 60 4 0 0 -16 3 4 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.6998542122  0.0000000000  0.7142857143
-0.5248906592  0.4629100499  0.7142857143
-0.1166423687  0.6900655593  0.7142857143
-0.3689536881 -0.5947008445  0.7142857143
 0.8748177653  0.4629100499  0.1428571429
 0.5832118435  0.6900655593  0.4285714286
 0.7634342145 -0.5947008445  0.2519902889
 0.2077578990  0.4039714148  0.8908668539
-0.8938443472 -0.1317907946  0.4285714286
-0.3499271061  0.9258200998  0.1428571429
-0.6022384255  0.7854302742  0.1428571429
-0.4528017108  0.0364260797  0.8908668539
 0.1028746047 -0.9622461795  0.2519902889
-0.8545497448 -0.4993361296  0.1428571429
 0.4750784209  0.4039714148  0.7817337079
 0.9383977675 -0.1317907946 -0.3194382825
 0.3499271061  0.9258200998 -0.1428571429
 0.5301494771  0.7854302742 -0.3194382825
 0.9469067137  0.0364260797  0.3194382825
 0.7103718480 -0.4993361296 -0.4960194221
 0.5714527692 -0.2496680648  0.7817337079
 0.3827214521  0.8668814647  0.3194382825
-0.9469067137 -0.0364260797 -0.3194382825
-0.5301494771 -0.7854302742  0.3194382825
-0.6107473716  0.6172133998 -0.4960194221
-0.2024990811  0.8443689093 -0.4960194221
-0.9383977675  0.1317907946  0.3194382825
-0.9711921135  0.1907294297 -0.1428571429
-0.0891068406 -0.6172133998  0.7817337079
 0.0498122382 -0.8668814647 -0.4960194221
-0.3827214521 -0.8668814647 -0.3194382825
-0.5937294793 -0.1907294297  0.7817337079
 0.1389190789 -0.2496680648  0.9583148475
-0.0498122382  0.8668814647  0.4960194221
 0.4528017108 -0.0364260797 -0.8908668539
 0.6022384255 -0.7854302742 -0.1428571429
 0.0891068406  0.6172133998 -0.7817337079
 0.8938443472  0.1317907946 -0.4285714286
 0.5937294793  0.1907294297 -0.7817337079
 0.6107473716 -0.6172133998  0.4960194221
 0.9711921135 -0.1907294297  0.1428571429
 0.2024990811 -0.8443689093  0.4960194221
-0.1028746047  0.9622461795 -0.2519902889
 0.8545497448  0.4993361296 -0.1428571429
-0.4750784209 -0.4039714148 -0.7817337079
-0.5832118435 -0.6900655593 -0.4285714286
-0.1389190789  0.2496680648 -0.9583148475
-0.5714527692  0.2496680648 -0.7817337079
-0.7634342145  0.5947008445 -0.2519902889
-0.8748177653 -0.4629100499 -0.1428571429
-0.7103718480  0.4993361296  0.4960194221
-0.3499271061 -0.9258200998  0.1428571429
-0.2077578990 -0.4039714148 -0.8908668539
 0.3499271061 -0.9258200998 -0.1428571429
 0.1166423687 -0.6900655593 -0.7142857143
 0.3689536881  0.5947008445 -0.7142857143
 0.5248906592 -0.4629100499 -0.7142857143
-0.6998542122  0.0000000000 -0.7142857143
-0.0000000000  0.0000000000 -1.0000000000
 0.2672612419  0.7071067812  0.6546536707
-0.1378524272  0.2477510578  0.6546536707
-0.7417602291  0.1456720081  0.6546536707
 0.2672612419 -0.4803270912  0.6546536707
 0.9879908641  0.1456720081 -0.0515142560
 0.5566281484  0.2477510578  0.3711331629
-0.7425563482  0.4102483131  0.1049785976
-0.2462306350 -0.2913440163  0.9243858169
 0.3773789295  0.0556417559  0.9243858169
 0.0428573330  0.8472643375  0.1049785976
-0.5039732067 -0.3423835411  0.3711331629
-0.6446401714 -0.7627485371 -0.0515142560
 0.8228143327 -0.2913440163  0.4879500365
 0.6038671053  0.4102483131 -0.4446964755
 0.4244047962 -0.7627485371 -0.4879500365
 0.6197199693 -0.3423835411 -0.0876126552
 0.6669589261  0.2968584681  0.4446964755
-0.4244047962  0.7627485371  0.4879500365
 0.0357677167  0.7071067812  0.0876126552
 0.1862071383  0.8527787893 -0.4879500365
-0.8228143327  0.2913440163 -0.4879500365
-0.6197199693  0.3423835411  0.0876126552
-0.6038671053 -0.4102483131  0.4446964755
-0.0357677167 -0.7071067812 -0.0876126552
-0.6669589261 -0.2968584681 -0.4446964755
-0.1862071383 -0.8527787893  0.4879500365
 0.6446401714  0.7627485371  0.0515142560
-0.1651765314  0.2968584681  0.7844143535
-0.4744989872  0.8527787893 -0.2182178902
 0.5039732067  0.3423835411 -0.3711331629
 0.2462306350  0.2913440163 -0.9243858169
 0.7425563482 -0.4102483131 -0.1049785976
 0.4744989872 -0.8527787893  0.2182178902
 0.1651765314 -0.2968584681 -0.7844143535
 0.2230499127 -0.4008696323  0.5463584732
-0.3773789295 -0.0556417559 -0.9243858169
-0.5566281484 -0.2477510578 -0.3711331629
-0.9879908641 -0.1456720081  0.0515142560
-0.0428573330 -0.8472643375 -0.1049785976
-0.2230499127  0.4008696323 -0.5463584732
 0.1378524272 -0.2477510578 -0.6546536707
 0.7417602291 -0.1456720081 -0.6546536707
-0.2672612419  0.4803270912 -0.6546536707
-0.2672612419 -0.7071067812 -0.6546536707
6 0 2 10 17 5 1 
5 0 3 12 8 2 3
6 0 4 14 28 11 3 
5 0 1 7 13 4 
6 1 6 18 39 20 7 
5 1 5 15 19 6 3
5 2 9 23 25 10 
6 2 8 21 42 24 9 
6 3 6 19 40 29 12 
5 3 11 26 18 6 
5 4 9 24 32 14 3
6 4 13 30 45 23 9 
6 5 16 36 42 33 15 
5 5 17 37 35 16 
6 7 16 35 53 31 13 
5 7 20 41 36 16 3
5 8 22 44 41 21 
6 8 12 27 49 43 22 
5 10 22 43 34 17 3
6 10 25 47 39 44 22 
6 11 27 50 45 47 26 
5 11 28 51 49 27 3
5 12 29 52 50 27 
5 13 31 54 52 30 3
5 14 31 53 48 28 
6 14 32 33 40 54 31 
6 15 34 43 56 38 19 
5 15 33 32 51 34 
6 17 34 51 28 48 37 
5 18 38 56 44 39 3
6 18 26 48 53 57 38 
5 19 38 57 54 40 
6 20 30 52 29 21 41 
5 20 39 47 45 30 
5 21 29 40 33 42 3
6 23 46 55 35 37 25 
5 23 45 50 58 46 3
6 24 46 58 49 51 32 
5 24 42 36 55 46 
5 25 37 48 26 47 3
5 35 55 59 57 53 3
6 36 41 44 56 59 55 
5 43 49 58 59 56 
6 50 52 54 57 59 58 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 1 8 9 2 
4 2 10 11 3 
4 5 12 13 0 
4 4 9 8 5 
4 3 14 15 4 
4 7 16 17 1 
4 6 11 10 7 
4 0 18 19 6 
4 9 20 21 2 
4 17 22 8 1 
4 11 23 14 3 
4 2 24 25 10 
4 5 26 27 12 
4 12 15 14 13 
4 13 28 18 0 
4 4 29 30 9 
4 8 31 26 5 
4 15 32 33 4 
4 7 34 32 16 
4 16 19 18 17 
4 6 35 36 11 
4 10 37 38 7 
4 19 39 35 6 
4 30 39 20 9 
4 20 22 17 21 
4 21 28 24 2 
4 22 32 34 8 
4 11 33 32 23 
4 23 25 24 14 
4 25 27 37 10 
4 25 34 12 27 
4 26 18 28 27 
4 14 40 35 13 
4 12 38 41 15 
4 39 28 13 35 
4 29 26 31 30 
4 33 19 29 4 
4 25 31 8 34 
4 41 16 32 15 
4 7 34 12 38 
4 26 42 17 18 
4 41 29 19 16 
4 36 20 33 11 
4 35 38 37 36 
4 19 39 20 33 
4 30 24 28 39 
4 42 37 21 17 
4 36 43 22 20 
4 21 28 27 37 
4 43 23 32 22 
4 30 40 14 24 
4 43 31 25 23 
4 40 41 38 35 
4 41 42 26 29 
4 43 40 30 31 
4 42 43 36 37 
4 40 41 42 43 
icositruncated dodecadodecahedron
tridyakisicosahedron
5/3 3 5|
(10/3.6.10)
icosahedral group
A5
12{10}+20{6}+12{10/3}
49 120 180 44 120 4 0 0 -16 3 3 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.4841229183  0.0000000000  0.8750000000
 0.1273008285  0.4670861795  0.8750000000
-0.4500494407 -0.1784110449  0.8750000000
 0.3122193286  0.4670861795  0.8272542486
 0.8174008141 -0.1784110449  0.5477457514
-0.1954477837  0.7557613141  0.6250000000
 0.5327475080  0.1784110449  0.8272542486
-0.6941218141 -0.4670861795  0.5477457514
-0.7727980529  0.1102640897  0.6250000000
 0.4735936346  0.7557613141  0.4522542486
-0.0656613285  0.1784110449  0.9817627458
 0.8725328589 -0.4670861795  0.1432372542
 0.9787751202  0.1102640897  0.1727457514
-0.3122193286  0.9341723590  0.1727457514
-0.6454972244  0.5773502692  0.5000000000
 0.1548668509 -0.1102640897  0.9817627458
 0.8660254038 -0.0000000000  0.5000000000
-0.8660254038  0.0000000000  0.5000000000
-0.6389897692 -0.7557613141  0.1432372542
-0.8174008141 -0.3568220898  0.4522542486
 0.3568220898  0.9341723590  0.0000000000
 0.8068715305  0.5773502692  0.1250000000
 0.3397853510 -0.1102640897  0.9340169944
-0.5157107692 -0.0000000000  0.8567627458
 0.9998336874  0.0000000000  0.0182372542
 0.6284604856 -0.7557613141 -0.1840169944
 0.9341723590 -0.3568220898  0.0000000000
-0.6900999856  0.6454972244  0.3272542486
-0.1784110449  0.9341723590 -0.3090169944
-0.4841229183  0.8660254038  0.1250000000
 0.1102640897 -0.5773502692  0.8090169944
-0.0170367388  0.3568220898  0.9340169944
 0.8214226426 -0.4670861795  0.3272542486
-0.9827969487  0.1784110449  0.0477457514
-0.3057118734 -0.9341723590 -0.1840169944
-0.7557613141 -0.5773502692 -0.3090169944
-0.4670861795 -0.3568220898  0.8090169944
-0.7622687692 -0.6454972244  0.0477457514
 0.7622687692  0.6454972244 -0.0477457514
 0.0065074552  0.9341723590 -0.3567627458
 0.4841229183  0.8660254038 -0.1250000000
 0.2951825898 -0.5773502692  0.7612712430
 0.4670861795  0.3568220898  0.8090169944
-0.5603135304 -0.4670861795  0.6840169944
 0.8830621426  0.1784110449 -0.4340169944
 0.1784110449 -0.9341723590 -0.3090169944
 0.5116889407 -0.5773502692 -0.6362712430
 0.8003640753 -0.3568220898  0.4817627458
 0.6900999856 -0.6454972244 -0.3272542486
-0.9341723590  0.3568220898  0.0000000000
-0.3397853510  0.6454972244  0.6840169944
 0.1548668509  0.7557613141 -0.6362712430
-0.4224834183  0.6454972244 -0.6362712430
-0.1338082837  0.8660254038  0.4817627458
-0.3503146346  0.8660254038 -0.3567627458
-0.1338082837 -0.8660254038  0.4817627458
 0.4435419855 -0.7557613141  0.4817627458
 0.9827969487 -0.1784110449 -0.0477457514
-0.8214226426  0.4670861795 -0.3272542486
-0.9276649038 -0.1102640897 -0.3567627458
-0.6284604856 -0.6454972244 -0.4340169944
-0.3503146346 -0.8660254038 -0.3567627458
-0.0616395000 -0.6454972244  0.7612712430
-0.6389897692  0.1102640897  0.7612712430
-0.3568220898 -0.9341723590 -0.0000000000
 0.8174008141  0.3568220898 -0.4522542486
 0.6284604856  0.6454972244  0.4340169944
-0.4435419855  0.7557613141 -0.4817627458
 0.0616395000  0.6454972244 -0.7612712430
 0.3503146346  0.8660254038  0.3567627458
 0.1338082837  0.8660254038 -0.4817627458
 0.3503146346 -0.8660254038  0.3567627458
-0.1548668509 -0.7557613141  0.6362712430
-0.8830621426 -0.1784110449  0.4340169944
 0.5603135304  0.4670861795 -0.6840169944
 0.6389897692 -0.1102640897 -0.7612712430
 0.3397853510 -0.6454972244 -0.6840169944
 0.1338082837 -0.8660254038 -0.4817627458
 0.4224834183 -0.6454972244  0.6362712430
 0.9276649038  0.1102640897  0.3567627458
 0.3122193286 -0.9341723590 -0.1727457514
-0.9787751202 -0.1102640897 -0.1727457514
-0.8003640753  0.3568220898 -0.4817627458
-0.1784110449  0.9341723590  0.3090169944
-0.2951825898  0.5773502692 -0.7612712430
-0.5116889407  0.5773502692  0.6362712430
-0.4841229183 -0.8660254038  0.1250000000
-0.0065074552 -0.9341723590  0.3567627458
 0.8660254038  0.0000000000 -0.5000000000
-0.8660254038 -0.0000000000 -0.5000000000
-0.4670861795 -0.3568220898 -0.8090169944
-0.4735936346 -0.7557613141 -0.4522542486
 0.7727980529 -0.1102640897 -0.6250000000
 0.4670861795  0.3568220898 -0.8090169944
 0.3057118734  0.9341723590  0.1840169944
-0.1102640897  0.5773502692 -0.8090169944
 0.7557613141  0.5773502692  0.3090169944
 0.4841229183 -0.8660254038 -0.1250000000
 0.1784110449 -0.9341723590  0.3090169944
-0.9998336874  0.0000000000 -0.0182372542
 0.5157107692 -0.0000000000 -0.8567627458
 0.0170367388 -0.3568220898 -0.9340169944
 0.1954477837 -0.7557613141 -0.6250000000
-0.8174008141  0.1784110449 -0.5477457514
-0.8068715305 -0.5773502692 -0.1250000000
-0.6284604856  0.7557613141  0.1840169944
-0.3397853510  0.1102640897 -0.9340169944
 0.6941218141  0.4670861795 -0.5477457514
-0.5327475080 -0.1784110449 -0.8272542486
-0.3122193286 -0.4670861795 -0.8272542486
 0.4500494407  0.1784110449 -0.8750000000
 0.6454972244 -0.5773502692 -0.5000000000
 0.6389897692  0.7557613141 -0.1432372542
-0.1548668509  0.1102640897 -0.9817627458
-0.8725328589  0.4670861795 -0.1432372542
 0.0656613285 -0.1784110449 -0.9817627458
-0.1273008285 -0.4670861795 -0.8750000000
-0.4841229183 -0.0000000000 -0.8750000000
-0.0000000000 -0.0000000000 -1.0000000000
 0.1517654996  0.1159385250  0.5877852523
-0.2529424993  0.2262386491  0.5877852523
 0.1517654996 -0.7946544723  0.5877852523
 0.5058849985  0.2262386491  0.3918568349
 0.5849197102  0.7946544723  0.1624598481
-0.4331542107 -0.1159385250  0.4253254042
-0.4331542107  0.7946544723  0.4253254042
 0.5849197102 -0.1159385250  0.1624598481
-0.2677040246  0.4911234732  0.2628655561
 0.3825657108 -0.2262386491  0.5129472562
-0.6355082101 -0.2262386491  0.0748379961
-0.9464199718  0.1875924741 -0.2628655561
 0.3615002616  0.4911234732  0.1004057079
-0.0864154744 -0.2262386491  0.6340376775
 0.5923004729 -0.2262386491 -0.2421808427
 0.7008582352  0.1875924741 -0.6881909602
-0.4359734112  0.5058849985 -0.1210904213
-0.7008582352 -0.1875924741  0.6881909602
-0.3615002616 -0.4911234732 -0.1004057079
-0.3228540866 -0.5058849985  0.3170188388
 0.3228540866  0.5058849985 -0.3170188388
 0.9464199718 -0.1875924741  0.2628655561
 0.2677040246 -0.4911234732 -0.2628655561
 0.4359734112 -0.5058849985  0.1210904213
-0.0937962370  0.4911234732 -0.3632712640
 0.0000000000  0.6787159473 -0.0000000000
 0.0937962370 -0.4911234732  0.3632712640
 0.1131193245  0.5058849985  0.4381092601
 0.4331542107 -0.7946544723 -0.4253254042
-0.5849197102  0.1159385250 -0.1624598481
-0.1131193245 -0.5058849985 -0.4381092601
-0.2455617366 -0.1875924741 -0.9510565163
 0.2455617366  0.1875924741  0.9510565163
-0.5849197102 -0.7946544723 -0.1624598481
 0.4331542107  0.1159385250 -0.4253254042
 0.0864154744  0.2262386491 -0.6340376775
-0.0000000000 -0.6787159473 -0.0000000000
 0.6355082101  0.2262386491 -0.0748379961
-0.3825657108  0.2262386491 -0.5129472562
-0.5923004729  0.2262386491  0.2421808427
-0.5058849985 -0.2262386491 -0.3918568349
-0.1517654996  0.7946544723 -0.5877852523
-0.1517654996 -0.1159385250 -0.5877852523
 0.2529424993 -0.2262386491 -0.5877852523
10 0 2 7 16 32 43 23 11 4 1 3
6 0 3 9 15 6 2 
10 0 1 5 12 26 46 35 19 8 3 
6 1 4 10 22 13 5 
10 2 6 14 29 52 75 45 25 17 7 
10 3 8 18 24 44 74 64 37 20 9 3
10 4 11 24 18 34 59 68 40 21 10 
10 5 13 27 48 80 58 33 17 25 12 3
10 6 15 30 54 86 106 84 51 28 14 3
6 7 17 33 57 31 16 
6 8 19 36 60 34 18 
10 9 20 38 61 91 107 85 55 30 15 
10 10 21 39 67 95 113 97 70 41 22 3
6 11 23 42 73 44 24 
6 12 25 45 76 47 26 
10 13 22 41 71 96 114 102 77 49 27 
6 14 28 50 83 53 29 
10 16 31 56 87 105 82 50 28 51 32 
10 19 35 61 38 65 92 105 87 62 36 3
6 20 37 63 88 65 38 
6 21 40 69 94 66 39 
10 23 43 67 39 66 93 112 98 72 42 
10 26 47 78 98 112 103 81 49 77 46 3
6 27 49 81 99 79 48 
10 29 53 69 40 68 96 71 55 85 52 3
6 30 55 71 41 70 54 
10 31 57 88 63 79 99 73 42 72 56 3
6 32 51 84 95 67 43 
10 33 58 89 101 116 110 92 65 88 57 
10 34 60 83 50 82 104 115 100 90 59 3
6 35 46 77 102 91 61 
10 36 62 78 47 76 94 69 53 83 60 
10 37 64 86 54 70 97 80 48 79 63 
10 44 73 99 81 103 117 109 90 100 74 
10 45 75 101 89 108 111 93 66 94 76 3
6 52 85 107 116 101 75 
6 56 72 98 78 62 87 
6 58 80 97 113 108 89 
6 59 90 109 114 96 68 
6 64 74 100 115 106 86 
6 82 105 92 110 118 104 
10 84 106 115 104 118 119 111 108 113 95 
10 91 102 114 109 117 119 118 110 116 107 3
6 93 111 119 117 103 112 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 6 0 
3 2 7 3 
3 4 8 1 
3 0 9 4 
3 5 10 2 
3 1 11 5 
3 3 12 6 
3 6 13 0 
3 2 14 7 
3 7 15 3 
3 4 16 8 
3 8 11 1 
3 0 17 9 
3 9 7 4 
3 5 6 10 
3 10 18 2 
3 11 19 5 
3 12 20 6 
3 15 12 3 
3 13 21 0 
3 5 13 6 
3 14 4 7 
3 2 22 14 
3 7 23 15 
3 16 17 8 
3 4 24 16 
3 8 25 11 
3 17 26 9 
3 0 27 17 
3 9 28 7 
3 6 29 10 
3 18 30 2 
3 10 31 18 
3 19 32 5 
3 11 18 19 
3 12 21 20 
3 20 24 6 
3 15 25 12 
3 13 26 21 
3 21 27 0 
3 5 33 13 
3 14 34 4 
3 30 22 2 
3 22 31 14 
3 7 32 23 
3 23 22 15 
3 16 29 17 
3 27 8 17 
3 4 35 24 
3 24 31 16 
3 8 32 25 
3 25 24 11 
3 17 36 26 
3 26 28 9 
3 28 37 7 
3 6 38 29 
3 29 31 10 
3 11 30 18 
3 31 36 18 
3 19 26 32 
3 32 39 5 
3 18 28 19 
3 21 34 20 
3 12 27 21 
3 24 38 6 
3 20 31 24 
3 32 12 25 
3 15 24 25 
3 36 21 26 
3 33 26 13 
3 39 33 5 
3 34 35 4 
3 31 34 14 
3 30 15 22 
3 22 36 31 
3 26 23 32 
3 37 32 7 
3 23 33 22 
3 29 40 17 
3 16 29 31 
3 27 41 8 
3 35 11 24 
3 8 39 32 
3 17 18 36 
3 26 28 19 
3 28 34 37 
3 38 33 29 
3 11 42 30 
3 18 40 28 
3 21 43 34 
3 34 20 31 
3 12 41 27 
3 15 38 24 
3 37 12 32 
3 22 21 36 
3 33 26 23 
3 39 29 33 
3 28 35 34 
3 42 15 30 
3 33 43 22 
3 29 41 40 
3 40 17 18 
3 41 39 8 
3 35 42 11 
3 34 41 37 
3 38 42 33 
3 40 42 28 
3 43 41 34 
3 21 43 22 
3 12 41 37 
3 15 38 42 
3 39 29 41 
3 28 35 42 
3 42 43 33 
3 41 42 40 
3 43 41 42 
snub icosidodecadodecahedron
medial hexagonal hexecontahedron
|5/3 3 5
(3.5/3.3.3.3.5)
icosahedral group
A5
12{5}+80{3}+12{5/3}
50 60 180 104 60 4 0 0 -16 3 6 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.7952605037  0.0000000000  0.6062678709
 0.3001621965  0.7364386767  0.6062678709
 0.7055094406  0.3670091252  0.6062678709
-0.0735764581  0.7918495902  0.6062678709
-0.7610506656  0.2307404455  0.6062678709
-0.5009236922 -0.6176687813  0.6062678709
 0.7858348327 -0.6176687813 -0.0308040965
 0.9435414590  0.2307404455 -0.2376728044
 0.9243781868 -0.3167862469 -0.2125357417
 0.8269101315  0.5559211096 -0.0846838490
 0.0555412250  0.9755735394 -0.2125357417
-0.3193254687  0.1889119844  0.9286245243
 0.5199990010 -0.0881350076  0.8496077091
-0.1358666171  0.5096145631  0.8496077091
 0.2176453044 -0.3004779764  0.9286245243
 0.8327355166 -0.4593916847  0.3090482801
-0.3170460053  0.9181467577 -0.2376728044
-0.8371873340  0.4512278009  0.3090482801
-0.6300413753  0.7719303797 -0.0846838490
-0.7338395293 -0.6049534741  0.3090482801
-0.1585581578 -0.3354337541  0.9286245243
-0.9468108730  0.0896567415  0.3090482801
-0.7735370212 -0.5874964807 -0.2376728044
-0.0152510561 -0.9994090819 -0.0308040965
 0.2799588487 -0.5874964807 -0.7592568262
 0.0348116018 -0.9174921690 -0.3962275509
 0.5102070354 -0.2920835591 -0.8089350873
 0.3115674381  0.5713622348 -0.7592568262
 0.8637423423  0.4265251132  0.2683756583
 0.6801235098 -0.3583093162  0.6395673892
 0.3474601540 -0.9361396763  0.0539809952
 0.1222522224  0.8245736843 -0.5523881184
 0.1385433541  0.9344550281  0.3280236873
 0.6152755562  0.6750955630  0.4070405025
 0.7537879313  0.4809955435 -0.4477131243
-0.0043310515  0.4244359070 -0.9054476257
-0.7151305151  0.5758403202 -0.3962275509
-0.8732845400 -0.2677538824  0.4070405025
-0.1486782288 -0.6603643877  0.7360799276
 0.5996272266 -0.7539374610  0.2683756583
-0.1581038998  0.9824462228  0.0990079602
-0.2651930296 -0.8595294620  0.4369001728
 0.0873995822 -0.9406177617  0.3280236873
 0.8765539540 -0.0526433046 -0.4784159782
-0.5218620448  0.2707102338 -0.8089350873
-0.7977285113  0.2418606808 -0.5523881184
-0.9171154526 -0.3949497421  0.0539809952
-0.4932731016  0.4635385501  0.7360799276
-0.5860128319 -0.5802507864 -0.5655952490
-0.3294249208 -0.8312834534 -0.4477131243
-0.8249774859 -0.3008825344 -0.4784159782
-0.2157822605  0.1179027501 -0.9692971462
 0.7441167318 -0.4021954364 -0.5334127111
 0.1582993033 -0.2824850577 -0.9461202475
 0.4809752902  0.7416267119 -0.4676030266
-0.0705157735 -0.7139676727 -0.6966187538
 0.1610261654  0.0935730734 -0.9825042768
-0.8730256855  0.4832272272 -0.0657084418
-0.6757924584 -0.0661265908 -0.7341197635
 0.3247276953  0.2183102780  0.6558852870
 0.2330291401  0.2556853380  0.6558852870
 0.1873305537  0.3435327018  0.6558852870
-0.2474173141  0.3031371410  0.6558852870
-0.3741003584 -0.1147012443  0.6558852870
 0.3247276953 -0.6814443588  0.6558852870
 0.7484046915 -0.1147012443  0.1001349371
 0.7309860539 -0.0199380975  0.1229835081
 0.7549003045  0.0708892675  0.0916144386
 0.5698573801  0.3831078312  0.3343410226
 0.3505745987  0.6723073767  0.0916144386
-0.4956852875  0.7825823548  0.3766443331
 0.1484680132  0.2481846593  0.7068624953
 0.2333841167  0.1707929452  0.7068624953
 0.5205170549 -0.1164597889  0.5466187670
 0.7357021020  0.0410148862  0.2008809586
 0.4787409949  0.8779303974 -0.0067288271
-0.3639725977  0.6406744508  0.2008809586
-0.3675642883  0.5803063628  0.2792921431
-0.4341871188  0.5319685985  0.3343410226
-0.9857841031  0.0268878721 -0.1658515735
-0.4901491203 -0.2103680745  0.5466187670
-0.4381469231 -0.1343382762  0.5829610478
-0.5238282283 -0.1005230031  0.5466187670
-0.6584749455 -0.3306819467  0.2008809586
-0.3823228516 -0.6535252059  0.1001349371
 0.3114234217 -0.6535252059 -0.2433376685
 0.3675642883 -0.5803063628 -0.2792921431
 0.3945189195 -0.5416693466 -0.3663906446
 0.6639032878 -0.2012866519 -0.3193885901
 0.5233112059  0.1511903430 -0.5353315097
 0.7316875924 -0.0736863580  0.2061469163
 0.5786406224 -0.4776354422  0.1425916469
 0.4600155947 -0.5455758087 -0.2720765570
 0.5908707414  0.1811642457 -0.7861623770
 0.3224400660  0.6862449721 -0.0916144386
 0.3549996288  0.6510095616 -0.0049896105
 0.4223105883  0.6319118158 -0.0750612237
 0.2386340718  0.5576061324 -0.4641359113
-0.1968129036  0.5857219691 -0.4488735002
-0.3976122076 -0.2191307095  0.6141491902
 0.0154135158 -0.1658843935  0.7453440513
 0.2878283477 -0.4453831909  0.5496195218
 0.9857841031 -0.0268878721  0.1658515735
 0.2962650281  0.3250693188  0.6243796397
 0.0952478389  0.6424329954  0.4018714458
-0.3353210426  0.5760695154  0.3728225786
-0.5908707414 -0.1811642457  0.7861623770
 0.1636587448 -0.5673708569  0.4843543014
 0.2407945267 -0.5053097542  0.4863569987
 0.3372842356 -0.5040934076  0.4641359113
 0.4956852875 -0.7825823548 -0.3766443331
 0.7627509365 -0.0253485937  0.0293499730
-0.1563251351  0.5218003355 -0.5353315097
-0.2407945267  0.5053097542 -0.4863569987
-0.3317482574  0.4696932387 -0.5026174674
-0.5786406224  0.4776354422 -0.1425916469
-0.7565255326  0.0883804086 -0.0561336374
-0.2919260821  0.6432534269  0.2903397229
-0.1094594235  0.7502788765 -0.0916144386
-0.3052303557  0.5535180122 -0.4286551102
-0.3957787761 -0.6476079559 -0.0851825046
-0.3549996288 -0.6510095616  0.0049896105
-0.2892859071 -0.7045960843  0.0561336374
-0.2386340718 -0.5576061324  0.4641359113
 0.1805218931 -0.4844908053  0.5621151741
 0.3142555466  0.3448089608  0.8845056427
-0.4521061491 -0.0413976504  0.6141491902
-0.7372235705  0.1080865268 -0.1676653603
-0.7309860539  0.0199380975 -0.1229835081
-0.7464599260 -0.0758825700 -0.1425916469
-0.3142555466 -0.3448089608 -0.8845056427
-0.2976021258 -0.7009390227 -0.0583988402
-0.0952478389 -0.6424329954 -0.4018714458
-0.1546934172 -0.3112164741 -0.6800788309
 0.4086597528 -0.6147065316 -0.1960256353
 0.1094594235 -0.7502788765  0.0916144386
 0.3734154496  0.1818211793 -0.6409328546
 0.4381469231  0.1343382762 -0.5829610478
 0.3991336762  0.0700292964 -0.6473647886
-0.0154135158  0.1658843935 -0.7453440513
 0.6584749455  0.3306819467 -0.2008809586
 0.4396986858  0.6232979081  0.0381804502
 0.2605432005 -0.5794859313  0.4237997869
-0.4787409949 -0.8779303974  0.0067288271
 0.3026839061 -0.6083857431 -0.3486290347
-0.2397197699  0.4500906365 -0.5685471081
 0.2781047861  0.7112108017  0.0113967858
 0.4917743484  0.0510983985 -0.5820995682
-0.5205170549  0.1164597889 -0.5466187670
-0.6639032878  0.2012866519  0.3193885901
-0.7622339142 -0.0253187462 -0.0406372303
-0.3247276953  0.6814443588 -0.6558852870
-0.4518947536  0.5718966444  0.2280752574
-0.4481390643 -0.6183046056  0.0127967581
 0.4501613836  0.2319814646 -0.5716924804
-0.2814926945 -0.1755003908 -0.6879349090
-0.7310026836  0.0065664230 -0.2210993487
-0.5698573801 -0.3831078312 -0.3343410226
-0.2330291401 -0.2556853380 -0.6558852870
-0.2510608506 -0.3497687395 -0.6308115736
-0.3294271137 -0.2658915873 -0.6356668969
 0.2474173141 -0.3031371410 -0.6558852870
-0.1735013310 -0.2035127114 -0.7153829937
3 0 2 1 
5 0 3 14 13 2 3
3 0 4 3 
3 0 5 4 
3 0 6 5 
5 0 1 7 24 6 
3 1 8 7 
5 1 9 29 16 8 3
3 1 10 9 
3 1 2 10 
3 2 11 10 
5 2 12 22 37 11 
3 2 13 12 
3 3 15 14 
3 3 16 15 
3 3 8 16 
5 3 4 17 28 8 
3 4 18 17 
5 4 19 48 41 18 3
3 4 5 19 
5 5 20 49 45 19 
3 5 21 20 
5 5 6 12 38 21 3
3 6 22 12 
3 6 23 22 
3 6 24 23 
3 7 25 24 
5 7 26 53 31 25 3
3 7 27 26 
3 7 8 27 
3 8 28 27 
3 9 30 29 
3 9 31 30 
3 9 25 31 
5 9 10 32 52 25 
3 10 33 32 
5 10 11 34 55 33 3
3 11 35 34 
3 11 36 35 
3 11 37 36 
3 12 39 38 
3 12 13 39 
3 13 40 39 
5 13 34 35 53 40 
3 13 14 34 
3 14 41 34 
3 14 18 41 
5 14 15 42 47 18 
3 15 40 42 
5 15 43 30 39 40 3
3 15 16 43 
5 16 44 54 50 43 
3 16 29 44 
3 17 45 28 
5 17 36 37 32 45 3
3 17 46 36 
3 17 18 46 
3 18 47 46 
3 19 33 48 
3 19 32 33 
3 19 45 32 
3 20 24 49 
5 20 50 42 23 24 3
3 20 43 50 
3 20 21 43 
3 21 30 43 
5 21 48 33 29 30 
3 21 38 48 
3 22 51 37 
5 22 46 47 58 51 3
3 22 23 46 
5 23 26 27 36 46 
3 23 42 26 
3 24 25 49 
3 25 52 49 
3 26 40 53 
3 26 42 40 
3 27 35 36 
5 27 28 44 57 35 3
3 28 54 44 
3 28 45 54 
3 29 55 44 
3 29 33 55 
3 30 31 39 
5 31 56 51 38 39 
3 31 53 56 
3 32 37 52 
3 34 41 55 
3 35 57 53 
3 37 51 52 
3 38 58 48 
3 38 51 58 
5 41 58 59 57 55 
3 41 48 58 
3 42 50 47 
3 44 55 57 
3 45 49 54 
3 47 59 58 
3 47 50 59 
5 49 52 56 59 54 3
3 50 54 59 
3 51 56 52 
3 53 57 56 
3 56 57 59 
6 5 0 1 2 3 4 
6 5 6 7 8 9 0 
6 9 10 11 12 1 0 
6 1 13 14 15 16 2 
6 16 17 18 19 3 2 
6 19 20 21 22 4 3 
6 22 23 24 25 5 4 
6 5 26 27 28 29 6 
6 29 30 16 15 7 6 
6 7 31 32 33 34 8 
6 34 35 36 10 9 8 
6 36 37 38 39 11 10 
6 11 23 22 40 41 12 
6 41 42 43 44 1 12 
6 44 45 46 47 13 1 
6 47 48 49 50 14 13 
6 50 51 52 7 15 14 
6 16 53 54 55 56 17 
6 56 57 47 46 18 17 
6 18 58 59 60 20 19 
6 20 61 62 63 64 21 
6 64 65 66 67 22 21 
6 11 68 69 70 24 23 
6 70 71 72 62 25 24 
6 61 73 26 5 25 62 
6 73 74 34 33 27 26 
6 27 75 76 72 71 28 
6 71 77 78 30 29 28 
6 78 79 80 53 16 30 
6 52 81 82 66 31 7 
6 65 49 83 32 31 66 
6 83 84 85 27 33 32 
6 34 86 54 60 59 35 
6 58 66 82 36 35 59 
6 36 87 45 44 43 37 
6 43 88 78 77 38 37 
6 71 55 54 39 38 77 
6 86 89 68 11 39 54 
6 67 90 91 84 40 22 
6 49 42 41 40 84 83 
6 48 76 75 43 42 49 
6 87 92 93 18 46 45 
6 47 94 62 72 76 48 
6 63 51 50 49 65 64 
6 51 79 78 95 81 52 
6 80 96 20 60 54 53 
6 69 57 56 55 71 70 
6 69 97 98 94 47 57 
6 93 90 67 66 58 18 
6 96 99 74 73 61 20 
6 98 100 51 63 62 94 
6 89 101 84 91 69 68 
6 99 101 89 86 34 74 
6 85 102 88 43 75 27 
6 100 99 96 80 79 51 
6 95 92 87 36 82 81 
6 99 103 102 85 84 101 
6 103 92 95 78 88 102 
6 92 97 69 91 90 93 
6 97 98 100 99 103 92 
great ditrigonal icosidodecahedron
great triambic icosahedron
3/2|3 5
(3.5.3.5.3.5)/2
icosahedral group
A5
12{5}+20{3}
51 20 60 32 20 6 0 0 -8 2 6 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9428090416  0.0000000000  0.3333333333
 0.2357022604  0.9128709292  0.3333333333
-0.4714045208 -0.8164965809  0.3333333333
 0.6727182848 -0.6605596098  0.3333333333
-0.4714045208  0.8164965809  0.3333333333
-0.9084205452 -0.2523113194  0.3333333333
 0.4714045208 -0.8164965809 -0.3333333333
 0.0900302522 -0.6605596098  0.7453559925
 0.4714045208  0.8164965809 -0.3333333333
 0.6170765289 -0.2523113194 -0.7453559925
-0.0900302522  0.6605596098 -0.7453559925
 0.9084205452  0.2523113194 -0.3333333333
-0.6170765289  0.2523113194  0.7453559925
-0.6727182848  0.6605596098 -0.3333333333
-0.9428090416  0.0000000000 -0.3333333333
-0.5270462767 -0.4082482905 -0.7453559925
-0.2357022604 -0.9128709292 -0.3333333333
 0.5270462767  0.4082482905  0.7453559925
-0.0000000000  0.0000000000 -1.0000000000
 0.1326479105  0.1027486297  0.1875924741
-0.9091823043  0.3717480345  0.1875924741
 0.0226589682 -0.1662507751  0.1875924741
 0.7765343938  0.6015009550  0.1875924741
-0.1553068788  0.0635021454  0.1875924741
 0.1326479105 -0.9732489895  0.1875924741
 0.2286328403  0.0635021454 -0.0838939048
-0.0819809172  0.6015009550  0.7946544723
 0.1693108913 -0.1662507751  0.0838939048
 0.4799246488  0.3717480345 -0.7946544723
-0.1186438980  0.2054972593  0.0838939048
 0.5619055661 -0.2297529205  0.7946544723
 0.1186438980  0.2054972593 -0.0838939048
-0.0593219490 -0.2297529205 -0.0838939048
-0.2286328403 -0.0635021454  0.0838939048
 0.0819809172 -0.6015009550 -0.7946544723
 0.2372877960  0.0000000000  0.0838939048
-0.4799246488 -0.3717480345  0.7946544723
 0.1186438980 -0.2054972593 -0.0838939048
-0.1693108913  0.1662507751 -0.0838939048
 0.0593219490  0.2297529205  0.0838939048
-0.5619055661  0.2297529205 -0.7946544723
-0.1186438980 -0.2054972593  0.0838939048
-0.2372877960 -0.0000000000 -0.0838939048
-0.7765343938 -0.6015009550 -0.1875924741
 0.1553068788 -0.0635021454 -0.1875924741
 0.9091823043 -0.3717480345 -0.1875924741
 0.0000000000  0.0000000000  0.2516817145
-0.0226589682  0.1662507751 -0.1875924741
 0.0000000000 -0.0000000000 -0.2516817145
-0.1326479105  0.9732489895 -0.1875924741
-0.1326479105 -0.1027486297 -0.1875924741
3 0 2 1 
5 0 3 16 11 2 
3 0 4 3 
5 0 5 11 10 4 
3 0 6 5 
5 0 1 10 16 6 
3 1 9 10 
5 1 8 6 14 9 
3 1 7 8 
5 1 2 14 16 7 
3 2 13 14 
5 2 12 7 3 13 
3 2 11 12 
3 3 7 16 
3 3 15 13 
5 3 4 12 11 15 
3 4 18 12 
5 4 17 15 5 18 
3 4 10 17 
3 5 15 11 
3 5 9 18 
5 5 6 17 10 9 
3 6 8 17 
3 6 16 14 
5 7 19 14 13 8 
3 7 12 19 
5 8 18 9 19 17 
3 8 13 18 
3 9 14 19 
3 10 11 16 
5 12 18 13 15 19 
3 15 17 19 
6 5 0 1 2 3 4 
6 5 6 7 8 9 0 
6 9 10 11 12 1 0 
6 1 13 11 14 15 2 
6 15 16 17 18 3 2 
6 3 19 17 20 21 4 
6 21 22 7 23 5 4 
6 8 24 25 11 13 9 
6 22 26 27 24 8 7 
6 6 21 20 26 28 7 
6 5 29 3 18 21 6 
6 12 15 19 3 29 1 
6 25 30 16 15 12 11 
6 10 24 27 30 14 11 
6 9 23 7 28 24 10 
6 30 31 17 19 15 14 
6 1 13 9 23 5 29 
6 31 26 22 21 18 17 
6 16 17 20 26 27 30 
6 24 25 30 31 26 28 
great icosicosidodecahedron
great icosacronic hexecontahedron
3/2 5|3
(6.3/2.6.5)
icosahedral group
A5
20{6}+12{5}+20{3/2}
52 60 120 52 60 6 0 0 -8 3 4 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.7913673487  0.0000000000  0.6113409191
-0.6820030709  0.4014151117  0.6113409191
 0.1126514014  0.7833083316  0.6113409191
-0.4944105968 -0.6179162098  0.6113409191
 0.9007316265  0.4014151117 -0.1659772426
 0.4149268310  0.7833083316  0.4628863603
 0.7860486710 -0.6179162098 -0.0175226837
-0.7549125894 -0.4645892808  0.4628863603
-0.5726387930  0.8028302234 -0.1659772426
-0.2691077939  0.9487004534 -0.1659772426
 0.8343963552  0.2991971590  0.4628863603
-0.0086058013 -0.9998094297 -0.0175226837
-0.8708511144  0.1653921218  0.4628863603
-0.8761697921 -0.4525240881 -0.1659772426
 0.8278221080 -0.4645892808 -0.3144318014
 0.2187285557  0.8028302234 -0.5546363234
 0.0331676357  0.9487004534 -0.3144318014
-0.1437874830  0.2991971590  0.9432954043
 0.8987000724  0.1653921218 -0.4061817646
 0.4042894756 -0.4525240881 -0.7948408455
-0.6906088722 -0.5983943180 -0.4061817646
-0.0278489580 -0.3307842435  0.9432954043
-0.0331676357 -0.9487004534  0.3144318014
 0.1544248384  0.9366352607  0.3144318014
-0.5779574707  0.1849140136 -0.7948408455
 0.2166970016  0.5668072335 -0.7948408455
-0.8278221080  0.4645892808  0.3144318014
-0.7635183907  0.3307842435 -0.5546363234
 0.7614868366 -0.5668072335  0.3144318014
 0.2756820411 -0.1849140136  0.9432954043
 0.1007584765 -0.5983943180 -0.7948408455
-0.7614868366  0.5668072335 -0.3144318014
-0.1544248384 -0.9366352607 -0.3144318014
 0.7635183907 -0.3307842435  0.5546363234
 0.2691077939 -0.9487004534  0.1659772426
-0.2756820411  0.1849140136 -0.9432954043
 0.7549125894  0.4645892808 -0.4628863603
 0.0278489580  0.3307842435 -0.9432954043
-0.2166970016 -0.5668072335  0.7948408455
 0.5779574707 -0.1849140136  0.7948408455
-0.4042894756  0.4525240881  0.7948408455
-0.4149268310 -0.7833083316 -0.4628863603
 0.8761697921  0.4525240881  0.1659772426
 0.1437874830 -0.2991971590 -0.9432954043
-0.1007584765  0.5983943180  0.7948408455
-0.9007316265 -0.4014151117  0.1659772426
 0.8708511144 -0.1653921218 -0.4628863603
-0.2187285557 -0.8028302234  0.5546363234
-0.8343963552 -0.2991971590 -0.4628863603
 0.5726387930 -0.8028302234  0.1659772426
-0.1126514014 -0.7833083316 -0.6113409191
 0.6906088722  0.5983943180  0.4061817646
 0.6820030709 -0.4014151117 -0.6113409191
-0.8987000724 -0.1653921218  0.4061817646
-0.7860486710  0.6179162098  0.0175226837
-0.7913673487  0.0000000000 -0.6113409191
 0.4944105968  0.6179162098 -0.6113409191
 0.0086058013  0.9998094297  0.0175226837
 0.0000000000  0.0000000000 -1.0000000000
 0.2317571228  0.8506508084  0.4718917654
-0.1208775632  0.2515255344  0.4718917654
-0.8089973662  0.3504874081  0.4718917654
 0.2317571228 -0.4822469333  0.4718917654
 0.8680129287  0.3504874081 -0.3517273552
 0.4473371359  0.2515255344  0.1928281889
-0.7071184954  0.0703588793 -0.0631535304
 0.0842182165 -0.1752437040  0.9809163757
 0.3868380289  0.5960899915 -0.0631535304
-0.4758724578 -0.1921484102  0.1928281889
-0.8159632084 -0.4587939735 -0.3517273552
 0.7247791497 -0.1752437040  0.6663218655
 0.3823128290  0.0703588793 -0.5981988263
-0.2864675581  0.5960899915  0.2675226479
 0.2204861533 -0.4587939735 -0.8607519655
 0.4435182383 -0.1921484102 -0.2587061630
 0.0772523743 -0.9845250856  0.1572972551
-0.1732277900 -0.3702797828  0.3652989642
-0.0423522231  0.5397481497 -0.0862353877
 0.3159753393  0.6754071043 -0.6663218655
-0.7247791497  0.1752437040 -0.6663218655
-0.3949869091  0.3702797828 -0.0862353877
 0.3973471176 -0.0960742051  0.3652989642
 0.7204740224 -0.6754071043  0.1572972551
-0.1270566693 -0.4663539879 -0.2587061630
-0.3159753393 -0.6754071043  0.6663218655
-0.2937894852 -0.2545608169 -0.5981988263
 0.3949869091 -0.3702797828  0.0862353877
-0.7204740224  0.6754071043 -0.1572972551
 0.1732277900  0.3702797828 -0.3652989642
-0.0842182165  0.1752437040 -0.9809163757
 0.0461711207 -0.0960742051  0.5377697395
 0.2937894852  0.2545608169  0.5981988263
-0.8680129287 -0.3504874081  0.3517273552
 0.2864675581 -0.5960899915 -0.2675226479
-0.0461711207  0.0960742051 -0.5377697395
-0.3823128290 -0.0703588793  0.5981988263
-0.0772523743  0.9845250856 -0.1572972551
 0.8159632084  0.4587939735  0.3517273552
-0.3973471176  0.0960742051 -0.3652989642
 0.0423522231 -0.5397481497  0.0862353877
 0.8089973662 -0.3504874081 -0.4718917654
-0.3868380289 -0.5960899915  0.0631535304
 0.7071184954 -0.0703588793  0.0631535304
-0.2204861533  0.4587939735  0.8607519655
-0.4435182383  0.1921484102  0.2587061630
-0.4473371359 -0.2515255344 -0.1928281889
 0.4758724578  0.1921484102 -0.1928281889
 0.1270566693  0.4663539879  0.2587061630
-0.2317571228 -0.8506508084 -0.4718917654
 0.1208775632 -0.2515255344 -0.4718917654
-0.2317571228  0.4822469333 -0.4718917654
6 0 2 9 16 5 1 
3 0 3 2 2
6 0 4 14 28 10 3 
5 0 1 7 12 4 
6 1 6 17 38 20 7 
3 1 5 6 2
5 2 8 21 25 9 
6 2 3 11 29 23 8 
5 3 10 26 19 11 
3 4 13 14 2
6 4 12 31 36 32 13 
6 5 15 35 39 18 6 
5 5 16 36 31 15 
5 6 18 13 32 17 
6 7 19 26 25 21 12 
3 7 20 19 2
6 8 22 34 15 31 21 
3 8 23 22 2
3 9 24 16 2
6 9 25 44 47 43 24 
6 10 27 46 42 44 26 
3 10 28 27 2
3 11 30 29 2
6 11 19 20 33 48 30 
3 12 21 31 2
6 13 18 40 50 33 14 
5 14 33 20 38 28 
3 15 34 35 2
6 16 24 41 54 49 36 
3 17 37 38 2
6 17 32 49 51 53 37 
3 18 39 40 2
5 22 41 24 43 34 
6 22 23 42 56 55 41 
5 23 29 47 44 42 
3 25 26 44 2
5 27 45 30 48 46 
6 27 28 38 37 52 45 
6 29 30 45 58 57 47 
3 32 36 49 2
3 33 50 48 2
6 34 43 57 59 51 35 
5 35 51 49 54 39 
5 37 53 50 40 52 
6 39 54 55 58 52 40 
3 41 55 54 2
3 42 46 56 2
3 43 47 57 2
3 45 52 58 2
6 46 48 50 53 59 56 
3 51 59 53 2
5 55 56 59 57 58 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 7 8 2 1 
4 2 9 10 3 
4 5 11 12 0 
4 4 13 11 5 
4 3 14 15 4 
4 6 16 17 7 
4 0 18 19 6 
4 8 20 21 2 
4 7 22 23 8 
4 10 24 14 3 
4 9 25 13 10 
4 2 26 25 9 
4 11 27 16 12 
4 12 28 18 0 
4 4 29 30 13 
4 25 31 11 13 
4 14 8 23 15 
4 23 26 4 15 
4 6 14 24 16 
4 16 32 33 17 
4 33 34 7 17 
4 28 32 19 18 
4 19 35 14 6 
4 35 20 8 14 
4 20 36 37 21 
4 37 26 2 21 
4 34 38 22 7 
4 38 36 23 22 
4 10 12 16 24 
4 30 39 10 13 
4 23 40 25 26 
4 27 41 32 16 
4 11 42 41 27 
4 39 28 12 10 
4 29 37 43 30 
4 4 29 37 26 
4 31 44 42 11 
4 25 43 44 31 
4 28 45 33 32 
4 33 46 20 34 
4 41 47 19 32 
4 19 34 20 35 
4 38 48 37 36 
4 46 49 36 20 
4 47 38 34 19 
4 49 40 23 36 
4 30 42 28 39 
4 49 43 25 40 
4 30 50 41 42 
4 48 44 43 37 
4 49 50 30 43 
4 44 45 28 42 
4 44 51 33 45 
4 51 49 46 33 
4 41 51 38 47 
4 38 48 44 51 
4 50 41 51 49 
small icosihemidodecahedron
small icosihemidodecacron
3/2 3|5
(10.3/2.10.3)
icosahedral group
A5
6{10}+10{3}+10{3/2}
53 30 60 26 30 0 1 1 -4 3 4 120 5 1 -1
 0.0000000000  0.0000000000  1.0000000000
 0.5877852523  0.0000000000  0.8090169944
-0.5877852523  0.0000000000  0.8090169944
-0.2628655561  0.5257311121  0.8090169944
 0.2628655561 -0.5257311121  0.8090169944
 0.9510565163  0.0000000000  0.3090169944
 0.6881909602  0.5257311121  0.5000000000
-0.6881909602 -0.5257311121  0.5000000000
-0.9510565163  0.0000000000  0.3090169944
-0.4253254042  0.8506508084  0.3090169944
 0.1624598481  0.8506508084  0.5000000000
-0.1624598481 -0.8506508084  0.5000000000
 0.4253254042 -0.8506508084  0.3090169944
 0.8506508084 -0.5257311121  0.0000000000
 0.9510565163  0.0000000000 -0.3090169944
 0.5257311121  0.8506508084  0.0000000000
-0.5257311121 -0.8506508084  0.0000000000
-0.9510565163  0.0000000000 -0.3090169944
-0.8506508084  0.5257311121  0.0000000000
-0.4253254042  0.8506508084 -0.3090169944
 0.4253254042 -0.8506508084 -0.3090169944
 0.5877852523  0.0000000000 -0.8090169944
 0.6881909602  0.5257311121 -0.5000000000
 0.1624598481  0.8506508084 -0.5000000000
-0.1624598481 -0.8506508084 -0.5000000000
-0.6881909602 -0.5257311121 -0.5000000000
-0.5877852523  0.0000000000 -0.8090169944
-0.2628655561  0.5257311121 -0.8090169944
 0.2628655561 -0.5257311121 -0.8090169944
 0.0000000000  0.0000000000 -1.0000000000
 0.0000000000  1.0000000000  0.0000000000
-0.3035309991  0.1875924741  0.9341723590
-0.8944271910 -0.4472135955  0.0000000000
 0.3035309991 -0.1875924741  0.9341723590
 0.7236067977 -0.4472135955 -0.5257311121
 0.7946544723  0.1875924741  0.5773502692
-0.7946544723 -0.1875924741  0.5773502692
 0.7236067977 -0.4472135955  0.5257311121
-0.1875924741  0.7946544723  0.5773502692
 0.1875924741 -0.7946544723  0.5773502692
-0.2763932023 -0.4472135955  0.8506508084
 0.9822469464 -0.1875924741  0.0000000000
 0.4911234732  0.7946544723  0.3568220898
-0.2763932023 -0.4472135955 -0.8506508084
-0.4911234732 -0.7946544723  0.3568220898
-0.9822469464  0.1875924741  0.0000000000
-0.6070619982  0.7946544723  0.0000000000
 0.6070619982 -0.7946544723  0.0000000000
 0.7946544723  0.1875924741 -0.5773502692
 0.4911234732  0.7946544723 -0.3568220898
-0.4911234732 -0.7946544723 -0.3568220898
-0.7946544723 -0.1875924741 -0.5773502692
-0.1875924741  0.7946544723 -0.5773502692
 0.1875924741 -0.7946544723 -0.5773502692
 0.3035309991 -0.1875924741 -0.9341723590
-0.3035309991  0.1875924741 -0.9341723590
10 0 1 5 14 21 29 26 17 8 2 
3 0 2 3 2
10 0 3 9 19 27 29 28 20 12 4 
3 0 1 4 
10 1 4 11 16 25 26 27 23 15 6 
3 1 6 5 2
3 2 8 7 
10 2 7 16 24 28 21 22 15 10 3 
3 3 10 9 
3 4 12 11 2
10 5 6 10 9 18 17 25 24 20 13 
3 5 13 14 
3 6 15 10 
10 7 8 18 19 23 22 14 13 12 11 
3 7 11 16 2
3 8 17 18 2
3 9 18 19 2
3 12 20 13 
3 14 22 21 2
3 15 23 22 2
3 16 25 24 
3 17 26 25 
3 19 23 27 
3 20 28 24 2
3 21 28 29 
3 26 29 27 2
4 3 0 1 2 
4 3 4 5 0 
4 6 0 1 7 
4 8 7 1 2 
4 9 2 3 4 
4 5 10 11 0 
4 12 4 5 10 
4 6 13 14 7 
4 15 0 6 13 
4 8 10 16 2 
4 12 7 8 10 
4 9 13 14 4 
4 17 2 9 13 
4 17 10 11 13 
4 18 13 11 0 
4 19 4 12 7 
4 20 4 14 7 
4 21 0 15 10 
4 16 13 15 10 
4 22 13 16 2 
4 23 2 17 10 
4 18 7 24 0 
4 19 13 18 7 
4 22 4 19 13 
4 20 10 23 7 
4 21 4 20 10 
4 25 0 21 4 
4 25 2 22 4 
4 24 2 23 7 
4 24 0 25 2 
small dodecicosahedron
small dodecicosacron
3/2 3 5|
(10.6.10/9.6/5)
icosahedral group
A5
6{10}+10{6}+10{6/5}+6{10/9}
54 60 120 32 60 0 0 1 -28 4 4 120 5 0 2
 0.0000000000  0.0000000000  1.0000000000
 0.5558508647  0.0000000000  0.8312820317
-0.5423346067  0.1218333214  0.8312820317
 0.2523198656 -0.4952826155  0.8312820317
-0.3547421326  0.4279348118  0.8312820317
 0.9129018498  0.1218333214  0.3895726561
 0.7569595968  0.4279348118  0.4938460950
-0.8323493477 -0.2516159727  0.4938460950
-0.0195609124  0.3526376782  0.9355554706
-0.8639995688  0.3189637764  0.3895726561
 0.3058398516 -0.8687319096  0.3895726561
-0.0376948755 -0.8687319096  0.4938460950
-0.1536334005  0.8558696236  0.4938460950
-0.3230919115 -0.1426449373  0.9355554706
-0.6764070948  0.6250652668  0.3895726561
 0.9664218358 -0.2516159727 -0.0521367195
 0.5362899523  0.3526376782  0.7668375023
 0.9347716147  0.3189637764 -0.1564101584
 0.4022174642  0.8558696236  0.3251281267
 0.7886098179 -0.1426449373  0.5981195340
 0.7788293617  0.6250652668 -0.0521367195
-0.7788293617 -0.6250652668  0.0521367195
-0.5800294821 -0.7468985882  0.3251281267
 0.1815478197  0.7805724901  0.5981195340
-0.8421298039  0.5160942314 -0.1564101584
-0.6628908367  0.7468985882  0.0521367195
 0.6628908367 -0.7468985882 -0.0521367195
-0.0707720459 -0.6379275528  0.7668375023
 0.1401171424 -0.9777029450 -0.1564101584
 0.4850788188 -0.6379275528  0.5981195340
-0.2034175846 -0.9777029450 -0.0521367195
 0.2034175846  0.9777029450  0.0521367195
-0.6131066526 -0.5160942314  0.5981195340
-0.9664218358  0.2516159727  0.0521367195
 0.6764070948 -0.6250652668 -0.3895726561
 0.6131066526  0.5160942314 -0.5981195340
 0.5800294821  0.7468985882 -0.3251281267
-0.1401171424  0.9777029450  0.1564101584
 0.8421298039 -0.5160942314  0.1564101584
 0.8323493477  0.2516159727 -0.4938460950
-0.7569595968 -0.4279348118 -0.4938460950
-0.4022174642 -0.8558696236 -0.3251281267
-0.9347716147 -0.3189637764  0.1564101584
-0.7886098179  0.1426449373 -0.5981195340
-0.4850788188  0.6379275528 -0.5981195340
-0.3058398516  0.8687319096 -0.3895726561
 0.8639995688 -0.3189637764 -0.3895726561
-0.1815478197 -0.7805724901 -0.5981195340
 0.1536334005 -0.8558696236 -0.4938460950
 0.0376948755  0.8687319096 -0.4938460950
-0.9129018498 -0.1218333214 -0.3895726561
 0.3547421326 -0.4279348118 -0.8312820317
 0.3230919115  0.1426449373 -0.9355554706
 0.0707720459  0.6379275528 -0.7668375023
 0.5423346067 -0.1218333214 -0.8312820317
-0.5558508647 -0.0000000000 -0.8312820317
-0.5362899523 -0.3526376782 -0.7668375023
-0.2523198656  0.4952826155 -0.8312820317
 0.0195609124 -0.3526376782 -0.9355554706
 0.0000000000 -0.0000000000 -1.0000000000
 0.1036376133  0.9341723590  0.3414399638
-0.1494536576 -0.1924500897  0.3414399638
-0.7853356508 -0.5163977795  0.3414399638
 0.1036376133  0.2205281794  0.3414399638
 0.8426251145 -0.5163977795 -0.1526965938
 0.3140278393 -0.1924500897  0.2007589619
-0.1758443548  0.2833126966  0.2544943231
 0.1963339127 -0.7369259589  0.6468331514
-0.3322633625  0.0280780897  0.2544943231
 0.7457496051  0.1595756897  0.6468331514
 0.2876371421  0.2833126966  0.1138133213
-0.2603854803  0.1595756897  0.9522263391
 0.4176654526  0.0280780897  0.0268676806
-0.4176654526 -0.0280780897 -0.0268676806
-0.7457496051 -0.1595756897 -0.6468331514
-0.8426251145  0.5163977795  0.1526965938
 0.1199479612 -0.0735093931  0.3951753249
-0.1218731366 -0.3849001795  0.1138133213
 0.1645741816 -0.3849001795  0.0268676806
-0.1645741816  0.3849001795 -0.0268676806
-0.1963339127  0.7369259589 -0.6468331514
 0.2603854803 -0.1595756897 -0.9522263391
 0.3322633625 -0.0280780897 -0.2544943231
 0.7853356508  0.5163977795 -0.3414399638
 0.1218731366  0.3849001795 -0.1138133213
-0.2876371421 -0.2833126966 -0.1138133213
-0.3140278393  0.1924500897 -0.2007589619
 0.1758443548 -0.2833126966 -0.2544943231
-0.1036376133 -0.9341723590 -0.3414399638
 0.1494536576  0.1924500897 -0.3414399638
-0.1036376133 -0.2205281794 -0.3414399638
-0.1199479612  0.0735093931 -0.3951753249
10 0 2 9 24 44 53 35 17 5 1 
6 0 3 11 22 7 2 
10 0 4 14 24 43 56 47 28 10 3 9
6 0 1 6 18 12 4 5
10 1 3 11 30 47 58 52 35 20 6 9
6 1 5 15 26 10 3 
6 2 8 23 37 25 9 5
10 2 7 21 41 48 34 15 5 16 8 9
6 4 13 32 42 33 14 
10 4 12 31 36 39 46 26 10 27 13 
6 5 17 36 31 23 16 5
10 6 19 29 11 22 42 33 25 37 18 
6 6 20 39 46 38 19 
6 7 9 24 43 40 21 5
10 7 22 30 48 51 52 53 45 25 9 
10 8 13 32 21 40 55 57 49 31 23 
6 8 16 19 29 27 13 
6 10 28 41 21 32 27 
6 11 30 48 34 38 29 5
6 12 14 24 44 49 31 
10 12 18 20 39 54 58 56 50 33 14 9
10 15 17 36 49 44 43 40 41 28 26 
6 15 34 51 52 35 17 5
10 16 23 37 45 57 59 51 34 38 19 
6 18 37 45 53 35 20 
6 22 42 50 56 47 30 5
6 25 33 50 55 57 45 
6 26 46 54 58 47 28 
10 27 32 42 50 55 59 54 46 38 29 9
6 36 49 57 59 54 39 
6 40 41 48 51 59 55 
6 43 44 53 52 58 56 5
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 1 4 5 2 
4 2 8 9 3 
4 5 7 10 0 
4 3 11 12 4 
4 7 13 14 1 
4 6 15 16 7 
4 0 13 14 6 
4 5 9 17 2 
4 1 11 18 4 
4 9 19 20 3 
4 8 15 16 9 
4 2 19 20 8 
4 5 21 22 7 
4 16 23 10 7 
4 10 21 22 0 
4 20 24 11 3 
4 11 16 23 12 
4 12 20 24 4 
4 7 17 15 13 
4 14 25 11 1 
4 6 23 10 15 
4 0 19 2 13 
4 14 26 11 6 
4 21 27 9 5 
4 16 28 17 9 
4 17 21 27 2 
4 28 18 11 16 
4 18 14 25 4 
4 9 10 15 19 
4 8 28 17 15 
4 20 26 11 8 
4 22 23 18 7 
4 22 4 24 0 
4 9 29 21 10 
4 24 23 6 11 
4 28 12 23 18 
4 12 9 29 20 
4 15 30 21 13 
4 7 30 21 17 
4 25 28 8 11 
4 2 31 21 13 
4 0 31 21 19 
4 14 24 23 26 
4 27 28 12 9 
4 27 4 25 2 
4 30 14 18 7 
4 15 29 21 19 
4 20 25 28 26 
4 22 14 30 23 
4 14 31 4 22 
4 24 0 31 14 
4 29 28 27 20 
4 15 26 28 30 
4 20 31 2 25 
4 23 29 15 26 
4 27 4 31 20 
4 30 23 29 28 
small dodecahemidodecahedron
small dodecahemidodecacron
5/4 5|5
(10.5/4.10.5)
icosahedral group
A5
6{10}+6{5}+6{5/4}
55 30 60 18 30 0 1 1 -12 3 4 120 5 1 -1
 0.0000000000  0.0000000000  1.0000000000
 0.5877852523  0.0000000000  0.8090169944
-0.5877852523  0.0000000000  0.8090169944
 0.2628655561  0.5257311121  0.8090169944
-0.2628655561 -0.5257311121  0.8090169944
 0.9510565163  0.0000000000  0.3090169944
 0.6881909602 -0.5257311121  0.5000000000
-0.6881909602  0.5257311121  0.5000000000
-0.9510565163 -0.0000000000  0.3090169944
 0.4253254042  0.8506508084  0.3090169944
-0.1624598481  0.8506508084  0.5000000000
 0.1624598481 -0.8506508084  0.5000000000
-0.4253254042 -0.8506508084  0.3090169944
 0.8506508084  0.5257311121  0.0000000000
 0.9510565163  0.0000000000 -0.3090169944
 0.5257311121 -0.8506508084  0.0000000000
-0.5257311121  0.8506508084  0.0000000000
-0.9510565163 -0.0000000000 -0.3090169944
-0.8506508084 -0.5257311121  0.0000000000
 0.4253254042  0.8506508084 -0.3090169944
-0.4253254042 -0.8506508084 -0.3090169944
 0.5877852523  0.0000000000 -0.8090169944
 0.6881909602 -0.5257311121 -0.5000000000
 0.1624598481 -0.8506508084 -0.5000000000
-0.6881909602  0.5257311121 -0.5000000000
-0.1624598481  0.8506508084 -0.5000000000
-0.5877852523 -0.0000000000 -0.8090169944
 0.2628655561  0.5257311121 -0.8090169944
-0.2628655561 -0.5257311121 -0.8090169944
 0.0000000000  0.0000000000 -1.0000000000
 0.0000000000  1.0000000000  0.0000000000
-0.2763932023  0.4472135955  0.8506508084
-0.8944271910  0.4472135955  0.0000000000
 0.2763932023 -0.4472135955  0.8506508084
 0.7236067977  0.4472135955 -0.5257311121
 0.7236067977  0.4472135955  0.5257311121
-0.7236067977 -0.4472135955  0.5257311121
 0.7236067977  0.4472135955  0.5257311121
-0.2763932023  0.4472135955  0.8506508084
 0.8944271910 -0.4472135955  0.0000000000
-0.8944271910  0.4472135955  0.0000000000
 0.2763932023 -0.4472135955  0.8506508084
-0.0000000000  1.0000000000  0.0000000000
 0.0000000000 -1.0000000000  0.0000000000
 0.7236067977  0.4472135955 -0.5257311121
-0.7236067977 -0.4472135955 -0.5257311121
 0.2763932023 -0.4472135955 -0.8506508084
-0.2763932023  0.4472135955 -0.8506508084
10 0 1 5 14 21 29 26 17 8 2 
5 0 2 7 10 3 4
10 0 3 9 19 27 29 28 20 12 4 
5 0 1 6 11 4 
10 1 6 15 23 28 26 24 16 10 3 
5 1 3 9 13 5 4
5 2 8 18 12 4 
10 2 4 11 15 22 21 27 25 16 7 
10 5 13 19 25 24 17 18 12 11 6 
5 5 6 15 22 14 
5 7 16 24 17 8 
10 7 8 18 20 23 22 14 13 9 10 
5 9 10 16 25 19 4
5 11 15 23 20 12 4
5 13 14 21 27 19 
5 17 26 28 20 18 
5 21 22 23 28 29 
5 24 26 29 27 25 4
4 3 0 1 2 
4 3 4 5 0 
4 6 0 1 7 
4 1 4 5 2 
4 6 2 3 7 
4 5 8 9 0 
4 3 8 9 4 
4 10 7 1 11 
4 10 0 6 11 
4 5 11 12 2 
4 12 4 1 11 
4 13 7 3 8 
4 13 2 6 8 
4 14 11 5 8 
4 9 11 14 0 
4 9 7 13 4 
4 12 7 10 4 
4 15 0 10 8 
4 15 11 6 8 
4 12 8 14 2 
4 15 2 13 11 
4 14 7 16 0 
4 16 11 9 7 
4 16 4 13 11 
4 17 4 10 8 
4 17 7 12 8 
4 17 0 15 4 
4 17 2 14 7 
4 16 2 15 4 
4 16 0 17 2 
great stellated dodecahedron
great icosahedron
3|2 5/2
(5/2.5/2.5/2)
icosahedral group
A5
12{5/2}
56 20 30 12 20 7 0 0 2 1 3 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.6666666667  0.0000000000 -0.7453559925
-0.3333333333  0.5773502692 -0.7453559925
-0.3333333333 -0.5773502692 -0.7453559925
-0.7453559925  0.5773502692  0.3333333333
-0.7453559925 -0.5773502692  0.3333333333
-0.1273220038 -0.9341723590  0.3333333333
 0.8726779962 -0.3568220898  0.3333333333
 0.8726779962  0.3568220898  0.3333333333
-0.1273220038  0.9341723590  0.3333333333
 0.1273220038 -0.9341723590 -0.3333333333
 0.1273220038  0.9341723590 -0.3333333333
 0.7453559925  0.5773502692 -0.3333333333
-0.8726779962 -0.3568220898 -0.3333333333
-0.8726779962  0.3568220898 -0.3333333333
 0.7453559925 -0.5773502692 -0.3333333333
 0.3333333333  0.5773502692  0.7453559925
 0.3333333333 -0.5773502692  0.7453559925
-0.6666666667  0.0000000000  0.7453559925
 0.0000000000  0.0000000000 -1.0000000000
 0.4911234732  0.8506508084  0.1875924741
-0.9822469464  0.0000000000  0.1875924741
 0.4911234732 -0.8506508084  0.1875924741
-0.6070619982  0.0000000000 -0.7946544723
 0.3035309991 -0.5257311121 -0.7946544723
 0.3035309991  0.5257311121 -0.7946544723
-0.3035309991 -0.5257311121  0.7946544723
-0.3035309991  0.5257311121  0.7946544723
 0.6070619982 -0.0000000000  0.7946544723
 0.9822469464  0.0000000000 -0.1875924741
-0.4911234732  0.8506508084 -0.1875924741
-0.4911234732 -0.8506508084 -0.1875924741
5 0 2 7 4 1 2
5 0 3 9 6 2 2
5 0 1 5 8 3 2
5 1 4 10 11 5 2
5 2 6 12 13 7 2
5 3 8 14 15 9 2
5 4 7 13 16 10 2
5 5 11 17 14 8 2
5 6 9 15 18 12 2
5 10 16 19 17 11 2
5 12 18 19 16 13 2
5 14 17 19 18 15 2
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 6 0 
3 2 7 3 
3 4 8 1 
3 6 4 0 
3 5 7 2 
3 8 5 1 
3 3 9 6 
3 7 9 3 
3 4 10 8 
3 6 10 4 
3 5 11 7 
3 8 11 5 
3 9 10 6 
3 11 9 7 
3 10 11 8 
3 9 10 11 
great icosahedron
great stellated dodecahedron
5/2|2 3
(3.3.3.3.3)/2
icosahedral group
A5
20{3}
57 12 30 20 12 7 0 0 2 1 5 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8944271910  0.0000000000 -0.4472135955
-0.7236067977  0.5257311121 -0.4472135955
 0.2763932023 -0.8506508084 -0.4472135955
 0.2763932023  0.8506508084 -0.4472135955
-0.7236067977 -0.5257311121 -0.4472135955
-0.2763932023 -0.8506508084  0.4472135955
-0.2763932023  0.8506508084  0.4472135955
 0.7236067977  0.5257311121  0.4472135955
-0.8944271910 -0.0000000000  0.4472135955
 0.7236067977 -0.5257311121  0.4472135955
 0.0000000000 -0.0000000000 -1.0000000000
 0.3035309991  0.9341723590  0.1875924741
-0.7946544723 -0.5773502692  0.1875924741
 0.9822469464  0.0000000000  0.1875924741
-0.7946544723  0.5773502692  0.1875924741
 0.3035309991 -0.9341723590  0.1875924741
-0.1875924741  0.5773502692 -0.7946544723
 0.6070619982  0.0000000000  0.7946544723
-0.1875924741 -0.5773502692 -0.7946544723
-0.4911234732  0.3568220898  0.7946544723
 0.4911234732  0.3568220898 -0.7946544723
 0.1875924741 -0.5773502692  0.7946544723
-0.6070619982 -0.0000000000 -0.7946544723
 0.1875924741  0.5773502692  0.7946544723
 0.4911234732 -0.3568220898 -0.7946544723
-0.4911234732 -0.3568220898  0.7946544723
-0.9822469464 -0.0000000000 -0.1875924741
 0.7946544723 -0.5773502692 -0.1875924741
 0.7946544723  0.5773502692 -0.1875924741
-0.3035309991  0.9341723590 -0.1875924741
-0.3035309991 -0.9341723590 -0.1875924741
3 0 2 1 
3 0 3 2 
3 0 4 3 
3 0 5 4 
3 0 1 5 
3 1 7 5 
3 1 6 7 
3 1 2 6 
3 2 8 6 
3 2 3 8 
3 3 9 8 
3 3 4 9 
3 4 10 9 
3 4 5 10 
3 5 7 10 
3 6 11 7 
3 6 8 11 
3 7 11 10 
3 8 9 11 
3 9 10 11 
5 4 0 1 2 3 
5 4 5 6 7 0 
5 7 8 9 1 0 
5 9 10 11 2 1 
5 11 12 13 3 2 
5 13 14 5 4 3 
5 6 15 16 8 7 
5 14 17 15 6 5 
5 16 18 10 9 8 
5 18 19 12 11 10 
5 19 17 14 13 12 
5 15 16 18 19 17 
great icosidodecahedron
great rhombic triacontahedron
2|5/2 3
(5/2.3.5/2.3)
icosahedral group
A5
20{3}+12{5/2}
58 30 60 32 30 7 0 0 2 2 4 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9510565163  0.0000000000 -0.3090169944
 0.4253254042  0.8506508084 -0.3090169944
-0.9510565163  0.0000000000 -0.3090169944
-0.4253254042 -0.8506508084 -0.3090169944
-0.1624598481  0.8506508084  0.5000000000
-0.5877852523  0.0000000000 -0.8090169944
-0.2628655561 -0.5257311121 -0.8090169944
 0.6881909602 -0.5257311121  0.5000000000
 0.1624598481 -0.8506508084  0.5000000000
 0.5877852523 -0.0000000000 -0.8090169944
 0.2628655561  0.5257311121 -0.8090169944
-0.6881909602  0.5257311121  0.5000000000
-0.8506508084 -0.5257311121 -0.0000000000
 0.5257311121 -0.8506508084 -0.0000000000
-0.5877852523 -0.0000000000  0.8090169944
-0.2628655561 -0.5257311121  0.8090169944
-0.5257311121  0.8506508084  0.0000000000
 0.8506508084  0.5257311121 -0.0000000000
 0.5877852523 -0.0000000000  0.8090169944
 0.2628655561  0.5257311121  0.8090169944
 0.6881909602 -0.5257311121 -0.5000000000
-0.1624598481  0.8506508084 -0.5000000000
 0.9510565163 -0.0000000000  0.3090169944
 0.4253254042  0.8506508084  0.3090169944
-0.6881909602  0.5257311121 -0.5000000000
 0.1624598481 -0.8506508084 -0.5000000000
-0.9510565163  0.0000000000  0.3090169944
-0.4253254042 -0.8506508084  0.3090169944
 0.0000000000  0.0000000000 -1.0000000000
 0.4911234732  0.3035309991  0.3568220898
-0.4911234732  0.7946544723  0.3568220898
-0.4911234732 -0.3035309991  0.3568220898
 0.4911234732 -0.7946544723  0.3568220898
 0.1875924741 -0.3035309991 -0.5773502692
 0.1875924741  0.7946544723 -0.5773502692
 0.7946544723 -0.1875924741 -0.5773502692
-0.1875924741  0.3035309991 -0.5773502692
-0.1875924741 -0.7946544723 -0.5773502692
-0.7946544723  0.1875924741 -0.5773502692
-0.6070619982  0.3035309991 -0.0000000000
-0.3035309991 -0.1875924741  0.9341723590
-0.6070619982 -0.7946544723 -0.0000000000
-0.0000000000 -0.6787159473 -0.0000000000
-0.9822469464 -0.1875924741  0.0000000000
 0.6070619982 -0.3035309991 -0.0000000000
 0.3035309991  0.1875924741  0.9341723590
 0.6070619982  0.7946544723 -0.0000000000
 0.0000000000  0.6787159473  0.0000000000
 0.9822469464  0.1875924741  0.0000000000
-0.3035309991 -0.1875924741 -0.9341723590
 0.1875924741 -0.3035309991  0.5773502692
 0.1875924741  0.7946544723  0.5773502692
 0.7946544723 -0.1875924741  0.5773502692
-0.1875924741  0.3035309991  0.5773502692
 0.3035309991  0.1875924741 -0.9341723590
-0.1875924741 -0.7946544723  0.5773502692
-0.7946544723  0.1875924741  0.5773502692
 0.4911234732  0.3035309991 -0.3568220898
 0.4911234732 -0.7946544723 -0.3568220898
-0.4911234732  0.7946544723 -0.3568220898
-0.4911234732 -0.3035309991 -0.3568220898
5 0 2 8 5 1 2
3 0 3 2 
5 0 4 12 9 3 2
3 0 1 4 
5 1 6 14 11 4 2
3 1 5 6 
3 2 7 8 
5 2 3 10 17 7 2
3 3 9 10 
3 4 11 12 
5 5 13 22 15 6 2
3 5 8 13 
3 6 15 14 
5 7 16 21 13 8 2
3 7 17 16 
5 9 18 26 19 10 2
3 9 12 18 
3 10 19 17 
5 11 20 25 18 12 2
3 11 14 20 
3 13 21 22 
5 14 15 23 28 20 2
3 15 22 23 
3 16 24 21 
5 16 17 19 27 24 2
3 18 25 26 
3 19 26 27 
3 20 28 25 
5 21 24 29 23 22 2
3 23 29 28 
3 24 27 29 
5 25 28 29 27 26 2
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 7 8 2 1 
4 2 9 4 3 
4 5 10 11 0 
4 4 12 10 5 
4 6 13 14 7 
4 11 13 6 0 
4 8 15 16 2 
4 7 17 15 8 
4 9 18 19 4 
4 16 18 9 2 
4 10 20 13 11 
4 19 21 12 4 
4 21 22 10 12 
4 13 23 24 14 
4 24 17 7 14 
4 15 25 18 16 
4 24 26 15 17 
4 18 27 21 19 
4 20 28 23 13 
4 22 28 20 10 
4 21 29 28 22 
4 28 30 24 23 
4 25 31 27 18 
4 26 31 25 15 
4 30 31 26 24 
4 31 29 21 27 
4 29 28 30 31 
great truncated icosahedron
great stellapentakisdodecahedron
2 5/2|3
(6.6.5/2)
icosahedral group
A5
20{6}+12{5/2}
59 60 90 32 60 7 0 0 2 2 3 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8356150397  0.0000000000  0.5493154881
-0.7824189491  0.2933821444  0.5493154881
 0.6296037101 -0.5494102864  0.5493154881
 0.8888111303  0.2933821444 -0.3520535357
 0.1131652141 -0.5494102864  0.8278538347
-0.9352341880  0.0373540025 -0.3520535357
-0.7292228585  0.5867642889 -0.3520535357
 0.4464985474  0.3395542307  0.8278538347
 0.4767884711 -0.8054384283 -0.3520535357
 0.2195573953  0.0373540025 -0.9748842130
 0.1063921812  0.5867642889 -0.8027380476
-0.5560885209 -0.8054384283  0.2050231574
-0.6347778468  0.7449983827  0.2050231574
-0.3056304780 -0.5120562839 -0.8027380476
-0.9681111801 -0.1439661345  0.2050231574
 0.1105781457  0.9724906059  0.2050231574
 0.1408680694 -0.1725020531 -0.9748842130
 0.5200137365  0.7449983827 -0.4178075198
-0.5028924303 -0.5120562839 -0.6963458664
 0.7031188992 -0.1439661345 -0.6963458664
-0.8920089226 -0.1725020531 -0.4178075198
 0.2952822046  0.9032324765  0.3114153386
 0.6244295734 -0.3538221901 -0.6963458664
-0.3713844621 -0.8746965578  0.3114153386
-0.5586755893  0.7164624640 -0.4178075198
-0.0422370933  0.7164624640 -0.6963458664
-0.0980202522 -0.9032324765 -0.4178075198
 0.0980202522  0.9032324765  0.4178075198
-0.9248859147 -0.3538221901  0.1392691733
 0.4642305776 -0.8746965578 -0.1392691733
-0.2952822046 -0.9032324765 -0.3114153386
 0.8920089226  0.1725020531  0.4178075198
 0.9248859147  0.3538221901 -0.1392691733
 0.5586755893 -0.7164624640  0.4178075198
 0.3713844621  0.8746965578 -0.3114153386
-0.4642305776  0.8746965578  0.1392691733
-0.5200137365 -0.7449983827  0.4178075198
-0.1408680694  0.1725020531  0.9748842130
-0.6244295734  0.3538221901  0.6963458664
 0.0422370933 -0.7164624640  0.6963458664
 0.6347778468 -0.7449983827 -0.2050231574
 0.5560885209  0.8054384283 -0.2050231574
 0.5028924303  0.5120562839  0.6963458664
-0.1105781457 -0.9724906059 -0.2050231574
 0.9681111801  0.1439661345 -0.2050231574
-0.7031188992  0.1439661345  0.6963458664
-0.2195573953 -0.0373540025  0.9748842130
-0.4767884711  0.8054384283  0.3520535357
 0.3056304780  0.5120562839  0.8027380476
 0.9352341880 -0.0373540025  0.3520535357
-0.1131652141  0.5494102864 -0.8278538347
-0.4464985474 -0.3395542307 -0.8278538347
 0.7292228585 -0.5867642889  0.3520535357
-0.1063921812 -0.5867642889  0.8027380476
-0.8888111303 -0.2933821444  0.3520535357
-0.6296037101  0.5494102864 -0.5493154881
 0.7824189491 -0.2933821444 -0.5493154881
-0.8356150397 -0.0000000000 -0.5493154881
 0.0000000000 -0.0000000000 -1.0000000000
 0.1693842601  0.9341723590  0.3140556896
-0.4865864368 -0.8152316624  0.3140556896
 0.1693842601 -0.0635136937  0.3140556896
 0.5297191236 -0.8152316624 -0.2340832902
-0.3387685201  0.1270273873  0.0213524160
 0.9351313099  0.2659594829 -0.2340832902
 0.2039331950  0.1270273873 -0.2713508575
-0.7092856298  0.2659594829  0.6528242098
-0.0164752203  0.6227815726 -0.7822222701
-0.4218874066 -0.4584095726 -0.7822222701
 0.0701362950 -0.2297947024 -0.2713508575
-0.6445865996  0.6227815726 -0.4434537500
-0.2652718107 -0.2297947024 -0.0904502858
-0.1211604502  0.0454313035  0.9915927299
-0.0487838789  0.3475555668 -0.0904502858
-0.8951451102 -0.0454313035 -0.4434537500
 0.8951451102  0.0454313035  0.4434537500
 0.1211604502 -0.0454313035 -0.9915927299
 0.2652718107  0.2297947024  0.0904502858
 0.6445865996 -0.6227815726  0.4434537500
 0.0487838789 -0.3475555668  0.0904502858
-0.0701362950  0.2297947024  0.2713508575
 0.0164752203 -0.6227815726  0.7822222701
 0.7092856298 -0.2659594829 -0.6528242098
 0.4218874066  0.4584095726  0.7822222701
-0.2039331950 -0.1270273873  0.2713508575
-0.9351313099 -0.2659594829  0.2340832902
 0.3387685201 -0.1270273873 -0.0213524160
-0.5297191236  0.8152316624  0.2340832902
 0.4865864368  0.8152316624 -0.3140556896
-0.1693842601  0.0635136937 -0.3140556896
-0.1693842601 -0.9341723590 -0.3140556896
6 0 2 7 11 4 1 
6 0 3 9 14 6 2 
5 0 1 5 8 3 2
6 1 4 10 19 12 5 
5 2 6 13 15 7 2
6 3 8 16 26 17 9 
5 4 11 20 18 10 2
6 5 12 21 25 16 8 
6 6 14 23 33 22 13 
6 7 15 24 30 20 11 
5 9 17 27 23 14 2
6 10 18 28 39 29 19 
5 12 19 29 31 21 2
6 13 22 32 34 24 15 
5 16 25 35 36 26 2
6 17 26 36 46 37 27 
6 18 20 30 40 38 28 
6 21 31 41 45 35 25 
5 22 33 43 42 32 2
6 23 27 37 47 43 33 
5 24 34 44 40 30 2
5 28 38 48 49 39 2
6 29 39 49 50 41 31 
6 32 42 51 52 44 34 
6 35 45 53 54 46 36 
5 37 46 54 55 47 2
6 38 40 44 52 56 48 
5 41 50 57 53 45 2
6 42 43 47 55 58 51 
6 48 56 59 57 50 49 
5 51 58 59 56 52 2
6 53 57 59 58 55 54 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 6 0 
3 2 7 3 
3 4 8 1 
3 0 9 4 
3 5 7 2 
3 1 10 5 
3 3 11 6 
3 6 9 0 
3 7 12 3 
3 4 13 8 
3 8 10 1 
3 9 13 4 
3 5 14 7 
3 10 15 5 
3 11 16 6 
3 12 11 3 
3 16 9 6 
3 7 17 12 
3 13 18 8 
3 8 19 10 
3 9 20 13 
3 14 17 7 
3 15 14 5 
3 19 15 10 
3 11 21 16 
3 12 22 11 
3 16 20 9 
3 17 22 12 
3 13 23 18 
3 18 19 8 
3 20 23 13 
3 14 24 17 
3 15 24 14 
3 19 25 15 
3 21 26 16 
3 22 21 11 
3 26 20 16 
3 17 27 22 
3 23 28 18 
3 28 19 18 
3 26 23 20 
3 24 27 17 
3 25 24 15 
3 28 25 19 
3 21 29 26 
3 22 29 21 
3 27 29 22 
3 23 30 28 
3 26 30 23 
3 24 31 27 
3 25 31 24 
3 28 31 25 
3 29 30 26 
3 31 29 27 
3 30 31 28 
3 29 30 31 
rhombicosahedron
rhombicosacron
2 5/2 3|
(6.4.6/5.4/3)
icosahedral group
A5
10{6}+15{4}+15{4/3}+10{6/5}
60 60 120 50 60 0 0 1 -10 4 4 120 5 0 1
 0.0000000000  0.0000000000  1.0000000000
 0.6998542122  0.0000000000  0.7142857143
-0.5248906592  0.4629100499  0.7142857143
-0.3689536881 -0.5947008445  0.7142857143
-0.1166423687  0.6900655593  0.7142857143
 0.8748177653  0.4629100499  0.1428571429
 0.7634342145 -0.5947008445  0.2519902889
 0.5832118435  0.6900655593  0.4285714286
-0.8938443472 -0.1317907946  0.4285714286
 0.2077578990  0.4039714148  0.8908668539
-0.3499271061  0.9258200998  0.1428571429
-0.8545497448 -0.4993361296  0.1428571429
 0.1028746047 -0.9622461795  0.2519902889
-0.4528017108  0.0364260797  0.8908668539
-0.6022384255  0.7854302742  0.1428571429
 0.9383977675 -0.1317907946 -0.3194382825
 0.4750784209  0.4039714148  0.7817337079
 0.3499271061  0.9258200998 -0.1428571429
 0.7103718480 -0.4993361296 -0.4960194221
 0.9469067137  0.0364260797  0.3194382825
 0.5301494771  0.7854302742 -0.3194382825
-0.5301494771 -0.7854302742  0.3194382825
-0.9469067137 -0.0364260797 -0.3194382825
 0.3827214521  0.8668814647  0.3194382825
 0.5714527692 -0.2496680648  0.7817337079
-0.6107473716  0.6172133998 -0.4960194221
-0.3827214521 -0.8668814647 -0.3194382825
-0.5937294793 -0.1907294297  0.7817337079
-0.9711921135  0.1907294297 -0.1428571429
 0.0498122382 -0.8668814647 -0.4960194221
-0.9383977675  0.1317907946  0.3194382825
-0.0891068406 -0.6172133998  0.7817337079
-0.2024990811  0.8443689093 -0.4960194221
 0.6022384255 -0.7854302742 -0.1428571429
 0.4528017108 -0.0364260797 -0.8908668539
-0.0498122382  0.8668814647  0.4960194221
 0.1389190789 -0.2496680648  0.9583148475
 0.0891068406  0.6172133998 -0.7817337079
 0.9711921135 -0.1907294297  0.1428571429
 0.5937294793  0.1907294297 -0.7817337079
 0.8938443472  0.1317907946 -0.4285714286
 0.6107473716 -0.6172133998  0.4960194221
-0.5832118435 -0.6900655593 -0.4285714286
 0.2024990811 -0.8443689093  0.4960194221
-0.4750784209 -0.4039714148 -0.7817337079
-0.1028746047  0.9622461795 -0.2519902889
 0.8545497448  0.4993361296 -0.1428571429
-0.1389190789  0.2496680648 -0.9583148475
 0.3499271061 -0.9258200998 -0.1428571429
-0.2077578990 -0.4039714148 -0.8908668539
-0.7103718480  0.4993361296  0.4960194221
-0.5714527692  0.2496680648 -0.7817337079
-0.3499271061 -0.9258200998  0.1428571429
-0.7634342145  0.5947008445 -0.2519902889
-0.8748177653 -0.4629100499 -0.1428571429
 0.1166423687 -0.6900655593 -0.7142857143
 0.3689536881  0.5947008445 -0.7142857143
 0.5248906592 -0.4629100499 -0.7142857143
-0.6998542122  0.0000000000 -0.7142857143
-0.0000000000  0.0000000000 -1.0000000000
 0.2672612419  0.7071067812  0.6546536707
-0.4096109381 -0.0603941292  0.6546536707
-0.7417602291  0.1456720081  0.6546536707
 0.2672612419  0.3162277660  0.6546536707
 0.9879908641  0.1456720081 -0.0515142560
 0.7507413705 -0.0603941292  0.1809418244
-0.0651501153  0.6093870274  0.4737118463
-0.2462306350 -0.2913440163  0.9243858169
-0.6446401714 -0.7627485371 -0.0515142560
-0.3444608228 -0.6697811566  0.1809418244
-0.4834801286  0.3766218952  0.4737118463
 0.3773789295  0.0556417559  0.9243858169
 0.8228143327 -0.2913440163  0.4879500365
 0.3780650276  0.6093870274  0.2927700219
 0.3726763428 -0.6697811566 -0.1118281975
 0.4244047962 -0.7627485371 -0.4879500365
 0.6768721800  0.3766218952 -0.0000000000
-0.6768721800 -0.3766218952 -0.0000000000
-0.4244047962  0.7627485371  0.4879500365
 0.0543727456 -0.0977197538  0.7664818682
-0.1195228609  0.7071067812 -0.2927700219
 0.1862071383  0.8527787893 -0.4879500365
-0.1862071383 -0.8527787893  0.4879500365
-0.7171371656  0.0000000000  0.2927700219
-0.5378528742  0.4743416490 -0.2927700219
-0.8228143327  0.2913440163 -0.4879500365
 0.4834801286 -0.3766218952 -0.4737118463
 0.4975878886 -0.0977197538  0.5855400438
 0.6446401714  0.7627485371  0.0515142560
-0.4744989872  0.8527787893 -0.2182178902
 0.7171371656  0.0000000000 -0.2927700219
 0.4744989872 -0.8527787893  0.2182178902
 0.2462306350  0.2913440163 -0.9243858169
 0.1792842914  0.4743416490 -0.5855400438
-0.1792842914 -0.4743416490  0.5855400438
-0.9879908641 -0.1456720081  0.0515142560
-0.3773789295 -0.0556417559 -0.9243858169
-0.4975878886  0.0977197538 -0.5855400438
 0.3444608228  0.6697811566 -0.1809418244
 0.5378528742 -0.4743416490  0.2927700219
 0.0651501153 -0.6093870274 -0.4737118463
-0.3780650276 -0.6093870274 -0.2927700219
-0.7507413705  0.0603941292 -0.1809418244
 0.1195228609 -0.7071067812  0.2927700219
 0.7417602291 -0.1456720081 -0.6546536707
-0.0543727456  0.0977197538 -0.7664818682
-0.3726763428  0.6697811566  0.1118281975
 0.4096109381  0.0603941292 -0.6546536707
-0.2672612419 -0.3162277660 -0.6546536707
-0.2672612419 -0.7071067812 -0.6546536707
6 0 2 10 17 5 1 
4 0 3 8 2 
6 0 4 14 28 11 3 5
4 0 1 7 4 3
6 1 6 18 39 20 7 5
4 1 5 15 6 
4 2 9 23 10 3
6 2 8 21 43 24 9 5
6 3 12 29 44 22 8 
4 3 11 26 12 3
4 4 13 30 14 
6 4 7 19 41 31 13 
6 5 16 36 43 33 15 5
4 5 17 35 16 3
4 6 12 29 18 3
6 6 15 34 49 26 12 
4 7 20 40 19 
4 8 22 42 21 3
6 9 13 30 53 45 23 
4 9 24 31 13 
4 10 25 37 17 
6 10 23 46 39 47 25 5
6 11 27 36 41 48 26 
4 11 28 50 27 
4 14 32 51 28 3
6 14 30 54 44 47 32 
4 15 33 55 34 3
4 16 19 41 36 
6 16 35 45 56 40 19 
6 17 37 51 28 50 35 5
4 18 38 46 39 
6 18 29 52 31 24 38 
6 20 32 51 49 57 40 
4 20 39 47 32 3
4 21 27 36 43 
6 21 42 58 53 50 27 
6 22 25 37 34 55 42 5
4 22 44 47 25 
4 23 45 56 46 
4 24 43 33 38 3
4 26 48 57 49 
4 29 52 54 44 3
4 30 53 58 54 3
4 31 41 48 52 
6 33 38 46 56 59 55 
4 34 37 51 49 
4 35 50 53 45 
4 40 57 59 56 3
4 42 55 59 58 
6 48 52 54 58 59 57 5
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 1 8 9 2 
4 2 10 11 3 
4 5 12 13 0 
4 4 14 15 5 
4 11 16 4 3 
4 7 17 8 1 
4 6 18 19 7 
4 0 20 21 6 
4 9 22 23 2 
4 8 14 15 9 
4 10 18 19 11 
4 2 24 25 10 
4 15 26 12 5 
4 12 27 28 13 
4 13 29 20 0 
4 4 30 31 14 
4 11 27 28 16 
4 16 32 33 4 
4 7 34 35 17 
4 17 36 37 8 
4 21 38 18 6 
4 19 31 39 7 
4 20 36 37 21 
4 15 40 22 9 
4 22 34 35 23 
4 23 29 24 2 
4 8 41 31 14 
4 25 42 18 10 
4 31 43 11 19 
4 24 32 33 25 
4 26 44 39 12 
4 15 45 36 26 
4 28 46 29 13 
4 12 34 22 27 
4 29 45 36 20 
4 30 44 39 31 
4 33 21 30 4 
4 28 47 32 16 
4 43 22 27 11 
4 35 48 36 17 
4 7 34 12 39 
4 37 25 41 8 
4 38 28 46 18 
4 44 38 21 30 
4 37 21 33 25 
4 40 49 43 22 
4 45 32 40 15 
4 35 46 29 23 
4 29 24 32 45 
4 41 49 43 31 
4 42 35 46 18 
4 49 42 25 41 
4 48 44 26 36 
4 44 47 28 38 
4 47 49 40 32 
4 49 48 35 42 
4 48 44 47 49 
great snub icosidodecahedron
great pentagonal hexecontahedron
|2 5/2 3
(3.3.5/2.3.3)
icosahedral group
A5
80{3}+12{5/2}
61 60 150 92 60 7 0 0 2 2 5 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9684429470  0.0000000000  0.2492353475
 0.1932143650  0.9489731033  0.2492353475
-0.8913464263  0.3786598604  0.2492353475
-0.8913464263 -0.3786598604  0.2492353475
 0.1932143650 -0.9489731033  0.2492353475
 0.4635252507 -0.3786598604 -0.8010999015
 0.3781705098  0.7978800013 -0.4694406981
 0.8572881225  0.2113823691 -0.4694406981
-0.2785691059  0.5297529623 -0.8010999015
-0.6600348160 -0.5864976322 -0.4694406981
-0.3404640391 -0.6126845243  0.7132334203
-0.3404640391  0.6126845243  0.7132334203
-0.6600348160  0.5864976322 -0.4694406981
-0.2785691059 -0.5297529623 -0.8010999015
-0.4456304207 -0.8822259307 -0.1519570181
-0.6325889612  0.1672774913 -0.7562072778
-0.5650434654  0.7637776262  0.3120410548
 0.5580227938  0.4558561435  0.6934015705
 0.6356904263 -0.7060651967  0.3120410548
 0.0377064707 -0.6532448048 -0.7562072778
 0.2734652451  0.0366360026 -0.9611839382
 0.4921267272 -0.8571582987 -0.1519570181
 0.7205513597  0.0000000000  0.6934015705
 0.4921267272  0.8571582987 -0.1519570181
 0.5168240834  0.4013021552 -0.7562072778
 0.7551034710 -0.6377521562 -0.1519570181
 0.0981457100 -0.4820430356  0.8706330636
-0.8937570446  0.0933806725  0.4387235978
-0.9355024568 -0.2752766852 -0.2214901802
-0.3809719027 -0.3112209470  0.8706330636
-0.5885888579 -0.7537751235  0.2922092050
-0.8555038721  0.1446351965 -0.4971858654
 0.0022546911  0.9751599953 -0.2214901802
 0.9655218191  0.2590922959  0.0252744751
 0.8243476323 -0.2706606665 -0.4971858654
-0.1952509108  0.2340246639 -0.9524229830
-0.2352120726  0.9716153981  0.0252744751
 0.7860944598  0.4354045303  0.4387235978
 0.1281650723  0.7271416236  0.6744173585
-0.4036327131  0.8094483719 -0.4264668406
 0.0235453925 -0.1967638477 -0.9801681502
 0.0397430165 -0.9978022901 -0.0530196423
 0.3756743067 -0.2817345907  0.8828898208
-0.6139292842  0.4101853978  0.6744173585
 0.1126975629  0.4558561435  0.8828898208
 0.4279771028 -0.6898808074  0.5838664839
-0.2411041472 -0.8717768201 -0.4264668406
-0.9984623093  0.0161843893 -0.0530196423
-0.2970106376  0.1601278451  0.9413520884
 0.7675414736 -0.3119126878  0.5599915727
 0.7838397687  0.5197504596 -0.3397862220
 0.9607558386 -0.2013798664 -0.1907730799
 0.4935202029  0.8050296475  0.3291885112
-0.6821867327  0.7311328287 -0.0081270187
-0.7497814649 -0.3524729683  0.5599915727
-0.2817083791 -0.9012631765  0.3291885112
 0.4908680726 -0.6442100617 -0.5865508773
 0.2046118584  0.5226033161 -0.8276592061
-0.6840824376 -0.3047630416 -0.6626844702
 0.5478898766  0.4475784305  0.7067462286
-0.3292705043  0.6261714648  0.7067462286
-0.5952793113 -0.0000000000  0.7067462286
-0.3292705043 -0.6261714648  0.7067462286
 0.5478898766 -0.4475784305  0.7067462286
 0.7665092489 -0.6261714648 -0.1427335557
 0.8537428920  0.1977230883 -0.4816935277
 0.7140436788  0.5833116520  0.0611296277
 0.3640785289  0.7971312126 -0.4816935277
-0.4606562335  0.8760268070 -0.1427335557
-0.8630869536  0.1518296938 -0.4816935277
-0.8922793901 -0.3869952480  0.2325342297
-0.8922793901  0.3869952480  0.2325342297
-0.8630869536 -0.1518296938 -0.4816935277
-0.4606562335 -0.8760268070 -0.1427335557
 0.1661538022 -0.8160650441 -0.4003479086
-0.2899174208 -0.5157948995 -0.8061659326
 0.0986241788  0.2766186827 -0.9559055266
-0.3864951254  0.8154436245 -0.4308981471
 0.1750509698  0.9515503064  0.2528026353
 0.9673445525 -0.0183124119  0.2528026353
 0.7219399541 -0.5414143418 -0.4308981471
 0.2907340063  0.0414531285 -0.9559055266
-0.3583185855 -0.1277530350 -0.8421013261
 0.0497855062 -0.6636139307 -0.7464167431
-0.2397711783 -0.9698627183  0.0433138518
 0.4113754049 -0.6932440356  0.5917626073
 0.0186881231 -0.0000000000  0.9998253618
 0.4113754049  0.6932440356  0.5917626073
-0.2397711783  0.9698627183  0.0433138518
-0.0197040197  0.7371093263 -0.5568925235
-0.1989303569  0.2160355002 -0.9559055266
 0.4685125572 -0.3613758057 -0.8061659326
 0.1922513550 -0.9442432760  0.2672902024
-0.5854254823 -0.5994081243  0.5458817685
-0.9300728450 -0.2931593368 -0.2214093636
-0.8289101298  0.3766028993 -0.1578795205
-0.8874084967  0.0836132249  0.4533376099
-0.1829947623  0.4284483765  0.8848417405
 0.3833253882 -0.2647956591  0.8848417405
 0.0197040197 -0.7371093263  0.5568925235
 0.0399992886 -0.9966260588 -0.0716697696
-0.6633150639 -0.5953974618 -0.4533376099
-0.2734522013  0.5454250043 -0.7922975819
 0.5854254823  0.5994081243 -0.5458817685
 0.8164711846 -0.2647956591 -0.5130867994
 0.8289101298 -0.3766028993  0.1578795205
 0.9607530194  0.2766186827  0.0208743890
 0.5288194467  0.3869952480 -0.7553705520
 0.5035784309  0.8528860904 -0.1378190139
 0.9706558172  0.0938359113 -0.2214093636
 0.7731882508 -0.3227894416  0.5458817685
 0.3583185855  0.1277530350  0.8421013261
-0.3147977002  0.1596420548  0.9356371210
-0.5514589905  0.7687675350  0.3238664214
-0.6204913561  0.1591367242 -0.7678971155
-0.4113754049 -0.6932440356 -0.5917626073
-0.6021639693 -0.7472271556  0.2811585531
-0.3899767705 -0.2949310946  0.8723151769
-0.9706558172 -0.0938359113  0.2214093636
-0.6919874045  0.7216077133 -0.0208743890
-0.1661538022  0.8160650441  0.4003479086
 0.5096002070  0.7971312126  0.3238664214
 0.7103900588  0.0118230236  0.7037088748
 0.4769371461 -0.8642037834 -0.1602584767
 0.1829947623 -0.4284483765 -0.8848417405
-0.6767244541 -0.2931593368 -0.6753529569
-0.6739454866  0.5762674078 -0.4622914188
-0.7219399541  0.5414143418  0.4308981471
 0.1197373444  0.7391374301  0.6628263934
 0.7921496414  0.4409783680  0.4219443382
 0.2397711783  0.9698627183 -0.0433138518
 0.1904278281  0.5341073114 -0.8236908535
 0.5952793113 -0.0000000000 -0.7067462286
 0.4829853613 -0.6583909696 -0.5772750401
 0.6490652071 -0.6984669967  0.3014269586
 0.8630869536  0.1518296938  0.4816935277
 0.1203945702  0.4402714001  0.8897562822
-0.6222274141  0.3935953105  0.6766947441
-0.0986241788 -0.2766186827  0.9559055266
-0.2654929905 -0.9027901475  0.3383539886
-0.7140436788 -0.5833116520 -0.0611296277
-0.7438697051 -0.3419194956  0.5742376863
 0.0890571699 -0.4966648455  0.8633613680
 0.4606562335 -0.8760268070  0.1427335557
 0.9632167023 -0.2058128138 -0.1727850402
 0.7824062032  0.5311916554 -0.3250783883
 0.0075205347  0.9710066165 -0.2389342846
-0.5478898766  0.4475784305 -0.7067462286
-0.9980247269  0.0348530660 -0.0522676607
-0.2239949432 -0.8726547120 -0.4339355010
 0.0053755709 -0.2010951833 -0.9795569562
3 0 2 1 
3 0 3 2 
5 0 4 12 11 3 2
3 0 5 4 
3 0 1 5 
3 1 6 5 
3 1 7 6 
5 1 2 8 18 7 2
3 2 9 8 
3 2 3 9 
3 3 10 9 
3 3 11 10 
3 4 13 12 
3 4 14 13 
3 4 5 14 
5 5 6 15 26 14 2
3 6 16 15 
3 6 7 16 
3 7 17 16 
3 7 18 17 
3 8 19 18 
3 8 20 19 
3 8 9 20 
5 9 10 21 32 20 2
3 10 22 21 
3 10 11 22 
3 11 23 22 
3 11 12 23 
3 12 24 23 
3 12 13 24 
5 13 25 37 36 24 2
3 13 14 25 
3 14 26 25 
3 15 27 26 
3 15 28 27 
3 15 16 28 
5 16 17 29 40 28 2
3 17 30 29 
3 17 18 30 
3 18 19 30 
5 19 31 43 42 30 2
3 19 20 31 
3 20 32 31 
3 21 33 32 
3 21 34 33 
3 21 22 34 
5 22 23 35 46 34 2
3 23 24 35 
3 24 36 35 
3 25 38 37 
3 25 26 38 
3 26 27 38 
5 27 39 50 49 38 2
3 27 28 39 
3 28 40 39 
3 29 41 40 
3 29 42 41 
3 29 30 42 
3 31 44 43 
3 31 32 44 
3 32 33 44 
5 33 45 54 53 44 2
3 33 34 45 
3 34 46 45 
3 35 47 46 
3 35 36 47 
3 36 48 47 
3 36 37 48 
3 37 49 48 
3 37 38 49 
3 39 51 50 
3 39 40 51 
3 40 41 51 
5 41 52 58 57 51 2
3 41 42 52 
3 42 43 52 
3 43 53 52 
3 43 44 53 
3 45 55 54 
3 45 46 55 
3 46 47 55 
5 47 48 56 59 55 2
3 48 49 56 
3 49 50 56 
3 50 57 56 
3 50 51 57 
3 52 53 58 
3 53 54 58 
3 54 59 58 
3 54 55 59 
3 56 57 59 
3 57 58 59 
5 4 0 1 2 3 
5 4 5 6 7 0 
5 7 8 9 1 0 
5 9 10 11 2 1 
5 2 12 13 14 3 
5 14 15 5 4 3 
5 15 16 17 6 5 
5 17 18 19 7 6 
5 7 20 21 22 8 
5 22 23 10 9 8 
5 23 24 25 11 10 
5 25 26 27 2 11 
5 27 28 29 12 2 
5 29 30 31 13 12 
5 31 32 15 14 13 
5 15 33 34 35 16 
5 35 36 18 17 16 
5 36 37 38 19 18 
5 38 39 20 7 19 
5 39 40 41 21 20 
5 41 42 23 22 21 
5 23 43 44 45 24 
5 45 46 26 25 24 
5 46 47 28 27 26 
5 47 48 30 29 28 
5 30 49 50 32 31 
5 50 51 33 15 32 
5 51 52 53 34 33 
5 53 54 36 35 34 
5 36 55 56 57 37 
5 57 40 39 38 37 
5 40 58 59 42 41 
5 59 60 43 23 42 
5 60 61 62 44 43 
5 62 63 46 45 44 
5 46 64 65 48 47 
5 65 66 67 30 48 
5 67 68 69 49 30 
5 69 52 51 50 49 
5 52 70 71 54 53 
5 71 72 55 36 54 
5 72 73 74 56 55 
5 74 75 40 57 56 
5 75 76 77 58 40 
5 77 61 60 59 58 
5 61 78 79 63 62 
5 79 80 64 46 63 
5 80 81 66 65 64 
5 81 82 68 67 66 
5 82 83 52 69 68 
5 83 84 85 70 52 
5 85 73 72 71 70 
5 73 86 76 75 74 
5 86 87 61 77 76 
5 87 88 89 78 61 
5 89 81 80 79 78 
5 81 90 84 83 82 
5 90 91 73 85 84 
5 91 88 87 86 73 
5 88 89 81 90 91 
small stellated truncated dodecahedron
great pentakisdodekahedron
2 5|5/3
(10/3.10/3.5)
icosahedral group
A5
12{5}+12{10/3}
62 60 90 24 60 9 0 0 -6 2 3 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9498602905  0.0000000000  0.3126746369
-0.0501397095  0.9485360199  0.3126746369
-0.9445669005 -0.1001396121  0.3126746369
 0.3126746369  0.9485360199  0.0501397095
 0.5923393341 -0.1001396121 -0.7994411620
-0.9637185654  0.2621689080  0.0501397095
 0.9307086256  0.3623085200  0.0501397095
-0.5784810592 -0.1620292959 -0.7994411620
-0.4109321609  0.9102860917  0.0501397095
 0.3489560715  0.2621689080 -0.8997205810
-0.2433832625  0.3623085200  0.8997205810
 0.1761137832  0.9102860917 -0.3746507262
-0.5474930145 -0.7482567958 -0.3746507262
-0.3489560715 -0.2621689080  0.8997205810
 0.3746507262 -0.2239189798  0.8997205810
 0.6233273787 -0.6863671119 -0.3746507262
-0.2710998123  0.8866463360 -0.3746507262
 0.2038303330  0.3859482757  0.8997205810
-0.3746507262  0.2239189798 -0.8997205810
-0.1846786681 -0.7482567958 -0.6371856536
 0.9637185654 -0.2621689080 -0.0501397095
 0.7374650726 -0.2239189798  0.6371856536
-0.5507645094 -0.6863671119  0.4749301452
 0.7908762771  0.3859482757  0.4749301452
-0.7374650726  0.2239189798 -0.6371856536
-0.1899720581 -0.6481171837  0.7374650726
 0.1846786681  0.7482567958  0.6371856536
-0.3126746369 -0.9485360199 -0.0501397095
 0.4109321609 -0.9102860917 -0.0501397095
-0.2625349274  0.7246170401  0.6371856536
 0.2572415374 -0.6244774280  0.7374650726
 0.7097485229  0.3004188362 -0.6371856536
-0.8271577117  0.3004188362  0.4749301452
 0.6200558838 -0.6244774280  0.4749301452
-0.7097485229 -0.3004188362  0.6371856536
-0.9307086256 -0.3623085200 -0.0501397095
 0.2625349274 -0.7246170401 -0.6371856536
 0.7598882324 -0.6481171837  0.0501397095
 0.5474930145  0.7482567958  0.3746507262
 0.0501397095 -0.9485360199 -0.3126746369
-0.1761137832 -0.9102860917  0.3746507262
 0.6873253631  0.7246170401 -0.0501397095
 0.8271577117 -0.3004188362 -0.4749301452
 0.2433832625 -0.3623085200 -0.8997205810
-0.6873253631 -0.7246170401  0.0501397095
 0.5507645094  0.6863671119 -0.4749301452
-0.7598882324  0.6481171837 -0.0501397095
-0.9498602905  0.0000000000 -0.3126746369
-0.2038303330 -0.3859482757 -0.8997205810
 0.9445669005  0.1001396121 -0.3126746369
-0.6200558838  0.6244774280 -0.4749301452
-0.7908762771 -0.3859482757 -0.4749301452
 0.2710998123 -0.8866463360  0.3746507262
-0.6233273787  0.6863671119  0.3746507262
 0.1899720581  0.6481171837 -0.7374650726
 0.0000000000  0.0000000000 -1.0000000000
-0.5923393341  0.1001396121  0.7994411620
-0.2572415374  0.6244774280 -0.7374650726
 0.5784810592  0.1620292959  0.7994411620
 0.0526465096  0.0555029103  0.0727556869
-0.0582045495  0.0496433121  0.0727556869
 0.0526465096 -0.9959593140  0.0727556869
 0.0873068243  0.0496433121 -0.0325373323
-0.0201091773  0.3804226065 -0.9245941063
-0.0920539571  0.0401622832 -0.0325373323
-0.8719475967  0.3804226065 -0.3081980354
-0.0021229823  0.0401622832 -0.0976119970
-0.0873068243 -0.0496433121  0.0325373323
 0.0920539571 -0.0401622832  0.0325373323
 0.8269821093  0.4702282018 -0.3081980354
 0.0582045495 -0.0496433121 -0.0727556869
 0.0021229823 -0.0401622832  0.0976119970
-0.5513214062  0.4702282018  0.6891517578
 0.0055580399 -0.1051462224  0.0076810222
 0.8719475967 -0.3804226065  0.3081980354
-0.8269821093 -0.4702282018  0.3081980354
 0.4986748966  0.5257311121  0.6891517578
-0.0526465096 -0.0555029103 -0.0727556869
 0.0201091773 -0.3804226065  0.9245941063
 0.5513214062 -0.4702282018 -0.6891517578
-0.0055580399  0.1051462224 -0.0076810222
-0.4986748966 -0.5257311121 -0.6891517578
-0.0526465096  0.9959593140 -0.0727556869
10 0 2 7 15 30 42 22 11 4 1 3
10 0 3 9 18 35 47 27 14 6 2 3
5 0 1 5 8 3 
10 1 4 10 21 39 55 43 24 12 5 3
5 2 6 13 16 7 
10 3 8 17 33 52 58 54 36 19 9 3
5 4 11 23 20 10 
10 5 12 25 44 46 51 49 32 17 8 3
10 6 14 28 48 57 41 52 33 26 13 3
10 7 16 31 24 43 53 59 50 29 15 3
5 9 19 37 34 18 
10 10 20 38 32 49 29 50 56 40 21 3
10 11 22 41 57 59 53 35 18 34 23 3
5 12 24 31 45 25 
10 13 26 38 20 23 34 37 45 31 16 3
5 14 27 46 44 28 
5 15 29 49 51 30 
5 17 32 38 26 33 
10 19 36 40 56 48 28 44 25 45 37 3
5 21 40 36 54 39 
5 22 42 58 52 41 
10 27 47 55 39 54 58 42 30 51 46 3
5 35 53 43 55 47 
5 48 56 50 59 57 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 6 0 
3 2 7 3 
3 4 8 1 
3 0 9 4 
3 5 7 2 
3 1 10 5 
3 3 11 6 
3 6 12 0 
3 7 13 3 
3 4 14 8 
3 8 15 1 
3 0 16 9 
3 9 14 4 
3 5 17 7 
3 1 12 10 
3 10 18 5 
3 11 14 6 
3 3 19 11 
3 12 20 0 
3 14 12 6 
3 13 9 3 
3 7 18 13 
3 14 17 8 
3 15 21 1 
3 8 18 15 
3 16 11 9 
3 0 21 16 
3 13 14 9 
3 17 11 7 
3 5 8 17 
3 14 10 12 
3 1 22 12 
3 18 19 5 
3 14 18 10 
3 11 14 17 
3 3 21 19 
3 18 11 19 
3 12 8 20 
3 20 21 0 
3 9 22 3 
3 7 15 18 
3 18 13 14 
3 7 21 15 
3 21 22 1 
3 8 23 18 
3 16 7 11 
3 11 23 9 
3 21 16 7 
3 5 20 8 
3 9 12 22 
3 21 5 19 
3 3 21 22 
3 18 11 23 
3 12 23 8 
3 20 21 5 
3 23 9 12 
truncated dodecadodecahedron
medial disdyakistriacontahedron
5/3 2 5|
(10/3.4.10)
icosahedral group
A5
12{10}+30{4}+12{10/3}
63 120 180 54 120 3 0 0 -6 3 3 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.5749595746  0.0000000000  0.8181818182
 0.1379435501  0.5581667218  0.8181818182
-0.5691632311  0.0814354272  0.8181818182
 0.3575585655  0.5581667218  0.7487334525
 0.9361004773  0.0814354272  0.3421756384
-0.4312196809  0.6396021491  0.6363636364
 0.6276493222  0.2132007164  0.7487334525
-0.9151291095  0.2132007164  0.3421756384
 0.7186994682  0.6396021491  0.2727272727
-0.0830397963  0.2132007164  0.9734730848
 0.9454791582  0.2132007164 -0.2462003575
-0.8624393619  0.4264014327  0.2727272727
 0.1870509604 -0.1317652891  0.9734730848
 0.8508466748 -0.2635305783  0.4545454545
-0.5633668875  0.6899320110  0.4545454545
-0.9057504287  0.3449660055 -0.2462003575
 0.8624393619  0.4264014327 -0.2727272727
 0.4066659758 -0.1317652891  0.9040247191
-0.4348020182 -0.2635305783  0.8611032686
 0.7222818055  0.6899320110  0.0479876405
 0.5995132797  0.3449660055 -0.7222065373
-0.7338744926  0.0000000000  0.6792850868
-0.9910042312  0.0000000000 -0.1338305414
 0.4102483131 -0.6084965838  0.6792850868
-0.0303500487  0.4264014327  0.9040247191
 0.7222818055 -0.6899320110  0.0479876405
-0.5539882067  0.8216973001 -0.1338305414
-0.4348020182  0.2635305783  0.8611032686
-0.5446095259  0.4264014327 -0.7222065373
 0.9910042312  0.0000000000  0.1338305414
 0.7338744926  0.0000000000 -0.6792850868
 0.0549037538 -0.6084965838  0.7916549030
 0.5446095259  0.4264014327  0.7222065373
-0.5633668875 -0.6899320110  0.4545454545
 0.3763159271  0.8216973001 -0.4280185393
 0.8508466748  0.2635305783  0.4545454545
 0.0303500487  0.4264014327 -0.9040247191
-0.8624393619 -0.4264014327  0.2727272727
-0.3821122706  0.4767312946  0.7916549030
-0.7678068785 -0.4767312946 -0.4280185393
 0.5539882067 -0.8216973001  0.1338305414
-0.1589149180  0.8528028654  0.4974669050
 0.3611409028 -0.7713674382  0.5239938202
 0.2910621246 -0.9031327273 -0.3156487232
-0.4102483131  0.6084965838 -0.6792850868
-0.8660216992  0.0503298619  0.4974669050
-0.2174010091 -0.2946361436  0.9305516343
-0.4160446566  0.8528028654 -0.3156487232
 0.8624393619 -0.4264014327 -0.2727272727
 0.7678068785  0.4767312946  0.4280185393
 0.3821122706 -0.4767312946 -0.7916549030
-0.3763159271 -0.8216973001  0.4280185393
 0.4160446566  0.8528028654  0.3156487232
 0.0057963435 -0.7713674382  0.6363636364
-0.4196269939 -0.9031327273 -0.0909090909
-0.0549037538  0.6084965838 -0.7916549030
 0.9945865685  0.0503298619 -0.0909090909
 0.7129031247 -0.2946361436  0.6363636364
 0.1589149180  0.8528028654 -0.4974669050
-0.7186994682 -0.6396021491 -0.2727272727
-0.7280781490  0.6084965838  0.3156487232
 0.0584860911  0.8216973001  0.5669152707
-0.7771855594 -0.6084965838  0.1603574566
-0.2781011065 -0.8216973001 -0.4974669050
 0.9057504287 -0.3449660055  0.2462003575
 0.5633668875 -0.6899320110 -0.4545454545
-0.1495362372  0.9845681546 -0.0909090909
-0.0700787782 -0.9845681546  0.1603574566
-0.8508466748  0.2635305783 -0.4545454545
-0.1870509604  0.1317652891 -0.9734730848
-0.6486206900 -0.5078368599  0.5669152707
-0.8566430183  0.5078368599 -0.0909090909
 0.4312196809 -0.6396021491 -0.6363636364
 0.7771855594  0.6084965838 -0.1603574566
 0.2781011065  0.8216973001  0.4974669050
 0.7280781490 -0.6084965838 -0.3156487232
-0.0584860911 -0.8216973001 -0.5669152707
-0.5995132797 -0.3449660055  0.7222065373
-0.7222818055 -0.6899320110 -0.0479876405
 0.0700787782  0.9845681546 -0.1603574566
 0.1495362372 -0.9845681546  0.0909090909
 0.4348020182  0.2635305783 -0.8611032686
-0.4066659758  0.1317652891 -0.9040247191
 0.8566430183 -0.5078368599  0.0909090909
 0.6486206900  0.5078368599 -0.5669152707
-0.9361004773 -0.0814354272 -0.3421756384
-0.3575585655 -0.5581667218 -0.7487334525
-0.2874797873  0.9534625892  0.0909090909
 0.4196269939  0.9031327273  0.0909090909
-0.2874797873 -0.9534625892  0.0909090909
-0.9945865685 -0.0503298619  0.0909090909
 0.9151291095 -0.2132007164 -0.3421756384
 0.5446095259 -0.4264014327  0.7222065373
 0.4348020182 -0.2635305783 -0.8611032686
-0.0057963435  0.7713674382 -0.6363636364
-0.4160446566 -0.8528028654 -0.3156487232
-0.6276493222 -0.2132007164 -0.7487334525
-0.7222818055  0.6899320110 -0.0479876405
 0.0303500487 -0.4264014327 -0.9040247191
-0.1589149180 -0.8528028654  0.4974669050
-0.7129031247  0.2946361436 -0.6363636364
 0.5691632311 -0.0814354272 -0.8181818182
-0.1379435501 -0.5581667218 -0.8181818182
 0.2874797873  0.9534625892 -0.0909090909
-0.2910621246  0.9031327273  0.3156487232
 0.2874797873 -0.9534625892 -0.0909090909
 0.8660216992 -0.0503298619 -0.4974669050
-0.9454791582 -0.2132007164  0.2462003575
-0.0303500487 -0.4264014327  0.9040247191
-0.8508466748 -0.2635305783 -0.4545454545
-0.3611409028  0.7713674382 -0.5239938202
 0.1589149180 -0.8528028654 -0.4974669050
 0.0830397963 -0.2132007164 -0.9734730848
 0.5633668875  0.6899320110 -0.4545454545
-0.5446095259 -0.4264014327 -0.7222065373
 0.4160446566 -0.8528028654  0.3156487232
 0.2174010091  0.2946361436 -0.9305516343
-0.5749595746  0.0000000000 -0.8181818182
-0.0000000000  0.0000000000 -1.0000000000
 0.0692731120  0.0542373073  0.2190608145
-0.0577275933  0.0856238581  0.2190608145
 0.0692731120  0.9732489895  0.2190608145
 0.1731827800  0.0856238581  0.1460405430
-0.3199055857 -0.6015009550  0.7320225525
-0.1650061983  0.0877578066  0.1442207056
 0.6826243091 -0.6015009550  0.4149947635
 0.2179261468  0.0877578066  0.0231268655
 0.1389438731 -0.0529184545  0.1911695527
-0.1966714664  0.1385423126  0.0278912618
-0.0037665860 -0.0529184545  0.2362985623
 0.1769493660  0.1385423126 -0.0902580193
-0.2309103733 -0.0000000000  0.0730202715
 0.9231499720  0.3717480345  0.0979669745
 0.1611457400 -0.1419951139  0.0979669745
-0.9231499720 -0.3717480345 -0.0979669745
-0.1611457400  0.1419951139 -0.0979669745
 0.2309103733 -0.0000000000 -0.0730202715
-0.6989774726  0.3717480345  0.6109287125
-0.0755194646 -0.1419951139  0.1728070835
 0.6989774726 -0.3717480345 -0.6109287125
 0.0755194646  0.1419951139 -0.1728070835
-0.6826243091  0.6015009550 -0.4149947635
-0.2179261468 -0.0877578066 -0.0231268655
 0.0516331291  0.1712477161  0.1632782908
 0.0873107439 -0.2241661707  0.0278912618
-0.1450383372 -0.0327054035  0.1911695527
-0.0516331291  0.1712477161 -0.1632782908
 0.3199055857  0.6015009550 -0.7320225525
 0.1650061983 -0.0877578066 -0.1442207056
-0.0553997152 -0.2241661707  0.0730202715
 0.2285824951 -0.0327054035  0.0730202715
-0.0896386221  0.1914607671  0.1181492812
-0.1412717512 -0.1914607671 -0.0451290097
 0.1966714664 -0.1385423126 -0.0278912618
 0.0163531634  0.2297529205  0.0517132434
-0.0163531634 -0.2297529205 -0.0517132434
-0.1389438731  0.0529184545 -0.1911695527
 0.2934456114  0.2297529205  0.9279565015
-0.2934456114 -0.2297529205 -0.9279565015
 0.1412717512  0.1914607671  0.0451290097
 0.0896386221 -0.1914607671 -0.1181492812
-0.1769493660 -0.1385423126  0.0902580193
 0.0037665860  0.0529184545 -0.2362985623
-0.1731827800 -0.0856238581 -0.1460405430
-0.0692731120 -0.9732489895 -0.2190608145
 0.0553997152  0.2241661707 -0.0730202715
-0.0692731120 -0.0542373073 -0.2190608145
-0.2285824951  0.0327054035 -0.0730202715
 0.0577275933 -0.0856238581 -0.2190608145
-0.0873107439  0.2241661707 -0.0278912618
 0.1450383372  0.0327054035 -0.1911695527
 0.0516331291 -0.1712477161  0.1632782908
-0.0516331291 -0.1712477161 -0.1632782908
10 0 2 7 13 25 33 18 10 4 1 3
4 0 3 6 2 
10 0 1 5 11 21 37 29 16 8 3 
4 1 4 9 5 
10 2 6 12 23 40 64 44 26 14 7 
10 3 8 15 28 46 61 39 22 12 6 3
10 4 10 19 34 55 77 51 31 17 9 
10 5 9 17 30 50 74 57 36 20 11 3
4 7 14 24 13 
4 8 16 27 15 
4 10 18 32 19 
4 11 20 35 21 
4 12 22 38 23 
10 13 24 41 66 94 117 95 67 42 25 
10 14 26 43 58 84 116 93 65 41 24 3
10 15 27 45 70 99 112 81 54 47 28 
10 16 29 48 72 101 111 98 69 45 27 3
4 17 31 49 30 
10 18 33 53 80 111 101 110 79 52 32 
10 19 32 52 78 109 100 71 47 54 34 3
10 20 36 58 43 68 96 115 83 56 35 
10 21 35 56 82 114 95 117 85 59 37 3
10 22 39 62 89 114 82 113 87 60 38 
10 23 38 60 86 108 79 110 91 63 40 3
4 25 42 53 33 
4 26 44 68 43 
4 28 47 71 46 
4 29 37 59 48 
10 30 49 73 103 97 69 98 105 75 50 
10 31 51 76 107 94 66 92 102 73 49 3
4 34 54 81 55 
4 36 57 84 58 
4 39 61 88 62 
4 40 63 90 64 
4 41 65 92 66 
10 42 67 89 62 88 104 75 105 80 53 3
10 44 64 90 106 77 55 81 112 96 68 3
4 45 69 97 70 
10 46 71 100 116 84 57 74 104 88 61 
10 48 59 85 107 76 106 90 63 91 72 
4 50 75 104 74 
4 51 77 106 76 
4 52 79 108 78 
4 56 83 113 82 
4 60 87 118 86 
10 65 93 109 78 108 86 118 119 102 92 
4 67 95 114 89 
10 70 97 103 119 118 87 113 83 115 99 3
4 72 91 110 101 
4 73 102 119 103 
4 80 105 98 111 
4 85 117 94 107 
4 93 116 100 109 
4 96 112 99 115 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 6 0 
3 2 7 3 
3 4 5 1 
3 0 8 4 
3 5 9 2 
3 7 6 3 
3 6 10 0 
3 2 11 7 
3 4 12 5 
3 0 13 8 
3 8 14 4 
3 5 15 9 
3 9 16 2 
3 7 17 6 
3 10 18 0 
3 6 19 10 
3 11 20 7 
3 2 21 11 
3 12 22 5 
3 4 23 12 
3 13 14 8 
3 0 24 13 
3 14 25 4 
3 15 16 9 
3 5 26 15 
3 16 27 2 
3 7 28 17 
3 17 29 6 
3 19 18 10 
3 18 24 0 
3 6 30 19 
3 21 20 11 
3 20 31 7 
3 27 21 2 
3 23 22 12 
3 22 32 5 
3 4 33 23 
3 13 34 14 
3 24 35 13 
3 14 20 25 
3 25 36 4 
3 15 37 16 
3 5 38 26 
3 26 19 15 
3 16 39 27 
3 28 29 17 
3 7 40 28 
3 29 41 6 
3 19 42 18 
3 18 35 24 
3 30 15 19 
3 6 36 30 
3 21 43 20 
3 31 38 7 
3 14 31 20 
3 39 21 27 
3 23 44 22 
3 32 38 5 
3 22 35 32 
3 33 39 23 
3 36 33 4 
3 34 45 14 
3 13 29 34 
3 35 46 13 
3 20 36 25 
3 37 28 16 
3 15 47 37 
3 38 19 26 
3 16 48 39 
3 28 49 29 
3 38 40 7 
3 40 35 28 
3 29 39 41 
3 41 36 6 
3 19 45 42 
3 42 23 18 
3 18 50 35 
3 36 15 30 
3 21 22 43 
3 43 47 20 
3 14 38 31 
3 39 51 21 
3 23 45 44 
3 44 47 22 
3 35 38 32 
3 22 46 35 
3 36 39 33 
3 48 23 39 
3 29 45 34 
3 45 52 14 
3 13 51 29 
3 46 21 13 
3 20 53 36 
3 47 28 37 
3 28 50 16 
3 15 53 47 
3 38 52 19 
3 16 18 48 
3 49 45 29 
3 47 49 28 
3 38 40 35 
3 35 28 50 
3 39 41 36 
3 29 39 51 
3 45 42 23 
3 19 45 52 
3 23 18 48 
3 18 50 16 
3 36 15 53 
3 22 43 47 
3 21 22 46 
3 47 20 53 
3 14 38 52 
3 51 21 13 
3 45 47 44 
3 49 45 47 
inverted snub dodecadodecahedron
medial inverted pentagonal hexecontahedron
|5/3 2 5
(3.5/3.3.3.5)
icosahedral group
A5
12{5}+60{3}+12{5/3}
64 60 150 84 60 9 0 0 -6 3 5 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9505389400  0.0000000000  0.3106054144
 0.2252718768  0.9234591805  0.3106054144
 0.8112598353  0.4953602287  0.3106054144
-0.2889844000  0.9055453015  0.3106054144
-0.9482348826 -0.0661429059  0.3106054144
 0.5897694300 -0.0661429059 -0.8048584567
 0.3850026607  0.9055453015 -0.1782152018
 0.5573198493  0.4377082809 -0.7055537162
-0.4709954327  0.1594257169  0.8676097874
 0.6720341587 -0.0753689321  0.7366747000
-0.2761142752  0.6173097225  0.7366747000
 0.2950721213 -0.4002320578  0.8676097874
 0.8005020002 -0.5722201408 -0.1782152018
-0.9797305684  0.0914732487 -0.1782152018
-0.4850646484 -0.1093871277  0.8676097874
-0.0776254431  0.4911492110  0.8676097874
-0.4470814740  0.8765600364 -0.1782152018
-0.5837373293 -0.1070214698 -0.8048584567
-0.0305345625  0.8765600364 -0.4803229570
-0.4885089715  0.3978663999 -0.7765702239
 0.6822034907  0.1918133228  0.7055537162
 0.9068404918 -0.1219494938 -0.4034459610
 0.6280254238  0.6350267068  0.4498056789
 0.9074753675 -0.4197944019  0.0161591306
 0.0662694728 -0.6265357487 -0.7765702239
-0.5692643226 -0.7985238317  0.1956982912
 0.4568451653 -0.5417438957  0.7055537162
-0.1299819960 -0.8836172995  0.4498056789
 0.5895721585  0.8070147898 -0.0336422200
-0.5234589817  0.7504812130 -0.4034459610
 0.4007400217 -0.8959359724 -0.1915885392
 0.9945763348  0.0855188418  0.0591983266
-0.0076279270 -0.7569762005  0.6533979236
-0.3063909428 -0.8218360221 -0.4803229570
-0.4897789665 -0.5772241483  0.6533979236
-0.4053104966 -0.9140362596  0.0161591306
 0.1584253171  0.8200264597  0.5499618390
-0.8270506245  0.5611198317 -0.0336422200
-0.7034190217 -0.4502706470  0.5499618390
-0.1409472501  0.0818639196 -0.9866266626
-0.9653847065 -0.1769920905 -0.1915885392
-0.8809267432  0.4308947110  0.1956982912
 0.8861844855  0.1438774958 -0.4404274331
-0.1051400207 -0.1847560597 -0.9771441933
 0.6358781390  0.5897865144 -0.4978060464
 0.2874702454 -0.4819231848 -0.8277142635
-0.7311680197 -0.6296283954 -0.2626050469
 0.3681846210 -0.8724307068  0.3214105579
 0.1681444855  0.7640334636 -0.6228806455
-0.5294657581  0.7850867877  0.3214105579
-0.0773062511 -0.9216496181 -0.3802442964
 0.3662906510  0.0161043166 -0.9303611180
 0.6023558347 -0.7546105427  0.2602506049
 0.4177101363 -0.7946961169 -0.4404274331
 0.2460872708  0.1028921402  0.9637708559
-0.8447900947  0.0442149038  0.5332679797
-0.7081172394 -0.5007585401 -0.4978060464
-0.2634083151  0.5441095536 -0.7965932797
-0.7705003202 -0.0094229209 -0.6373699594
 0.0347733835  0.0273103460  0.0479456261
 0.0221937153  0.0303790744  0.0479456261
 0.0154457535  0.0414303258  0.0479456261
-0.0365894750  0.0248244539  0.0479456261
 0.0347733835 -0.9982444734  0.0479456261
 0.0569390737  0.0248244539 -0.0198875498
 0.0531075573  0.0287610955 -0.0081620442
 0.0512555391  0.0402551137 -0.0024943533
-0.7983984023  0.3985080838 -0.4513881903
 0.0126076932  0.0297962381  0.0566308796
 0.0245528255  0.0210696106  0.0566308796
 0.0563926334 -0.0141094994  0.0295739612
 0.1529062285  0.4101421715 -0.8991123870
-0.0518662103  0.0262507772  0.0295739612
-0.0407008533  0.0276138549  0.0359881617
-0.0435607236  0.0384924725  0.0295739612
-0.0585284569  0.0208021960 -0.0198875498
-0.0007246349  0.0208021960 -0.0618107580
 0.0093187938  0.0249959101 -0.0547959559
 0.0143807266  0.0365909393 -0.0520396399
-0.6678347106  0.4530983827  0.5905071167
 0.0583803788  0.0288467118  0.0036639936
 0.0618929964  0.0193100395 -0.0070855930
 0.0452796477 -0.0179993596 -0.0433543864
-0.0172538804 -0.0349221758  0.0523122501
-0.0093187938 -0.0249959101  0.0547959559
 0.0021014290 -0.0236461716  0.0607475829
 0.6678347106 -0.4530983827 -0.5905071167
 0.0291449034  0.0398939600  0.0425778443
-0.0062105643  0.0643176201  0.0088599601
-0.8714085158 -0.4719227321  0.1339258511
 0.0499914832 -0.0358036921  0.0217433552
 0.0486579924 -0.0242868764  0.0275096281
 0.0436238866 -0.0336369212  0.0349190536
 0.0143872332 -0.0636145476 -0.0001520171
-0.0525204118 -0.0386705249 -0.0001520171
-0.0531075573 -0.0287610955  0.0081620442
-0.0553064338 -0.0275614572  0.0208660182
 0.7983984023 -0.3985080838  0.4513881903
-0.0341191820  0.0376109561  0.0409282746
-0.0475577418  0.0178034772  0.0409282746
-0.0095878575 -0.0148125719  0.0627892265
 0.8714085158  0.4719227321 -0.1339258511
-0.0459405885  0.0231100357 -0.0401150201
-0.0486579924  0.0242868764 -0.0275096281
-0.0442189464  0.0355015672 -0.0322203316
 0.3641627194  0.4984711306  0.7867096324
 0.0221955507  0.0247144114 -0.0561282608
 0.0128599239  0.0149564314 -0.0621671439
-0.0275690461 -0.0211064978 -0.0552113186
 0.0578830028 -0.0237350817  0.0184399064
-0.3641627194 -0.4984711306 -0.7867096324
 0.0503647635  0.0377692216 -0.0170500075
 0.0078874982  0.0645938774  0.0043868710
-0.1529062285 -0.4101421715  0.8991123870
 0.0353840547 -0.0391955450 -0.0382819042
 0.0407008533 -0.0276138549 -0.0359881617
 0.0459818845 -0.0365909393 -0.0282948002
 0.0029384979 -0.0644614796 -0.0094820427
 0.0021192465 -0.0608375115  0.0029220223
 0.0090286636 -0.0631393379  0.0136284081
-0.0215500966 -0.0217815257  0.0575759041
-0.0497697037 -0.0396338675  0.0143512855
-0.0060124429  0.0631762251 -0.0150479691
-0.0021192465  0.0608375115 -0.0029220223
 0.0080099440  0.0638884564 -0.0103890418
 0.0002152729  0.0341730572 -0.0555516163
 0.0349500485 -0.0277053167 -0.0475892403
 0.0520976973 -0.0234909763 -0.0314297666
-0.0347733835  0.9982444734 -0.0479456261
 0.0475800150 -0.0202291728  0.0397586343
-0.0094957793 -0.0645097026 -0.0014678904
-0.0057318499 -0.0636925741  0.0128151536
-0.0614790292 -0.0191369547  0.0103890418
-0.0597571729 -0.0260027361 -0.0026008184
-0.0262717496 -0.0415627235 -0.0428504544
-0.0148012004  0.0634414628 -0.0031514317
-0.0026364338 -0.0360745903  0.0542724553
-0.0134385598 -0.0397018775 -0.0499699139
-0.0221937153 -0.0303790744 -0.0479456261
-0.0350048704 -0.0300701469 -0.0460898207
-0.0519986769  0.0340752438 -0.0197190674
-0.0547843524  0.0140253247 -0.0324929418
-0.0142403331 -0.0270592347 -0.0576093481
3 0 2 1 
5 0 3 11 10 2 3
3 0 4 3 
3 0 5 4 
5 0 1 6 18 5 
3 1 7 6 
5 1 8 23 22 7 3
3 1 2 8 
5 2 9 26 25 8 
3 2 10 9 
3 3 12 11 
3 3 13 12 
5 3 4 14 34 13 
3 4 15 14 
5 4 5 16 38 15 3
3 5 17 16 
3 5 18 17 
3 6 19 18 
5 6 20 45 44 19 3
3 6 7 20 
5 7 21 33 47 20 
3 7 22 21 
3 8 24 23 
3 8 25 24 
3 9 27 26 
5 9 28 55 39 27 3
3 9 10 28 
5 10 29 58 57 28 
3 10 11 29 
3 11 30 29 
5 11 12 31 44 30 
3 12 32 31 
5 12 13 21 48 32 3
3 13 33 21 
3 13 34 33 
3 14 35 34 
5 14 36 56 57 35 3
3 14 15 36 
5 15 37 45 46 36 
3 15 38 37 
3 16 39 38 
3 16 27 39 
5 16 17 40 54 27 
3 17 41 40 
5 17 18 42 58 41 3
3 18 19 42 
5 19 43 53 35 42 
3 19 44 43 
3 20 46 45 
3 20 47 46 
3 21 22 48 
5 22 49 38 39 48 
3 22 23 49 
3 23 50 49 
5 23 24 51 41 50 
3 24 52 51 
5 24 25 43 31 52 3
3 25 53 43 
3 25 26 53 
5 26 54 33 34 53 3
3 26 27 54 
3 28 56 55 
3 28 57 56 
3 29 50 58 
5 29 30 37 49 50 3
3 30 45 37 
3 30 44 45 
3 31 43 44 
3 31 32 52 
5 32 55 56 59 52 
3 32 48 55 
3 33 54 47 
3 34 35 53 
3 35 57 42 
3 36 59 56 
3 36 46 59 
3 37 38 49 
3 39 55 48 
3 40 47 54 
5 40 51 59 46 47 3
3 40 41 51 
3 41 58 50 
3 42 57 58 
3 51 52 59 
5 4 0 1 2 3 
5 4 5 6 7 0 
5 7 8 9 1 0 
5 1 10 11 12 2 
5 12 13 14 3 2 
5 14 15 16 4 3 
5 4 17 18 19 5 
5 19 20 21 6 5 
5 6 22 23 8 7 
5 8 24 25 26 9 
5 26 27 28 1 9 
5 28 29 30 10 1 
5 30 31 32 11 10 
5 32 33 34 12 11 
5 12 35 36 37 13 
5 37 38 39 14 13 
5 14 40 41 42 15 
5 42 43 44 16 15 
5 44 45 17 4 16 
5 45 46 47 18 17 
5 18 48 49 20 19 
5 20 33 32 50 21 
5 50 51 52 6 21 
5 52 53 54 22 6 
5 54 55 56 23 22 
5 56 57 58 8 23 
5 58 59 60 24 8 
5 60 42 41 25 24 
5 25 61 62 27 26 
5 27 63 64 29 28 
5 64 65 66 30 29 
5 30 67 56 68 31 
5 68 69 70 32 31 
5 20 71 59 34 33 
5 59 72 35 12 34 
5 72 46 73 36 35 
5 36 74 75 38 37 
5 38 65 64 76 39 
5 76 51 40 14 39 
5 51 77 25 41 40 
5 42 78 79 80 43 
5 80 54 81 44 43 
5 44 82 73 46 45 
5 46 57 56 67 47 
5 66 18 47 67 30 
5 38 48 18 66 65 
5 75 79 49 48 38 
5 78 71 20 49 79 
5 70 77 51 50 32 
5 64 53 52 51 76 
5 63 81 54 53 64 
5 79 83 55 54 80 
5 83 69 68 56 55 
5 57 58 59 72 46 
5 59 60 42 78 71 
5 69 61 25 77 70 
5 69 74 36 62 61 
5 82 27 62 36 73 
5 27 63 81 44 82 
5 74 75 79 83 69 
great dodecicosidodecahedron
great dodecacronic hexecontahedron
5/2 3|5/3
(10/3.5/2.10/3.3)
icosahedral group
A5
12{10/3}+20{3}+12{5/2}
65 60 120 44 60 10 0 0 -16 3 4 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9996324920  0.0000000000  0.0271086873
-0.3453645319  0.9380770007  0.0271086873
-0.9468654869  0.3204853643  0.0271086873
 0.0263835025 -0.9992842588  0.0271086873
 0.0364611038  0.9380770007 -0.3445027268
 0.0527670051  0.3204853643 -0.9457826254
-0.7334184677 -0.2592781062  0.6283885859
-0.3189810294 -0.0612072581 -0.9457826254
 0.8677149793  0.3583135302 -0.3445027268
-0.3352869307 -0.8768697425 -0.3445027268
 0.2398305218  0.7400061526  0.6283885859
-0.9367878857 -0.0612072581 -0.3445027268
 0.6480396600 -0.2592781062 -0.7161141409
-0.3678987333  0.3583135302  0.8580570704
 0.6216561575  0.7400061526  0.2567771718
-0.4672044434 -0.5185562123 -0.7161141409
 0.4796610435 -0.8390415766  0.2567771718
-0.7233408665 -0.6409707286  0.2567771718
 0.4633551422 -0.2214499403  0.8580570704
 0.8514090780 -0.4573489542  0.2567771718
 0.2336022217 -0.4573489542  0.8580570704
 0.5060445461  0.4807280465 -0.7161141409
 0.2762916255 -0.6409707286 -0.7161141409
-0.7031856640 -0.5185562123 -0.4864456563
 0.2436798229 -0.8390415766  0.4864456563
 0.8451807779 -0.2214499403  0.4864456563
-0.7295691665  0.4807280465  0.4864456563
-0.2436798229  0.8390415766 -0.4864456563
 0.7031856640  0.5185562123  0.4864456563
-0.4998162460  0.7166270604  0.4864456563
 0.7295691665 -0.4807280465 -0.4864456563
-0.4998162460 -0.7166270604  0.4864456563
 0.4998162460 -0.7166270604 -0.4864456563
-0.8451807779  0.2214499403 -0.4864456563
 0.4998162460  0.7166270604 -0.4864456563
-0.4796610435  0.8390415766 -0.2567771718
 0.4672044434  0.5185562123  0.7161141409
-0.5060445461 -0.4807280465  0.7161141409
-0.4633551422  0.2214499403 -0.8580570704
-0.6480396600  0.2592781062  0.7161141409
 0.3678987333 -0.3583135302 -0.8580570704
-0.2336022217  0.4573489542 -0.8580570704
-0.6216561575 -0.7400061526 -0.2567771718
-0.2762916255  0.6409707286  0.7161141409
 0.7233408665  0.6409707286 -0.2567771718
-0.8514090780  0.4573489542 -0.2567771718
 0.7334184677  0.2592781062 -0.6283885859
-0.8677149793 -0.3583135302  0.3445027268
-0.2398305218 -0.7400061526 -0.6283885859
-0.0364611038 -0.9380770007  0.3445027268
 0.9367878857  0.0612072581  0.3445027268
 0.3352869307  0.8768697425  0.3445027268
-0.0527670051 -0.3204853643  0.9457826254
 0.3189810294  0.0612072581  0.9457826254
 0.3453645319 -0.9380770007 -0.0271086873
 0.9468654869 -0.3204853643 -0.0271086873
-0.9996324920  0.0000000000 -0.0271086873
-0.0263835025  0.9992842588 -0.0271086873
 0.0000000000  0.0000000000 -1.0000000000
 0.4931762648  0.7071067812  0.5067318540
-0.3915763668  0.3813742685  0.5067318540
-0.6938439517 -0.5116672736  0.5067318540
 0.4931762648 -0.4803270912  0.5067318540
 0.5253548247 -0.5116672736 -0.6798521231
 0.5171607473  0.3813742685 -0.3776956239
 0.0977538074  0.5937169362 -0.6071725516
-0.9541739697  0.1954395076 -0.2266173744
-0.2205551306  0.9486832981 -0.2266173744
-0.5909300722 -0.1133898450 -0.6071725516
-0.3675918843 -0.5270462767 -0.3776956239
-0.2006676869  0.1954395076 -0.9599666027
-0.6095993882  0.5937169362  0.0812582313
-0.3465455537 -0.7771855594  0.0812582313
 0.2006676869 -0.1954395076  0.9599666027
 0.7111992862 -0.1456720081  0.1689106180
 0.1643920883 -0.7071067812  0.1689106180
 0.7677683711  0.3669372463  0.0812582313
 0.9541739697 -0.1954395076  0.2266173744
 0.0906227633 -0.7771855594 -0.3442153914
 0.1495688629 -0.1456720081  0.7155168599
 0.0604151755  0.3669372463  0.7696890141
-0.1495688629  0.1456720081 -0.7155168599
 0.2205551306 -0.9486832981  0.2266173744
-0.3652148696 -0.0700787782  0.7696890141
 0.7793066430 -0.0700787782 -0.3442153914
-0.7111992862  0.1456720081 -0.1689106180
-0.0906227633  0.7771855594  0.3442153914
 0.6938439517  0.5116672736 -0.5067318540
-0.1643920883  0.7071067812 -0.1689106180
-0.0604151755 -0.3669372463 -0.7696890141
-0.7793066430  0.0700787782  0.3442153914
-0.4931762648 -0.7071067812 -0.5067318540
 0.3652148696  0.0700787782 -0.7696890141
-0.5253548247  0.5116672736  0.6798521231
 0.3465455537  0.7771855594 -0.0812582313
-0.7677683711 -0.3669372463 -0.0812582313
-0.5171607473 -0.3813742685  0.3776956239
 0.6095993882 -0.5937169362 -0.0812582313
 0.3675918843  0.5270462767  0.3776956239
 0.3915763668 -0.3813742685 -0.5067318540
-0.0977538074 -0.5937169362  0.6071725516
 0.5909300722  0.1133898450  0.6071725516
-0.4931762648  0.4803270912 -0.5067318540
10 0 2 9 19 30 35 26 14 5 1 3
5 0 3 11 7 2 2
10 0 4 12 14 25 24 27 21 10 3 3
3 0 1 4 
10 1 6 10 20 22 16 17 9 8 4 3
5 1 5 13 15 6 2
3 2 8 9 
10 2 7 16 28 40 43 42 30 18 8 3
10 3 6 15 27 39 45 44 34 22 11 3
3 3 10 6 
5 4 8 18 23 12 2
10 5 12 23 35 46 49 47 36 24 13 3
3 5 14 12 
3 7 17 16 
10 7 11 20 32 44 51 50 40 29 17 3
5 9 17 29 31 19 2
5 10 21 33 32 20 2
3 11 22 20 
10 13 25 37 47 55 54 45 33 21 15 3
3 13 24 25 
5 14 26 38 37 25 2
3 15 21 27 
5 16 22 34 41 28 2
10 18 19 31 43 53 56 49 38 26 23 3
3 18 30 19 
3 23 26 35 
5 24 36 48 39 27 2
3 28 29 40 
10 28 41 51 58 59 56 52 42 31 29 3
5 30 42 52 46 35 2
3 31 42 43 
3 32 34 44 
10 32 33 39 48 55 59 57 50 41 34 3
3 33 45 39 
10 36 37 38 46 52 53 57 58 54 48 3
3 36 47 37 
3 38 49 46 
5 40 50 57 53 43 2
3 41 50 51 
5 44 45 54 58 51 2
5 47 49 56 59 55 2
3 48 54 55 
3 52 56 53 
3 57 59 58 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 1 8 9 2 
4 2 10 4 3 
4 5 11 12 0 
4 4 9 8 5 
4 7 13 14 1 
4 6 4 10 7 
4 0 15 4 6 
4 4 16 2 9 
4 14 17 8 1 
4 2 12 11 10 
4 5 18 19 11 
4 2 20 0 12 
4 8 21 18 5 
4 7 22 4 13 
4 15 14 13 4 
4 10 23 24 7 
4 0 24 23 15 
4 4 17 14 16 
4 16 18 21 2 
4 22 8 17 4 
4 11 25 23 10 
4 19 2 26 11 
4 18 20 2 19 
4 20 23 25 0 
4 8 26 2 21 
4 7 27 28 22 
4 15 28 27 14 
4 0 29 7 24 
4 23 30 28 15 
4 14 31 32 16 
4 32 33 18 16 
4 22 32 31 8 
4 11 29 0 25 
4 26 34 35 11 
4 18 35 34 20 
4 34 36 23 20 
4 8 33 32 26 
4 7 37 14 27 
4 28 38 32 22 
4 29 28 30 7 
4 23 37 7 30 
4 14 39 8 31 
4 39 18 33 8 
4 11 36 34 29 
4 18 40 11 35 
4 32 41 34 26 
4 40 23 36 11 
4 37 32 38 14 
4 28 39 14 38 
4 34 42 28 29 
4 23 42 34 37 
4 39 34 41 18 
4 32 40 18 41 
4 40 28 42 23 
4 34 43 32 37 
4 28 43 34 39 
4 32 40 28 43 
small dodecahemicosahedron
small dodecahemicosacron
5/3 5/2|3
(6.5/3.6.5/2)
icosahedral group
A5
10{6}+6{5/2}+6{5/3}
66 30 60 22 30 0 1 1 -8 3 4 120 5 1 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8660254038  0.0000000000  0.5000000000
-0.8660254038  0.0000000000  0.5000000000
-0.6454972244  0.5773502692  0.5000000000
 0.6454972244 -0.5773502692  0.5000000000
 0.8660254038  0.0000000000 -0.5000000000
 0.7557613141  0.5773502692 -0.3090169944
 0.1102640897 -0.5773502692  0.8090169944
-0.1102640897  0.5773502692  0.8090169944
-0.7557613141 -0.5773502692 -0.3090169944
-0.8660254038  0.0000000000 -0.5000000000
-0.6454972244  0.5773502692 -0.5000000000
-0.1784110449  0.9341723590 -0.3090169944
-0.4670861795 -0.3568220898  0.8090169944
 0.4670861795  0.3568220898  0.8090169944
 0.1784110449 -0.9341723590 -0.3090169944
 0.6454972244 -0.5773502692 -0.5000000000
 0.7557613141  0.5773502692  0.3090169944
 0.1102640897 -0.5773502692 -0.8090169944
 0.0000000000 -0.0000000000 -1.0000000000
-0.1102640897  0.5773502692 -0.8090169944
 0.9341723590 -0.3568220898  0.0000000000
-0.3568220898 -0.9341723590  0.0000000000
-0.7557613141 -0.5773502692  0.3090169944
 0.3568220898  0.9341723590  0.0000000000
-0.9341723590  0.3568220898  0.0000000000
-0.1784110449  0.9341723590  0.3090169944
-0.4670861795 -0.3568220898 -0.8090169944
 0.4670861795  0.3568220898 -0.8090169944
 0.1784110449 -0.9341723590  0.3090169944
 0.0000000000  1.0000000000  0.0000000000
-0.4911234732  0.1875924741  0.8506508084
-0.6666666667 -0.7453559925  0.0000000000
 0.4911234732 -0.1875924741  0.8506508084
 0.3333333333 -0.7453559925 -0.5773502692
 0.9822469464  0.1875924741  0.0000000000
-0.9822469464 -0.1875924741  0.0000000000
 0.3333333333 -0.7453559925  0.5773502692
 0.7453559925  0.3333333333  0.5773502692
-0.6070619982  0.7946544723  0.0000000000
 0.6070619982 -0.7946544723  0.0000000000
 0.7453559925  0.3333333333 -0.5773502692
 0.4911234732 -0.1875924741 -0.8506508084
 0.3035309991  0.7946544723 -0.5257311121
 0.1273220038  0.3333333333  0.9341723590
-0.8726779962  0.3333333333  0.3568220898
-0.3035309991 -0.7946544723  0.5257311121
 0.3035309991  0.7946544723  0.5257311121
-0.8726779962  0.3333333333 -0.3568220898
 0.1273220038  0.3333333333 -0.9341723590
-0.3035309991 -0.7946544723 -0.5257311121
-0.4911234732  0.1875924741 -0.8506508084
6 0 1 5 19 10 2 
5 0 2 8 13 3 3
6 0 3 11 19 16 4 
5 0 1 7 14 4 2
6 1 7 23 10 20 6 
5 1 6 21 17 5 3
5 2 10 23 25 9 2
6 2 9 18 5 17 8 
6 3 13 29 16 28 12 
5 3 12 25 26 11 2
5 4 16 29 21 15 3
6 4 15 27 11 26 14 
5 5 18 28 16 19 2
5 6 20 24 28 12 2
6 6 12 25 23 29 21 
6 7 14 24 20 27 22 
5 7 22 13 29 23 3
5 8 17 26 14 24 2
6 8 24 28 18 22 13 
6 9 25 26 17 21 15 
5 9 15 27 22 18 3
5 10 19 11 27 20 3
4 3 0 1 2 
4 3 4 5 0 
4 6 0 1 7 
4 1 8 9 2 
4 10 2 3 11 
4 5 7 12 0 
4 13 4 5 14 
4 3 15 16 4 
4 17 7 1 18 
4 6 19 20 7 
4 21 0 6 4 
4 9 11 21 2 
4 13 8 9 14 
4 16 18 1 8 
4 17 11 3 15 
4 10 19 20 11 
4 12 2 10 8 
4 5 19 17 7 
4 20 18 12 7 
4 12 0 21 2 
4 21 15 13 4 
4 10 14 5 19 
4 20 15 16 18 
4 16 14 6 4 
4 13 18 17 15 
4 9 19 6 14 
4 9 11 17 19 
4 21 11 20 15 
4 13 8 12 18 
4 16 8 10 14 
great dodecicosahedron
great dodecicosacron
5/3 5/2 3|
(6.10/3.6/5.10/7)
icosahedral group
A5
10{6}+6{10/3}+6{10/7}+10{6/5}
67 60 120 32 60 0 0 1 -28 4 4 120 5 0 1
 0.0000000000  0.0000000000  1.0000000000
 0.7913673487  0.0000000000  0.6113409191
-0.6820030709  0.4014151117  0.6113409191
-0.4944105968 -0.6179162098  0.6113409191
 0.1126514014  0.7833083316  0.6113409191
 0.9007316265  0.4014151117 -0.1659772426
 0.7860486710 -0.6179162098 -0.0175226837
 0.4149268310  0.7833083316  0.4628863603
-0.7549125894 -0.4645892808  0.4628863603
-0.5726387930  0.8028302234 -0.1659772426
-0.8761697921 -0.4525240881 -0.1659772426
-0.0086058013 -0.9998094297 -0.0175226837
-0.8708511144  0.1653921218  0.4628863603
 0.8343963552  0.2991971590  0.4628863603
-0.2691077939  0.9487004534 -0.1659772426
 0.8278221080 -0.4645892808 -0.3144318014
 0.2187285557  0.8028302234 -0.5546363234
 0.4042894756 -0.4525240881 -0.7948408455
 0.8987000724  0.1653921218 -0.4061817646
-0.1437874830  0.2991971590  0.9432954043
 0.0331676357  0.9487004534 -0.3144318014
-0.0331676357 -0.9487004534  0.3144318014
-0.6906088722 -0.5983943180 -0.4061817646
-0.0278489580 -0.3307842435  0.9432954043
-0.5779574707  0.1849140136 -0.7948408455
 0.1544248384  0.9366352607  0.3144318014
-0.1544248384 -0.9366352607 -0.3144318014
-0.7635183907  0.3307842435 -0.5546363234
 0.1007584765 -0.5983943180 -0.7948408455
-0.7614868366  0.5668072335 -0.3144318014
 0.7614868366 -0.5668072335  0.3144318014
 0.2756820411 -0.1849140136  0.9432954043
 0.2166970016  0.5668072335 -0.7948408455
-0.8278221080  0.4645892808  0.3144318014
 0.2691077939 -0.9487004534  0.1659772426
 0.7635183907 -0.3307842435  0.5546363234
-0.2756820411  0.1849140136 -0.9432954043
 0.0278489580  0.3307842435 -0.9432954043
-0.2166970016 -0.5668072335  0.7948408455
 0.5779574707 -0.1849140136  0.7948408455
 0.7549125894  0.4645892808 -0.4628863603
-0.4149268310 -0.7833083316 -0.4628863603
-0.4042894756  0.4525240881  0.7948408455
 0.1437874830 -0.2991971590 -0.9432954043
 0.8761697921  0.4525240881  0.1659772426
 0.5726387930 -0.8028302234  0.1659772426
-0.2187285557 -0.8028302234  0.5546363234
-0.8343963552 -0.2991971590 -0.4628863603
 0.8708511144 -0.1653921218 -0.4628863603
-0.1007584765  0.5983943180  0.7948408455
-0.9007316265 -0.4014151117  0.1659772426
-0.1126514014 -0.7833083316 -0.6113409191
-0.8987000724 -0.1653921218  0.4061817646
 0.6906088722  0.5983943180  0.4061817646
 0.6820030709 -0.4014151117 -0.6113409191
-0.7913673487  0.0000000000 -0.6113409191
-0.7860486710  0.6179162098  0.0175226837
 0.4944105968  0.6179162098 -0.6113409191
 0.0086058013  0.9998094297  0.0175226837
 0.0000000000  0.0000000000 -1.0000000000
 0.2317571228  0.8506508084  0.4718917654
-0.3015891505 -0.0555029103  0.4718917654
-0.8089973662  0.3504874081  0.4718917654
 0.2317571228  0.2008114159  0.4718917654
 0.8680129287  0.3504874081 -0.3517273552
 0.5578135237 -0.0555029103  0.0498189392
-0.2259811885  0.4702282018  0.2110364131
 0.0842182165 -0.1752437040  0.9809163757
-0.8159632084 -0.4587939735 -0.3517273552
-0.3051588742 -0.4702282018  0.0498189392
 0.7247791497 -0.1752437040  0.6663218655
 0.3051588742  0.4702282018 -0.0498189392
 0.2259811885 -0.4702282018 -0.2110364131
 0.2204861533 -0.4587939735 -0.8607519655
 0.0772523743 -0.9845250856  0.1572972551
-0.1828226219  0.3804226065 -0.3722538870
 0.3159753393  0.6754071043 -0.6663218655
-0.3159753393 -0.6754071043  0.6663218655
-0.5578135237  0.0555029103 -0.0498189392
 0.7204740224 -0.6754071043  0.1572972551
-0.7247791497  0.1752437040 -0.6663218655
-0.7204740224  0.6754071043 -0.1572972551
 0.3015891505  0.0555029103 -0.4718917654
-0.0842182165  0.1752437040 -0.9809163757
 0.1828226219 -0.3804226065  0.3722538870
-0.8680129287 -0.3504874081  0.3517273552
-0.2317571228 -0.2008114159 -0.4718917654
-0.0772523743  0.9845250856 -0.1572972551
 0.8159632084  0.4587939735  0.3517273552
 0.8089973662 -0.3504874081 -0.4718917654
-0.2204861533  0.4587939735  0.8607519655
-0.2317571228 -0.8506508084 -0.4718917654
6 0 2 9 16 5 1 
10 0 3 12 19 38 52 42 23 8 2 3
6 0 4 14 27 10 3 5
10 0 1 7 19 39 53 49 31 13 4 7
6 1 6 17 37 20 7 5
10 1 5 15 35 44 48 30 13 18 6 3
10 2 4 14 33 49 58 56 42 25 9 7
6 2 8 21 30 13 4 5
6 3 11 28 36 29 12 
10 3 10 26 46 50 41 21 8 22 11 7
6 5 7 19 38 34 15 5
10 5 16 25 44 57 58 53 40 20 7 7
10 6 11 28 15 34 51 54 45 26 17 7
6 6 18 32 24 22 11 
6 8 23 35 15 28 22 
10 9 24 32 14 27 37 20 29 36 16 3
6 9 25 44 48 43 24 5
6 10 12 19 39 45 26 
10 10 27 33 50 55 56 52 47 29 12 3
6 13 31 46 26 17 18 5
6 14 33 50 41 43 32 
6 16 36 47 52 42 25 5
10 17 18 32 43 48 57 59 54 40 37 3
6 20 29 47 51 54 40 
10 21 23 35 34 38 39 45 46 31 30 3
6 21 41 55 56 42 23 
10 22 28 36 47 51 59 55 41 43 24 3
6 27 37 40 53 49 33 
6 30 48 57 58 49 31 5
6 34 35 44 57 59 51 
6 38 39 53 58 56 52 5
6 45 46 50 55 59 54 5
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 1 8 9 2 
4 2 6 7 3 
4 5 10 11 0 
4 4 12 13 5 
4 3 10 11 4 
4 7 9 14 1 
4 0 15 16 6 
4 9 17 18 2 
4 8 12 13 9 
4 1 17 18 8 
4 7 5 19 3 
4 2 15 20 6 
4 5 14 12 10 
4 11 21 15 0 
4 4 22 19 12 
4 13 22 19 5 
4 3 17 1 10 
4 11 23 15 4 
4 7 24 25 9 
4 13 26 14 9 
4 14 24 25 1 
4 15 13 26 16 
4 16 11 21 6 
4 9 19 12 17 
4 18 27 15 2 
4 8 26 14 12 
4 18 23 15 8 
4 24 28 5 7 
4 19 24 28 3 
4 22 20 15 13 
4 20 18 27 6 
4 12 29 24 10 
4 5 29 24 14 
4 21 26 8 15 
4 27 22 4 15 
4 1 30 24 10 
4 3 30 24 17 
4 11 27 22 23 
4 25 26 20 9 
4 25 6 21 1 
4 22 16 26 20 
4 16 5 29 11 
4 12 31 24 17 
4 9 31 24 19 
4 18 21 26 23 
4 28 22 16 5 
4 28 6 27 3 
4 31 18 20 9 
4 12 23 26 29 
4 18 30 1 21 
4 11 30 3 27 
4 22 31 12 23 
4 25 18 31 26 
4 30 6 25 18 
4 29 22 28 11 
4 28 6 30 11 
4 26 29 22 31 
great snub dodecicosidodecahedron
great hexagonal hexecontahedron
|5/3 5/2 3
(3.5/3.3.5/2.3.3)
icosahedral group
A5
80{3}+12{5/2}+12{5/3}
68 60 180 104 60 10 0 0 -16 3 6 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 1.0000000000  0.0000000000  0.0000000000
 0.0000000000  1.0000000000  0.0000000000
 0.7861513778  0.6180339887  0.0000000000
-0.6180339887  0.7861513778  0.0000000000
-1.0000000000 -0.0000000000  0.0000000000
 0.0000000000 -1.0000000000  0.0000000000
 0.0000000000 -0.0000000000 -1.0000000000
 0.0000000000 -0.7861513778 -0.6180339887
 0.0000000000  0.6180339887 -0.7861513778
 0.6180339887  0.0000000000 -0.7861513778
-0.7861513778  0.0000000000 -0.6180339887
-0.6180339887 -0.0000000000  0.7861513778
 0.7861513778 -0.0000000000  0.6180339887
-0.4858682718  0.6180339887  0.6180339887
 0.3819660113 -0.4858682718  0.7861513778
 0.6180339887 -0.7861513778  0.0000000000
-0.7861513778 -0.6180339887 -0.0000000000
-0.4858682718 -0.3819660113 -0.7861513778
-0.6180339887 -0.4858682718  0.6180339887
-0.0000000000  0.7861513778  0.6180339887
 0.0000000000 -0.6180339887  0.7861513778
 0.6180339887  0.4858682718 -0.6180339887
 0.7861513778 -0.3819660113  0.4858682718
-0.7861513778  0.4858682718  0.3819660113
 0.6180339887  0.6180339887  0.4858682718
 0.4858682718 -0.7861513778  0.3819660113
-0.6180339887 -0.6180339887 -0.4858682718
-0.4858682718  0.7861513778 -0.3819660113
 0.3819660113  0.7861513778 -0.4858682718
 0.4858682718 -0.6180339887 -0.6180339887
-0.3819660113 -0.7861513778  0.4858682718
-0.3819660113  0.4858682718 -0.7861513778
-0.3177508827 -0.8678342830 -0.3819660113
 0.8678342830 -0.1039022605 -0.4858682718
 0.4858682718  0.3819660113  0.7861513778
-0.8678342830  0.1039022605  0.4858682718
-0.1039022605  0.9183170948 -0.3819660113
-0.7861513778  0.3819660113 -0.4858682718
 0.7861513778 -0.4858682718 -0.3819660113
-0.3819660113  0.3177508827  0.8678342830
-0.4858682718 -0.8678342830  0.1039022605
 0.4858682718  0.8678342830 -0.1039022605
-0.3819660113  0.1039022605 -0.9183170948
 0.8678342830  0.3819660113 -0.3177508827
 0.1039022605  0.4858682718  0.8678342830
-0.8678342830 -0.3819660113  0.3177508827
-0.1039022605 -0.4858682718 -0.8678342830
-0.9183170948  0.3819660113 -0.1039022605
 0.9183170948 -0.3819660113  0.1039022605
 0.3177508827  0.8678342830  0.3819660113
-0.2360679775 -0.3177508827  0.9183170948
 0.1039022605 -0.9183170948  0.3819660113
 0.9183170948  0.2360679775  0.3177508827
 0.3819660113 -0.3177508827 -0.8678342830
 0.3819660113 -0.1039022605  0.9183170948
 0.3177508827 -0.9183170948 -0.2360679775
-0.3177508827  0.9183170948  0.2360679775
 0.2360679775  0.3177508827 -0.9183170948
-0.9183170948 -0.2360679775 -0.3177508827
 0.5773502692  0.5773502692  0.5773502692
 0.2805161775  0.5773502692  0.5773502692
 0.0970626198  0.8107067993  0.5773502692
-0.5773502692  0.2805161775  0.5773502692
-0.5773502692 -0.5773502692  0.5773502692
 0.5773502692 -0.5773502692  0.5773502692
 0.5773502692 -0.5773502692 -0.5773502692
 0.5773502692 -0.2805161775 -0.5773502692
 0.5773502692 -0.0970626198 -0.8107067993
 0.5773502692  0.5773502692 -0.2805161775
-0.0970626198  0.5773502692 -0.8107067993
-0.8107067993  0.5773502692  0.0970626198
 0.0970626198  0.5773502692  0.8107067993
 0.3938967115  0.4331280021  0.8107067993
 0.8107067993 -0.0970626198  0.2805161775
 0.8107067993 -0.0970626198 -0.5773502692
 0.0970626198  0.8107067993 -0.5773502692
-0.8107067993  0.0970626198 -0.5773502692
-0.8107067993  0.0970626198 -0.2805161775
-0.9941603570 -0.0471596473 -0.0970626198
-0.5773502692  0.8107067993 -0.0970626198
-0.5773502692 -0.0970626198 -0.8107067993
-0.5773502692 -0.8107067993  0.0970626198
-0.5773502692 -0.5773502692  0.2805161775
-0.8107067993 -0.5773502692  0.0970626198
-0.2805161775 -0.5773502692 -0.5773502692
 0.8107067993 -0.3938967115 -0.4331280021
 0.2805161775 -0.8107067993  0.0970626198
-0.2805161775  0.8107067993 -0.0970626198
-0.0970626198  0.9941603570  0.0471596473
 0.9941603570 -0.0970626198  0.0471596473
 0.2805161775 -0.8107067993 -0.5138727076
-0.2805161775  0.0970626198 -0.9549290665
-0.0970626198  0.2805161775 -0.8107067993
 0.0471596473  0.0970626198 -0.9941603570
-0.4331280021 -0.8107067993  0.3938967115
 0.0970626198 -0.2805161775  0.8107067993
 0.5138727076 -0.8107067993  0.2805161775
 0.9549290665  0.0970626198 -0.2805161775
 0.3938967115  0.8107067993  0.4331280021
-0.2805161775  0.8107067993 -0.0970626198
-0.9549290665  0.2805161775 -0.0970626198
-0.5138727076 -0.2805161775  0.8107067993
 0.0471596473 -0.9941603570  0.0970626198
 0.2805161775 -0.8107067993  0.0970626198
 0.5381189786 -0.8415485325 -0.0471596473
 0.2805161775 -0.5138727076  0.8107067993
-0.2805161775 -0.9549290665 -0.0970626198
 0.4331280021 -0.3938967115 -0.8107067993
-0.8415485325  0.3696504405 -0.3938967115
-0.0970626198  0.2805161775 -0.8107067993
 0.0970626198 -0.2805161775  0.8107067993
 0.0970626198 -0.0471596473  0.9941603570
 0.8107067993  0.5138727076  0.2805161775
-0.0970626198  0.9549290665 -0.2805161775
 0.8107067993 -0.2805161775  0.5138727076
-0.0970626198  0.2805161775  0.9549290665
-0.8107067993 -0.4331280021  0.3938967115
-0.0471596473 -0.5381189786  0.8415485325
-0.3938967115  0.8415485325 -0.3696504405
-0.8107067993  0.0970626198 -0.2805161775
 0.8107067993 -0.0970626198  0.2805161775
 0.8415485325  0.0471596473  0.5381189786
-0.7215725363  0.5138727076  0.4639697352
 0.2805161775  0.9549290665  0.0970626198
 0.1605401813  0.3938967115 -0.9050260940
-0.3696504405  0.3938967115 -0.8415485325
-0.6907308032  0.0471596473  0.7215725363
-0.8107067993 -0.5138727076 -0.2805161775
 0.2496744444 -0.9549290665 -0.1605401813
 0.4639697352  0.7215725363 -0.5138727076
 0.0970626198 -0.2805161775 -0.9549290665
-0.9050260940 -0.1605401813 -0.3938967115
 0.2104431538 -0.9050260940  0.3696504405
-0.5773502692 -0.5773502692  0.2805161775
 0.5773502692  0.5773502692 -0.2805161775
 0.7215725363  0.6907308032 -0.0471596473
-0.2805161775  0.8107067993  0.5138727076
-0.1605401813 -0.2496744444  0.9549290665
 0.6907308032  0.4830309745 -0.5381189786
-0.5138727076 -0.4639697352 -0.7215725363
-0.9549290665 -0.0970626198  0.2805161775
-0.3938967115  0.9050260940  0.1605401813
-0.0471596473 -0.7215725363 -0.6907308032
 0.5138727076  0.2805161775 -0.8107067993
 0.9549290665  0.1605401813  0.2496744444
 0.3696504405 -0.2104431538  0.9050260940
 0.2805161775  0.5773502692  0.5773502692
-0.2805161775 -0.5773502692 -0.5773502692
-0.5381189786 -0.6907308032 -0.4830309745
 0.9050260940 -0.3696504405  0.2104431538
 0.5773502692 -0.2805161775 -0.5773502692
-0.5773502692  0.2805161775  0.5773502692
-0.0970626198 -0.8107067993  0.5773502692
-0.4639697352  0.2496744444  0.8499380899
-0.4830309745  0.5381189786  0.6907308032
 0.8499380899  0.4639697352 -0.2496744444
 0.5773502692  0.0970626198  0.8107067993
-0.8499380899  0.2104431538  0.4830309745
-0.2496744444 -0.8499380899 -0.4639697352
 0.8107067993 -0.5773502692 -0.0970626198
 0.4830309745  0.8499380899 -0.2104431538
-0.2104431538 -0.4830309745 -0.8499380899
-0.5773502692  0.5773502692 -0.5773502692
3 0 2 1 
5 0 3 14 13 2 3
3 0 4 3 
5 0 5 20 19 4 2
3 0 6 5 
3 0 1 6 
3 1 7 6 
5 1 8 22 16 7 3
3 1 9 8 
5 1 2 10 25 9 2
3 2 11 10 
3 2 12 11 
3 2 13 12 
3 3 15 14 
5 3 16 35 34 15 2
3 3 7 16 
3 3 4 7 
3 4 17 7 
5 4 18 36 32 17 3
3 4 19 18 
3 5 9 20 
3 5 8 9 
3 5 21 8 
5 5 6 12 27 21 3
3 6 11 12 
5 6 7 17 30 11 2
3 8 23 22 
5 8 21 39 41 23 2
5 9 24 42 38 20 3
3 9 25 24 
3 10 26 25 
3 10 27 26 
3 10 28 27 
5 10 11 29 47 28 3
3 11 30 29 
3 12 26 27 
5 12 13 31 45 26 2
3 13 30 31 
3 13 29 30 
3 13 14 29 
5 14 32 50 48 29 2
3 14 17 32 
3 14 15 17 
3 15 30 17 
5 15 33 49 31 30 3
3 15 34 33 
3 16 19 35 
3 16 18 19 
3 16 22 18 
3 18 37 36 
5 18 22 38 54 37 2
5 19 23 40 52 35 3
3 19 20 23 
3 20 22 23 
3 20 38 22 
3 21 25 39 
3 21 24 25 
3 21 27 24 
3 23 41 40 
3 24 43 42 
5 24 27 28 46 43 2
5 25 26 44 55 39 3
3 26 45 44 
3 28 45 46 
3 28 44 45 
3 28 47 44 
3 29 48 47 
3 31 48 45 
3 31 47 48 
3 31 49 47 
3 32 34 50 
3 32 33 34 
3 32 36 33 
3 33 51 49 
5 33 36 52 59 51 2
5 34 37 53 58 50 3
3 34 35 37 
3 35 36 37 
3 35 52 36 
3 37 54 53 
3 38 41 54 
3 38 40 41 
3 38 42 40 
3 39 43 41 
3 39 42 43 
3 39 55 42 
3 40 53 52 
5 40 42 55 57 53 2
5 41 43 56 59 54 3
3 43 46 56 
3 44 56 55 
5 44 47 49 58 56 2
5 45 48 51 57 46 3
3 46 55 56 
3 46 57 55 
3 48 50 51 
3 49 50 58 
3 49 51 50 
3 51 59 57 
3 52 54 59 
3 52 53 54 
3 53 57 58 
3 56 58 59 
3 57 59 58 
6 5 0 1 2 3 4 
6 5 6 7 8 9 0 
6 9 10 11 12 1 0 
6 1 13 14 15 16 2 
6 16 17 18 19 3 2 
6 3 20 21 22 23 4 
6 23 24 25 6 5 4 
6 25 17 16 15 7 6 
6 7 26 27 22 21 8 
6 20 28 29 9 8 21 
6 9 30 31 32 33 10 
6 33 34 25 24 11 10 
6 23 35 36 12 11 24 
6 36 37 38 39 1 12 
6 39 40 41 42 13 1 
6 42 43 44 45 14 13 
6 14 46 47 48 7 15 
6 25 43 42 41 18 17 
6 18 49 50 48 47 19 
6 46 51 52 3 19 47 
6 52 53 54 28 20 3 
6 27 55 56 57 23 22 
6 50 54 53 26 7 48 
6 51 58 27 26 53 52 
6 28 59 60 57 56 29 
6 55 61 30 9 29 56 
6 61 62 36 35 31 30 
6 60 32 31 35 23 57 
6 60 63 64 65 33 32 
6 33 66 40 39 38 34 
6 37 44 43 25 34 38 
6 36 67 68 69 44 37 
6 40 70 71 72 18 41 
6 44 73 74 72 71 45 
6 70 75 76 14 45 71 
6 76 77 78 51 46 14 
6 74 78 77 49 18 72 
6 75 79 50 49 77 76 
6 50 80 81 82 28 54 
6 27 83 84 85 61 55 
6 51 86 87 82 81 58 
6 80 88 83 27 58 81 
6 87 85 84 59 28 82 
6 88 89 60 59 84 83 
6 61 90 91 65 64 62 
6 63 92 67 36 62 64 
6 89 93 94 92 63 60 
6 91 69 68 66 33 65 
6 92 95 40 66 68 67 
6 91 96 97 73 44 69 
6 95 97 96 75 70 40 
6 92 98 74 73 97 95 
6 74 99 100 86 51 78 
6 75 101 87 86 100 79 
6 99 88 80 50 79 100 
6 87 94 93 90 61 85 
6 88 102 91 90 93 89 
6 101 103 98 92 94 87 
6 102 103 101 75 96 91 
6 98 74 99 88 102 103 
great dodecahemicosahedron
great dodecahemicosacron
5/4 5|3
(6.5/4.6.5)
icosahedral group
A5
10{6}+6{5}+6{5/4}
69 30 60 22 30 0 1 1 -8 3 4 120 5 1 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8660254038  0.0000000000  0.5000000000
-0.8660254038  0.0000000000  0.5000000000
 0.6454972244  0.5773502692  0.5000000000
-0.6454972244 -0.5773502692  0.5000000000
 0.8660254038  0.0000000000 -0.5000000000
 0.1102640897  0.5773502692  0.8090169944
 0.7557613141 -0.5773502692 -0.3090169944
-0.7557613141  0.5773502692 -0.3090169944
-0.1102640897 -0.5773502692  0.8090169944
-0.8660254038 -0.0000000000 -0.5000000000
 0.6454972244  0.5773502692 -0.5000000000
 0.4670861795 -0.3568220898  0.8090169944
 0.1784110449  0.9341723590 -0.3090169944
-0.1784110449 -0.9341723590 -0.3090169944
-0.4670861795  0.3568220898  0.8090169944
-0.6454972244 -0.5773502692 -0.5000000000
 0.1102640897  0.5773502692 -0.8090169944
 0.7557613141 -0.5773502692  0.3090169944
 0.0000000000 -0.0000000000 -1.0000000000
-0.7557613141  0.5773502692  0.3090169944
-0.3568220898  0.9341723590 -0.0000000000
 0.9341723590  0.3568220898 -0.0000000000
-0.1102640897 -0.5773502692 -0.8090169944
-0.9341723590 -0.3568220898 -0.0000000000
 0.3568220898 -0.9341723590 -0.0000000000
 0.4670861795 -0.3568220898 -0.8090169944
 0.1784110449  0.9341723590  0.3090169944
-0.1784110449 -0.9341723590  0.3090169944
-0.4670861795  0.3568220898 -0.8090169944
 0.0000000000  1.0000000000  0.0000000000
-0.3035309991  0.7946544723  0.5257311121
-0.6666666667  0.7453559925 -0.0000000000
 0.3035309991 -0.7946544723  0.5257311121
 0.3333333333  0.7453559925 -0.5773502692
 0.6070619982  0.7946544723  0.0000000000
-0.6070619982 -0.7946544723  0.0000000000
 0.3333333333  0.7453559925  0.5773502692
-0.7453559925  0.3333333333  0.5773502692
 0.9822469464 -0.1875924741  0.0000000000
-0.9822469464  0.1875924741 -0.0000000000
-0.7453559925  0.3333333333 -0.5773502692
 0.3035309991 -0.7946544723 -0.5257311121
-0.4911234732 -0.1875924741  0.8506508084
 0.8726779962  0.3333333333 -0.3568220898
-0.1273220038  0.3333333333 -0.9341723590
 0.4911234732  0.1875924741 -0.8506508084
-0.4911234732 -0.1875924741 -0.8506508084
-0.1273220038  0.3333333333  0.9341723590
 0.8726779962  0.3333333333  0.3568220898
 0.4911234732  0.1875924741  0.8506508084
-0.3035309991  0.7946544723 -0.5257311121
6 0 1 5 19 10 2 
5 0 2 8 13 3 4
6 0 3 11 19 16 4 
5 0 1 7 14 4 
6 1 7 23 10 20 6 
5 1 6 21 17 5 4
5 2 10 23 25 9 
6 2 9 18 5 17 8 
6 3 13 29 16 28 12 
5 3 12 25 26 11 
5 4 16 29 21 15 4
6 4 15 27 11 26 14 
5 5 18 28 16 19 
5 6 20 24 28 12 
6 6 12 25 23 29 21 
6 7 14 24 20 27 22 
5 7 22 13 29 23 4
5 8 17 26 14 24 
6 8 24 28 18 22 13 
6 9 25 26 17 21 15 
5 9 15 27 22 18 4
5 10 19 11 27 20 4
4 3 0 1 2 
4 3 4 5 0 
4 6 0 1 7 
4 1 8 9 2 
4 10 2 3 11 
4 5 7 12 0 
4 13 4 5 14 
4 3 15 16 4 
4 17 7 1 18 
4 6 19 20 7 
4 21 0 6 4 
4 9 11 21 2 
4 13 8 9 14 
4 16 18 1 8 
4 17 11 3 15 
4 10 19 20 11 
4 12 2 10 8 
4 5 19 17 7 
4 20 18 12 7 
4 12 0 21 2 
4 21 15 13 4 
4 10 14 5 19 
4 20 15 16 18 
4 16 14 6 4 
4 13 18 17 15 
4 9 19 6 14 
4 9 11 17 19 
4 21 11 20 15 
4 13 8 12 18 
4 16 8 10 14 
great stellated truncated dodecahedron
great triakisicosahedron
2 3|5/3
(10/3.10/3.3)
icosahedral group
A5
12{10/3}+20{3}
70 60 90 32 60 13 0 0 2 2 3 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9876921901  0.0000000000 -0.1564101584
-0.6303417987  0.7603979742 -0.1564101584
-0.1831282032 -0.9705668053 -0.1564101584
-0.2530769525  0.7603979742 -0.5981195340
-0.4238973457 -0.6801206241 -0.5981195340
 0.7469230475  0.2904461812 -0.5981195340
-0.7002905480  0.3896744429 -0.5981195340
-0.6570598434 -0.6801206241 -0.3251281267
-0.4739316403  0.2904461812  0.8312820317
 0.0788547642 -0.5502291431  0.8312820317
 0.5260683597 -0.1795056119  0.8312820317
-0.1975384380  0.5195659239  0.8312820317
 0.7901537521  0.5195659239 -0.3251281267
 0.8333844566 -0.5502291431 -0.0521367195
 0.9033332059 -0.1795056119  0.3895726561
-0.4383075806  0.8100121051  0.3895726561
 0.9389572656  0.3400603121 -0.0521367195
-0.5082563299 -0.8596262360 -0.0521367195
-0.7147007828  0.5808923624  0.3895726561
 0.0089060149 -0.9209526744  0.3895726561
 0.3861708611 -0.9209526744 -0.0521367195
 0.3162221118  0.8100121051 -0.4938460950
 0.0953674240  0.3400603121  0.9355554706
-0.1309914837 -0.8596262360 -0.4938460950
 0.2729914073  0.5808923624 -0.7668375023
-0.6214357837 -0.1605547002 -0.7668375023
-0.0953674240 -0.3400603121 -0.9355554706
 0.3518461715  0.0306632192 -0.9355554706
 0.8690085163 -0.0306632192 -0.4938460950
-0.3518461715 -0.0306632192  0.9355554706
-0.8545982815 -0.1605547002 -0.4938460950
-0.9389572656 -0.3400603121  0.0521367195
-0.8690085163  0.0306632192  0.4938460950
-0.8333844566  0.5502291431  0.0521367195
-0.3162221118 -0.8100121051  0.4938460950
 0.8545982815  0.1605547002  0.4938460950
-0.3861708611  0.9209526744  0.0521367195
 0.1309914837  0.8596262360  0.4938460950
 0.5082563299  0.8596262360  0.0521367195
-0.0788547642  0.5502291431 -0.8312820317
 0.4383075806 -0.8100121051 -0.3895726561
 0.6214357837  0.1605547002  0.7668375023
-0.0089060149  0.9209526744 -0.3895726561
 0.6570598434  0.6801206241  0.3251281267
-0.7901537521 -0.5195659239  0.3251281267
-0.9033332059  0.1795056119 -0.3895726561
-0.2729914073 -0.5808923624  0.7668375023
 0.7147007828 -0.5808923624 -0.3895726561
-0.5260683597  0.1795056119 -0.8312820317
 0.4238973457  0.6801206241  0.5981195340
 0.1975384380 -0.5195659239 -0.8312820317
 0.4739316403 -0.2904461812 -0.8312820317
 0.2530769525 -0.7603979742  0.5981195340
 0.7002905480 -0.3896744429  0.5981195340
-0.7469230475 -0.2904461812  0.5981195340
 0.6303417987 -0.7603979742  0.1564101584
-0.9876921901 -0.0000000000  0.1564101584
 0.1831282032  0.9705668053  0.1564101584
-0.0000000000  0.0000000000 -1.0000000000
 0.3997648726  0.8506508084  0.3414399638
-0.9100220386 -0.2351141009  0.3414399638
 0.3997648726 -0.4822469333  0.3414399638
 0.1949008944 -0.2351141009 -0.9522263391
-0.1526965938  0.1842019375 -0.6720927788
-0.6877040871  0.1842019375 -0.0456950952
 0.6307125431 -0.7608452130 -0.1526965938
-0.0535007493  0.7099330497 -0.0456950952
-0.0521673844 -0.7608452130  0.6468331514
 0.2879392144  0.2980449957  0.5807025884
-0.3462641233 -0.2276861164  0.5807025884
 0.7573254447 -0.0898055953  0.6468331514
 0.6185920295  0.2980449957  0.1935675295
 0.5193961850 -0.2276861164 -0.4328301541
 0.0521673844  0.7608452130 -0.6468331514
-0.7573254447  0.0898055953 -0.6468331514
 0.1274369665 -0.5526058126 -0.4328301541
-0.4075705268 -0.5526058126  0.1935675295
-0.6307125431  0.7608452130  0.1526965938
-0.6185920295 -0.2980449957 -0.1935675295
 0.4075705268  0.5526058126 -0.1935675295
-0.2879392144 -0.2980449957 -0.5807025884
-0.1274369665  0.5526058126  0.4328301541
-0.1949008944  0.2351141009  0.9522263391
-0.5193961850  0.2276861164  0.4328301541
 0.3462641233  0.2276861164 -0.5807025884
 0.9100220386  0.2351141009 -0.3414399638
 0.6877040871 -0.1842019375  0.0456950952
 0.0535007493 -0.7099330497  0.0456950952
-0.3997648726 -0.8506508084 -0.3414399638
 0.1526965938 -0.1842019375  0.6720927788
-0.3997648726  0.4822469333 -0.3414399638
10 0 2 6 11 19 25 15 9 4 1 3
10 0 3 7 12 20 26 16 10 5 2 3
3 0 1 3 
10 1 4 8 14 22 31 21 13 7 3 3
3 2 5 6 
3 4 9 8 
10 5 10 17 27 35 36 28 18 11 6 3
3 7 13 12 
10 8 9 15 24 33 42 41 32 23 14 3
3 10 16 17 
3 11 18 19 
10 12 13 21 30 39 48 47 38 29 20 3
3 14 23 22 
3 15 25 24 
10 16 26 29 38 46 52 44 34 27 17 3
10 18 28 37 45 51 43 33 24 25 19 3
3 20 29 26 
3 21 31 30 
10 22 23 32 40 50 55 49 39 30 31 3
3 27 34 35 
3 28 36 37 
3 32 41 40 
3 33 43 42 
10 34 44 53 57 58 54 45 37 36 35 3
3 38 47 46 
3 39 49 48 
10 40 41 42 43 51 54 58 59 56 50 3
3 44 52 53 
3 45 54 51 
10 46 47 48 49 55 56 59 57 53 52 3
3 50 56 55 
3 57 59 58 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 3 2 
3 3 5 0 
3 4 6 1 
3 0 6 4 
3 1 7 3 
3 3 8 5 
3 8 0 5 
3 6 9 1 
3 0 10 6 
3 1 11 7 
3 11 3 7 
3 3 12 8 
3 8 13 0 
3 9 14 1 
3 6 14 9 
3 10 15 6 
3 0 15 10 
3 1 16 11 
3 11 17 3 
3 3 18 12 
3 18 8 12 
3 8 15 13 
3 13 0 15 
3 14 16 1 
3 6 19 14 
3 15 20 6 
3 14 11 16 
3 11 18 17 
3 17 3 18 
3 18 21 8 
3 8 22 15 
3 19 23 14 
3 6 23 19 
3 20 23 6 
3 15 23 20 
3 14 24 11 
3 11 25 18 
3 18 26 21 
3 26 8 21 
3 26 22 8 
3 26 15 22 
3 23 27 14 
3 15 28 23 
3 14 29 24 
3 29 11 24 
3 29 25 11 
3 29 18 25 
3 18 30 26 
3 26 28 15 
3 27 29 14 
3 23 29 27 
3 26 23 28 
3 29 30 18 
3 29 26 30 
3 23 31 29 
3 26 31 23 
3 29 26 31 
great rhombicosidodecahedron
great deltoidal hexecontahedron
5/3 3|2
(4.5/3.4.3)
icosahedral group
A5
30{4}+20{3}+12{5/3}
71 60 120 62 60 13 0 0 2 3 4 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9996324920  0.0000000000  0.0271086873
-0.9468654869  0.3204853643  0.0271086873
-0.3453645319  0.9380770007  0.0271086873
 0.0263835025 -0.9992842588  0.0271086873
 0.0527670051  0.3204853643 -0.9457826254
 0.0364611038  0.9380770007 -0.3445027268
 0.2398305218  0.7400061526  0.6283885859
-0.3352869307 -0.8768697425 -0.3445027268
-0.3189810294 -0.0612072581 -0.9457826254
 0.8677149793  0.3583135302 -0.3445027268
-0.7334184677 -0.2592781062  0.6283885859
-0.9367878857 -0.0612072581 -0.3445027268
 0.6216561575  0.7400061526  0.2567771718
-0.3678987333  0.3583135302  0.8580570704
 0.6480396600 -0.2592781062 -0.7161141409
 0.8514090780 -0.4573489542  0.2567771718
 0.5060445461  0.4807280465 -0.7161141409
 0.2336022217 -0.4573489542  0.8580570704
-0.7233408665 -0.6409707286  0.2567771718
 0.4796610435 -0.8390415766  0.2567771718
 0.4633551422 -0.2214499403  0.8580570704
-0.4672044434 -0.5185562123 -0.7161141409
 0.2762916255 -0.6409707286 -0.7161141409
-0.7295691665  0.4807280465  0.4864456563
 0.2436798229 -0.8390415766  0.4864456563
 0.8451807779 -0.2214499403  0.4864456563
-0.7031856640 -0.5185562123 -0.4864456563
-0.4998162460 -0.7166270604  0.4864456563
-0.8451807779  0.2214499403 -0.4864456563
 0.4998162460 -0.7166270604 -0.4864456563
-0.4998162460  0.7166270604  0.4864456563
 0.7031856640  0.5185562123  0.4864456563
 0.7295691665 -0.4807280465 -0.4864456563
-0.2436798229  0.8390415766 -0.4864456563
 0.4998162460  0.7166270604 -0.4864456563
-0.4633551422  0.2214499403 -0.8580570704
 0.4672044434  0.5185562123  0.7161141409
-0.5060445461 -0.4807280465  0.7161141409
-0.4796610435  0.8390415766 -0.2567771718
-0.2762916255  0.6409707286  0.7161141409
 0.3678987333 -0.3583135302 -0.8580570704
 0.7233408665  0.6409707286 -0.2567771718
-0.2336022217  0.4573489542 -0.8580570704
-0.6480396600  0.2592781062  0.7161141409
-0.6216561575 -0.7400061526 -0.2567771718
-0.8514090780  0.4573489542 -0.2567771718
-0.8677149793 -0.3583135302  0.3445027268
 0.7334184677  0.2592781062 -0.6283885859
-0.2398305218 -0.7400061526 -0.6283885859
 0.9367878857  0.0612072581  0.3445027268
-0.0364611038 -0.9380770007  0.3445027268
 0.3189810294  0.0612072581  0.9457826254
 0.3352869307  0.8768697425  0.3445027268
-0.0527670051 -0.3204853643  0.9457826254
 0.3453645319 -0.9380770007 -0.0271086873
 0.9468654869 -0.3204853643 -0.0271086873
-0.0263835025  0.9992842588 -0.0271086873
-0.9996324920 -0.0000000000 -0.0271086873
 0.0000000000 -0.0000000000 -1.0000000000
 0.1602426822  0.9732489895  0.1646471601
-0.1272308741  0.1239160115  0.1646471601
-0.9686806297 -0.1858740172  0.1646471601
 0.1602426822 -0.1560677326  0.1646471601
 0.1908463112 -0.1858740172 -0.9638612635
 0.1680357129  0.1239160115 -0.1227207474
-0.1920048196 -0.0368425940 -0.1972823210
-0.2898817352 -0.4156269378  0.8621037224
 0.4078312422  0.3007504775  0.8621037224
 0.0317621374  0.1929103266 -0.1972823210
-0.1194378434 -0.1712477161 -0.1227207474
 0.8696452057 -0.4156269378 -0.2664047011
-0.1980708480  0.1929103266  0.0264023998
 0.8507311228  0.3007504775  0.4310518612
 0.2494630659  0.1192251386  0.0264023998
-0.6904884406  0.6724985120 -0.2664047011
 0.0534142274 -0.2297529205  0.0548823867
 0.4384348713 -0.8583725292 -0.2664047011
 0.2310826560 -0.0473317046  0.0548823867
-0.1125994760 -0.2525228959  0.0264023998
-0.2781921891 -0.8583725292  0.4310518612
-0.2475885600  0.6724985120 -0.6974565623
 0.0196300805  0.1192251386  0.2500871207
 0.0485978695 -0.0473317046  0.2324855208
 0.0294451207 -0.2525228959 -0.1118423604
 0.0189140829 -0.7163774153 -0.6974565623
-0.0485978695  0.0473317046 -0.2324855208
-0.6977129774 -0.7163774153  0.0000000000
-0.1186655045 -0.0227699753  0.2500871207
-0.6787988945  0.2297529205 -0.6974565623
 0.7166270604  0.0000000000 -0.6974565623
 0.6977129774  0.7163774153  0.0000000000
 0.2532120777 -0.0227699753 -0.1118423604
-0.2310826560  0.0473317046 -0.0548823867
-0.7166270604 -0.0000000000  0.6974565623
-0.0189140829  0.7163774153  0.6974565623
 0.6787988945 -0.2297529205  0.6974565623
-0.2532120777  0.0227699753  0.1118423604
 0.2781921891  0.8583725292 -0.4310518612
 0.1186655045  0.0227699753 -0.2500871207
-0.0534142274  0.2297529205 -0.0548823867
-0.0294451207  0.2525228959  0.1118423604
 0.2475885600 -0.6724985120  0.6974565623
-0.0196300805 -0.1192251386 -0.2500871207
-0.8507311228 -0.3007504775 -0.4310518612
-0.4384348713  0.8583725292  0.2664047011
 0.6904884406 -0.6724985120  0.2664047011
 0.1125994760  0.2525228959 -0.0264023998
-0.2494630659 -0.1192251386 -0.0264023998
-0.4078312422 -0.3007504775 -0.8621037224
 0.1194378434  0.1712477161  0.1227207474
 0.1980708480 -0.1929103266 -0.0264023998
-0.8696452057  0.4156269378  0.2664047011
-0.1680357129 -0.1239160115  0.1227207474
 0.2898817352  0.4156269378 -0.8621037224
-0.0317621374 -0.1929103266  0.1972823210
 0.1272308741 -0.1239160115 -0.1646471601
-0.1908463112  0.1858740172  0.9638612635
 0.9686806297  0.1858740172 -0.1646471601
 0.1920048196  0.0368425940  0.1972823210
-0.1602426822 -0.9732489895 -0.1646471601
-0.1602426822  0.1560677326 -0.1646471601
4 0 2 5 1 
5 0 3 11 7 2 3
4 0 4 9 3 
3 0 1 4 
4 1 6 12 4 
5 1 5 13 15 6 3
3 2 8 5 
4 2 7 16 8 
4 3 10 20 11 
3 3 9 10 
5 4 12 23 19 9 3
4 5 8 18 13 
3 6 14 12 
4 6 15 25 14 
3 7 17 16 
4 7 11 22 17 
5 8 16 28 30 18 3
4 9 19 21 10 
5 10 21 33 32 20 3
3 11 20 22 
4 12 14 26 23 
4 13 24 27 15 
3 13 18 24 
5 14 25 37 38 26 3
3 15 27 25 
4 16 17 29 28 
5 17 22 34 41 29 3
4 18 30 36 24 
3 19 31 21 
4 19 23 35 31 
4 20 32 34 22 
4 21 31 43 33 
3 23 26 35 
5 24 36 47 39 27 3
4 25 27 39 37 
4 26 38 46 35 
4 28 40 42 30 
3 28 29 40 
4 29 41 50 40 
3 30 42 36 
5 31 35 46 53 43 3
3 32 44 34 
4 32 33 45 44 
3 33 43 45 
4 34 44 51 41 
4 36 42 52 47 
4 37 48 49 38 
3 37 39 48 
3 38 49 46 
4 39 47 55 48 
5 40 50 57 52 42 3
3 41 51 50 
4 43 53 54 45 
5 44 45 54 58 51 3
4 46 49 56 53 
3 47 52 55 
5 48 55 59 56 49 3
4 50 51 58 57 
4 52 57 59 55 
3 53 56 54 
4 54 56 59 58 
3 57 58 59 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 1 8 9 2 
4 2 10 4 3 
4 5 11 6 0 
4 4 12 13 5 
4 7 14 15 1 
4 11 16 7 6 
4 9 17 10 2 
4 8 18 17 9 
4 15 19 8 1 
4 10 20 12 4 
4 5 21 22 11 
4 20 23 13 12 
4 13 24 21 5 
4 16 25 14 7 
4 25 26 15 14 
4 22 27 16 11 
4 17 28 29 10 
4 19 30 18 8 
4 18 31 28 17 
4 26 30 19 15 
4 29 32 20 10 
4 21 33 27 22 
4 23 34 24 13 
4 32 35 23 20 
4 34 33 21 24 
4 16 36 37 25 
4 37 38 26 25 
4 27 39 36 16 
4 31 40 29 28 
4 30 41 42 18 
4 42 43 31 18 
4 26 44 41 30 
4 40 35 32 29 
4 33 45 39 27 
4 23 46 47 34 
4 35 48 46 23 
4 47 49 33 34 
4 36 50 38 37 
4 38 51 44 26 
4 45 50 36 39 
4 43 52 40 31 
4 44 53 42 41 
4 53 52 43 42 
4 40 54 48 35 
4 49 55 45 33 
4 46 56 49 47 
4 54 56 46 48 
4 50 57 51 38 
4 57 53 44 51 
4 55 58 50 45 
4 52 59 54 40 
4 53 60 59 52 
4 56 58 55 49 
4 60 56 54 59 
4 58 61 57 50 
4 61 60 53 57 
4 56 58 61 60 
great truncated icosidodecahedron
great disdyakistriacontahedron
5/3 2 3|
(10/3.4.6)
icosahedral group
A5
20{6}+30{4}+12{10/3}
72 120 180 62 120 13 0 0 2 3 3 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8541299615  0.0000000000  0.5200596205
 0.0775955677  0.8505979773  0.5200596205
-0.8315867367 -0.1949397099  0.5200596205
 0.4038441822  0.8505979773  0.3367387081
 0.8766731863 -0.1949397099 -0.4398211385
-0.7539911690  0.6556582674  0.0401192410
 0.8837688310  0.3248995166  0.3367387081
-0.8090435119 -0.3898794199 -0.4398211385
 0.4263874070  0.6556582674 -0.6231420509
-0.1719938631  0.3248995166  0.9299776423
 0.0450864496 -0.3898794199 -0.9197615180
-0.7794046424 -0.0649799033 -0.6231420509
 0.3079307858 -0.2007989442  0.9299776423
 0.8583553576 -0.3957386541 -0.3265225838
-0.7453804233  0.5811979239 -0.3265225838
-0.1269074134 -0.0649799033 -0.9897838757
 0.6341794002 -0.2007989442  0.7466567299
-0.7252886834 -0.3957386541  0.5633358175
 0.1087495382  0.5811979239 -0.8064629633
-0.8412938197 -0.4701989976  0.2667163504
 0.0267686209 -0.5906783641 -0.8064629633
 0.2825173124 -0.9214371149  0.2667163504
-0.1423549936  0.6497990331  0.7466567299
-0.8072696007  0.1759788297  0.5633358175
 0.6653333707 -0.4701989976 -0.5798658539
-0.7027454586 -0.5906783641 -0.3965449415
 0.0808845798 -0.9214371149  0.3800149051
 0.7117749679  0.6497990331  0.2667163504
 0.9009903223  0.1759788297 -0.3965449415
-0.0351205564 -0.9958974583  0.0833954380
-0.7776307312  0.5008783463  0.3800149051
-0.1931819403 -0.7914773082 -0.5798658539
-0.6180542463  0.7797588398 -0.0999254744
-0.8326830741 -0.5446593410 -0.0999254744
-0.0150288165 -0.2292402645  0.9732538393
 0.0894953255 -0.9958974583  0.0133730803
 0.7289964592  0.5008783463 -0.4665672992
-0.3948146729 -0.7914773082 -0.4665672992
 0.2360757152  0.7797588398 -0.5798658539
 0.3476955019 -0.5446593410 -0.7631867663
 0.8391011449 -0.2292402645  0.4933134598
 0.8347157954 -0.5505185752  0.0133730803
-0.7550875064  0.3059386363 -0.5798658539
 0.0922056206  0.9462572293  0.3099925474
 0.6766544115 -0.3460984252 -0.6498882116
-0.6434677197  0.0591206691 -0.7631867663
-0.0404422899 -0.9498784352  0.3099925474
-0.4226796312 -0.5505185752  0.7199105693
-0.1025902774  0.3059386363 -0.9465076787
 0.2168215026  0.9462572293  0.2399701898
-0.9069896296 -0.3460984252  0.2399701898
-0.3172191052  0.0591206691 -0.9465076787
 0.2858063246 -0.9498784352  0.1266716350
 0.3590165427 -0.4205587686 -0.8332091240
 0.8983788839  0.4205587686  0.1266716350
 0.1147488454  0.7513175194 -0.6498882116
 0.2263686321  0.5044995522 -0.8332091240
 0.6147652341 -0.7513175194  0.2399701898
 0.8293940619 -0.5044995522  0.2399701898
-0.8983788839 -0.4205587686 -0.1266716350
-0.3590165427  0.4205587686  0.8332091240
-0.6147652341  0.7513175194 -0.2399701898
-0.8293940619  0.5044995522 -0.2399701898
-0.1147488454 -0.7513175194  0.6498882116
-0.2263686321 -0.5044995522  0.8332091240
 0.4226796312  0.5505185752 -0.7199105693
-0.2168215026 -0.9462572293 -0.2399701898
 0.9069896296  0.3460984252 -0.2399701898
-0.2858063246  0.9498784352 -0.1266716350
 0.1025902774 -0.3059386363  0.9465076787
 0.3172191052 -0.0591206691  0.9465076787
-0.8347157954  0.5505185752 -0.0133730803
-0.0922056206 -0.9462572293 -0.3099925474
-0.6766544115  0.3460984252  0.6498882116
 0.0404422899  0.9498784352 -0.3099925474
 0.7550875064 -0.3059386363  0.5798658539
 0.6434677197 -0.0591206691  0.7631867663
-0.0894953255  0.9958974583 -0.0133730803
-0.7289964592 -0.5008783463  0.4665672992
 0.3948146729  0.7914773082  0.4665672992
-0.8391011449  0.2292402645 -0.4933134598
-0.3476955019  0.5446593410  0.7631867663
-0.2360757152 -0.7797588398  0.5798658539
 0.0351205564  0.9958974583 -0.0833954380
 0.7776307312 -0.5008783463 -0.3800149051
 0.1931819403  0.7914773082  0.5798658539
 0.0150288165  0.2292402645 -0.9732538393
 0.8326830741  0.5446593410  0.0999254744
 0.6180542463 -0.7797588398  0.0999254744
 0.7027454586  0.5906783641  0.3965449415
-0.6653333707  0.4701989976  0.5798658539
-0.0808845798  0.9214371149 -0.3800149051
-0.9009903223 -0.1759788297  0.3965449415
-0.7117749679 -0.6497990331 -0.2667163504
-0.0267686209  0.5906783641  0.8064629633
 0.8412938197  0.4701989976 -0.2667163504
-0.2825173124  0.9214371149 -0.2667163504
 0.8072696007 -0.1759788297 -0.5633358175
 0.1423549936 -0.6497990331 -0.7466567299
 0.1269074134  0.0649799033  0.9897838757
 0.7252886834  0.3957386541 -0.5633358175
-0.6341794002  0.2007989442 -0.7466567299
-0.1087495382 -0.5811979239  0.8064629633
 0.7794046424  0.0649799033  0.6231420509
-0.8583553576  0.3957386541  0.3265225838
-0.3079307858  0.2007989442 -0.9299776423
 0.7453804233 -0.5811979239  0.3265225838
-0.4263874070 -0.6556582674  0.6231420509
 0.1719938631 -0.3248995166 -0.9299776423
-0.0450864496  0.3898794199  0.9197615180
 0.7539911690 -0.6556582674 -0.0401192410
-0.8837688310 -0.3248995166 -0.3367387081
 0.8090435119  0.3898794199  0.4398211385
-0.8766731863  0.1949397099  0.4398211385
-0.4038441822 -0.8505979773 -0.3367387081
 0.8315867367  0.1949397099 -0.5200596205
-0.0775955677 -0.8505979773 -0.5200596205
-0.8541299615  0.0000000000 -0.5200596205
-0.0000000000  0.0000000000 -1.0000000000
 0.1125484940  0.1027486297  0.2002978807
-0.1451976151  0.1262614479  0.2002978807
 0.1125484940 -0.9732489895  0.2002978807
 0.2465918377  0.1262614479 -0.0198507936
 0.2605224485  0.6488326596 -0.7149435178
-0.2508908076  0.0175515613 -0.0094567831
-0.7461418850  0.6488326596 -0.1492932256
 0.1224008564  0.0175515613 -0.2192114469
 0.2245940980 -0.1148764603  0.1162085697
-0.1348570368  0.0368425940 -0.2399994678
-0.0175451002 -0.1148764603  0.2522679329
-0.1568547765 -0.2042953142 -0.1039401045
-0.8375948183 -0.3536689320  0.4163570665
 0.1014417091 -0.2122013592 -0.0895759354
 0.2339533531  0.8785855802  0.4163570665
-0.0072045220 -0.2042953142 -0.1880294155
 0.7912222885 -0.3536689320 -0.4988843319
-0.1292652270 -0.2122013592  0.0400595761
 0.1425004198 -0.1239160115  0.9820073587
 0.0180479902  0.2752928712  0.0321192587
-0.1632456053 -0.1490314232  0.1681786220
 0.7646531932 -0.1239160115  0.6324162524
 0.2285438474 -0.1490314232 -0.0519700523
-0.1276525148  0.2411379082 -0.0519700523
 0.0063908288 -0.0552638910 -0.2721187265
-0.0953526143  0.1595466752 -0.1696950876
 0.1854901192 -0.4956640459 -0.8484754382
 0.0953526143 -0.1595466752  0.1696950876
 0.0219977397  0.2411379082 -0.1360593633
-0.2357483694 -0.0552638910 -0.1360593633
-0.8211742143 -0.4956640459 -0.2828251461
 0.2421391982  0.0000000000 -0.1360593633
 0.1292652270  0.2122013592 -0.0400595761
 0.8211742143  0.4956640459  0.2828251461
-0.2421391982  0.0000000000  0.1360593633
-0.1014417091  0.2122013592  0.0895759354
-0.1854901192  0.4956640459  0.8484754382
-0.7646531932  0.1239160115 -0.6324162524
-0.0219977397 -0.2411379082  0.1360593633
 0.2357483694  0.0552638910  0.1360593633
-0.1425004198  0.1239160115 -0.9820073587
 0.1276525148 -0.2411379082  0.0519700523
-0.0063908288  0.0552638910  0.2721187265
-0.2285438474  0.1490314232  0.0519700523
-0.1224008564 -0.0175515613  0.2192114469
-0.7912222885  0.3536689320  0.4988843319
 0.1632456053  0.1490314232 -0.1681786220
 0.2508908076 -0.0175515613  0.0094567831
 0.8375948183  0.3536689320 -0.4163570665
 0.0072045220  0.2042953142  0.1880294155
-0.2339533531 -0.8785855802 -0.4163570665
-0.0180479902 -0.2752928712 -0.0321192587
 0.1568547765  0.2042953142  0.1039401045
 0.7461418850 -0.6488326596  0.1492932256
 0.0175451002  0.1148764603 -0.2522679329
-0.1125484940 -0.1027486297 -0.2002978807
-0.2605224485 -0.6488326596  0.7149435178
-0.2245940980  0.1148764603 -0.1162085697
 0.1348570368 -0.0368425940  0.2399994678
-0.2465918377 -0.1262614479  0.0198507936
-0.1125484940  0.9732489895 -0.2002978807
 0.1451976151 -0.1262614479 -0.2002978807
10 0 2 7 13 23 28 17 10 4 1 3
4 0 3 6 2 
6 0 1 5 11 8 3 
4 1 4 9 5 
6 2 6 12 21 14 7 
10 3 8 15 24 34 43 31 20 12 6 3
6 4 10 18 26 16 9 
10 5 9 16 25 37 49 40 29 19 11 3
4 7 14 22 13 
4 8 11 19 15 
4 10 17 27 18 
4 12 20 30 21 
6 13 22 32 46 33 23 
10 14 21 30 42 54 67 58 45 32 22 3
6 15 19 29 41 35 24 
4 16 26 36 25 
6 17 28 39 52 38 27 
10 18 27 38 51 64 73 60 48 36 26 3
6 20 31 44 55 42 30 
4 23 33 39 28 
4 24 35 47 34 
6 25 36 48 61 50 37 
4 29 40 53 41 
4 31 43 56 44 
4 32 45 57 46 
10 33 46 57 69 81 87 75 63 52 39 3
6 34 47 59 68 56 43 
10 35 41 53 65 77 89 83 71 59 47 3
4 37 50 62 49 
4 38 52 63 51 
6 40 49 62 74 65 53 
4 42 55 66 54 
10 44 56 68 80 92 101 90 78 66 55 3
6 45 58 70 82 69 57 
4 48 60 72 61 
10 50 61 72 84 95 105 97 86 74 62 3
6 51 63 75 88 76 64 
6 54 66 78 91 79 67 
4 58 67 79 70 
4 59 71 80 68 
6 60 73 85 96 84 72 
4 64 76 85 73 
4 65 74 86 77 
4 69 82 93 81 
10 70 79 91 100 108 114 110 103 93 82 3
6 71 83 94 102 92 80 
4 75 87 98 88 
10 76 88 98 107 113 116 111 104 96 85 3
6 77 86 97 106 99 89 
4 78 90 100 91 
6 81 93 103 107 98 87 
4 83 89 99 94 
4 84 96 104 95 
6 90 101 109 115 108 100 
4 92 102 109 101 
10 94 99 106 112 117 119 118 115 109 102 3
6 95 104 111 117 112 105 
4 97 105 112 106 
4 103 110 113 107 
4 108 115 118 114 
6 110 114 118 119 116 113 
4 111 116 119 117 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 6 0 
3 2 7 3 
3 4 5 1 
3 0 8 4 
3 5 9 2 
3 7 6 3 
3 6 10 0 
3 9 7 2 
3 4 11 5 
3 0 12 8 
3 8 13 4 
3 5 14 9 
3 7 15 6 
3 10 16 0 
3 6 17 10 
3 14 7 9 
3 11 18 5 
3 13 11 4 
3 12 13 8 
3 0 19 12 
3 5 20 14 
3 7 21 15 
3 15 17 6 
3 17 16 10 
3 16 19 0 
3 14 22 7 
3 13 18 11 
3 18 23 5 
3 12 24 13 
3 19 25 12 
3 5 26 20 
3 20 27 14 
3 21 17 15 
3 7 28 21 
3 17 29 16 
3 16 25 19 
3 22 30 7 
3 27 22 14 
3 13 31 18 
3 23 26 5 
3 18 32 23 
3 24 33 13 
3 25 24 12 
3 26 27 20 
3 21 34 17 
3 30 28 7 
3 28 35 21 
3 17 36 29 
3 29 25 16 
3 27 30 22 
3 13 37 31 
3 31 32 18 
3 32 26 23 
3 25 33 24 
3 33 38 13 
3 26 39 27 
3 34 40 17 
3 35 34 21 
3 30 35 28 
3 36 25 29 
3 17 41 36 
3 27 42 30 
3 37 32 31 
3 38 37 13 
3 32 39 26 
3 25 43 33 
3 33 44 38 
3 39 45 27 
3 35 40 34 
3 40 41 17 
3 42 35 30 
3 36 46 25 
3 41 47 36 
3 27 48 42 
3 37 49 32 
3 44 37 38 
3 32 45 39 
3 25 50 43 
3 43 44 33 
3 45 51 27 
3 35 52 40 
3 40 47 41 
3 48 35 42 
3 46 50 25 
3 47 46 36 
3 51 48 27 
3 49 53 32 
3 44 49 37 
3 32 54 45 
3 50 44 43 
3 45 55 51 
3 35 56 52 
3 52 47 40 
3 48 57 35 
3 47 50 46 
3 55 48 51 
3 44 53 49 
3 53 54 32 
3 54 55 45 
3 50 58 44 
3 56 47 52 
3 57 56 35 
3 55 57 48 
3 47 58 50 
3 44 59 53 
3 53 55 54 
3 58 60 44 
3 56 61 47 
3 55 56 57 
3 47 60 58 
3 60 59 44 
3 59 55 53 
3 61 60 47 
3 55 61 56 
3 60 55 59 
3 61 60 55 
great inverted snub icosidodecahedron
great inverted pentagonal hexecontahedron
|5/3 2 3
(3.5/3.3.3.3)
icosahedral group
A5
80{3}+12{5/3}
73 60 150 92 60 13 0 0 2 2 5 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9794318115  0.0000000000 -0.2017754361
-0.2475810566  0.9476234979 -0.2017754361
 0.6794635566  0.7054189880 -0.2017754361
-0.8542645893  0.4790810838 -0.2017754361
-0.2475810566 -0.9476234979 -0.2017754361
-0.3699948910  0.4790810838 -0.7959805875
-0.3699948910 -0.4790810838 -0.7959805875
-0.6672097581 -0.2368765739  0.7062015487
 0.8324770646  0.1197554578  0.5409626302
-0.6675126287  0.5116505870  0.5409626302
 0.4660769426 -0.5329649671  0.7062015487
 0.0883725112 -0.5988365416 -0.7959805875
-0.2922587145 -0.6448753495  0.7062015487
-0.6672097581  0.2368765739  0.7062015487
 0.7719508391  0.5856635302  0.2471641790
 0.4639966765 -0.7751694770 -0.4287416077
 0.4639966765  0.7751694770 -0.4287416077
 0.7719508391 -0.5856635302  0.2471641790
 0.1640284216 -0.8884116786 -0.4287416077
 0.1634158680  0.6254788577 -0.7629360738
-0.5776256146 -0.6946432777 -0.4287416077
 0.7239072399  0.1089797474 -0.6812354385
 0.9573414162  0.1496906193  0.2471641790
-0.4246121066  0.8491824202  0.3139964587
-0.5949197891 -0.2529802202 -0.7629360738
 0.3170419295 -0.8949249348  0.3139964587
-0.2548514500 -0.3832743477  0.8877789775
-0.8776864208 -0.0000000000 -0.4792353772
-0.2548514500  0.3832743477  0.8877789775
-0.7254217428 -0.6728494848 -0.1450409111
 0.2582173913 -0.1829926907  0.9485976249
-0.9980199890  0.0131730113  0.0615026278
-0.5400311657  0.8290533603 -0.1450409111
 0.4846651202  0.2204107171  0.8464743570
-0.0709753758 -0.9955801941  0.0615026278
 0.0229317766  0.1398845177 -0.9899022453
 0.8076938496  0.3434590203 -0.4792353772
 0.0262977179  0.5317796470  0.8464743570
 0.9516406439 -0.2960883932 -0.0819252605
 0.1085698247  0.9689378780  0.2221980688
-0.2763633567  0.7320613041 -0.6226632655
 0.7613145044 -0.4132095093 -0.4996580098
 0.2099866077  0.9742658140 -0.0819252605
 0.1401812208 -0.3162174531 -0.9382727469
-0.6959163498 -0.6395474135  0.3266183398
-0.9330524663  0.2829153818  0.2221980688
 0.5310965183  0.7818292322  0.3266183398
-0.7386751889  0.4524387678 -0.4996580098
-0.4475438832 -0.8410410515  0.3038987040
-0.2811491679  0.0431081729 -0.9586953796
-0.8643913313 -0.2155621938  0.4542692670
 0.4802495600  0.5116505870  0.7124423043
 0.8209889390 -0.3458563213  0.4542692670
-0.2034129914  0.8143987354  0.5434867567
 0.1802813051 -0.6781774208  0.7124423043
 0.5734078824 -0.3353176516 -0.7475061691
 0.4705702928 -0.8817519234  0.0328198885
 0.3836942965  0.4026708396 -0.8310444524
-0.9121320599 -0.2694460771 -0.3088914320
 0.5471106816  0.7084162097  0.4458882998
 0.1585623966  0.6069020586  0.4458882998
-0.1306762499  0.8854983579  0.4458882998
-0.8237082743 -0.3502689009  0.4458882998
 0.5471106816 -0.7084162097  0.4458882998
 0.2705130889 -0.3502689009 -0.8967353934
 0.3101487853 -0.0000000000 -0.7043410035
 0.2705130889  0.3502689009 -0.8967353934
-0.9604690280  0.1731867527 -0.2179577823
-0.0615354041  0.6208598148  0.7815027091
 0.3573599567  0.5114170284  0.7815027091
 0.9224380568 -0.3187513710 -0.2179577823
-0.0646114894  0.4378252958 -0.8967353934
-0.7910432524 -0.5716161107 -0.2179577823
-0.7056730782 -0.3000763028  0.0653317492
-0.9604690280 -0.1731867527 -0.2179577823
-0.1982961578  0.9730547528  0.1176566270
 0.6473614019  0.2164780859 -0.7307943990
 0.6473614019 -0.2164780859 -0.7307943990
-0.1982961578 -0.9730547528  0.1176566270
-0.0527175450 -0.6819118559  0.3528535099
 0.2461720631 -0.7517075429  0.6118292942
 0.8671240119 -0.1070352996 -0.4864559514
 0.2454877182  0.9396111859  0.2384671877
-0.8086646931  0.3307899962 -0.4864559514
-0.5824039347 -0.5352294570  0.6118292942
 0.4577817420 -0.8362546538 -0.3018510074
 0.5750948931 -0.4964545016 -0.1228304115
 0.5632615562 -0.8178589961  0.1176566270
 0.1797689355  0.2646385431  0.9474437035
-0.9806571218 -0.0363866537  0.1923216597
-0.7065204582 -0.6810588971  0.1923216597
 0.3153129089 -0.0541128280  0.9474437035
 0.4814093527 -0.1213684016  0.5880503928
 0.7334393435 -0.4281941574  0.5279360691
-0.4997822658 -0.8660194532 -0.0150994524
 0.0376080229 -0.0000000000 -0.9992925681
-0.4997822658  0.8660194532 -0.0150994524
 0.7334393435  0.4281941574  0.5279360691
-0.1557358302 -0.6543033817  0.7400225914
-0.4304322977 -0.7911034807  0.4346070868
-0.5013032036 -0.1867132865 -0.8448865289
-0.4814093527  0.1213684016 -0.5880503928
-0.2943558888  0.1819512721 -0.9382155111
 0.4997822658  0.8660194532  0.0150994524
 0.8504349518 -0.4980243781  0.1695054916
 0.6797650274 -0.5277891775 -0.5092721195
 0.4153963271  0.8513025630 -0.3205149570
 0.0527175450  0.6819118559 -0.3528535099
-0.1583640613  0.7024638389 -0.6938770635
 0.3960752728 -0.6013809101 -0.6938770635
 0.8604797042 -0.0147168902  0.5092721195
 0.6020633561  0.2164780859  0.7685420962
-0.7654892092  0.4378252958  0.4715244224
-0.5750948931  0.4964545016  0.1228304115
-0.9394255243  0.3307899962  0.0897644851
-0.1797689355 -0.2646385431 -0.9474437035
 0.2198683340 -0.9487067242  0.2271859747
 0.9191528491  0.2826295391  0.2743694290
-0.3960752728  0.6013809101  0.6938770635
-0.4843157361  0.5017858901 -0.7166932316
-0.8191635253 -0.0947258962 -0.5656837662
-0.5616372200  0.3064419676  0.7685420962
-0.3101487853 -0.0000000000  0.7043410035
-0.3882607088 -0.3679950751  0.8448865289
-0.7334393435 -0.4281941574 -0.5279360691
-0.2833476244  0.9005462671 -0.3297431494
 0.0712557971  0.9925336575 -0.0989926775
-0.8671240119  0.1070352996  0.4864559514
 0.3965077344 -0.4525421860  0.7987410009
 0.1666692405 -0.8178589961 -0.5507522372
 0.5824039347  0.5352294570 -0.6118292942
-0.7752096022  0.5954285393 -0.2109856093
-0.4937747326  0.7686152920  0.4067149449
 0.7215564288  0.6208598148 -0.3064137896
 0.7056730782  0.3000763028 -0.0653317492
 0.8755232855  0.2333858350 -0.4230721316
 0.1982961578 -0.9730547528 -0.1176566270
-0.0585650429 -0.1278384441  0.9900643757
-0.1657176196  0.2889865716  0.9428809214
 0.9604690280 -0.1731867527  0.2179577823
 0.2734834501  0.6720295560 -0.6881737269
-0.4581201091 -0.5411818279 -0.7051582764
-0.1585623966 -0.6069020586 -0.4458882998
-0.5045884113 -0.7880941967 -0.3525593176
 0.0646114894 -0.4378252958  0.8967353934
 0.9976445893  0.0243480286 -0.0641283625
 0.7485209820  0.6512940977  0.1246288001
-0.5471106816  0.7084162097 -0.4458882998
-0.6991764131 -0.0995950201  0.7079782309
-0.1184473574 -0.9590900905 -0.2571311373
-0.0432600651 -0.5595774856 -0.8276482371
3 0 2 1 
5 0 3 10 9 2 3
3 0 4 3 
3 0 5 4 
3 0 1 5 
3 1 6 5 
5 1 7 17 16 6 3
3 1 2 7 
3 2 8 7 
3 2 9 8 
3 3 11 10 
3 3 12 11 
3 3 4 12 
3 4 13 12 
5 4 5 14 25 13 3
3 5 6 14 
3 6 15 14 
3 6 16 15 
3 7 18 17 
3 7 8 18 
5 8 19 31 30 18 3
3 8 9 19 
3 9 20 19 
3 9 10 20 
3 10 21 20 
3 10 11 21 
3 11 22 21 
5 11 12 23 35 22 3
3 12 13 23 
3 13 24 23 
3 13 25 24 
3 14 26 25 
3 14 15 26 
5 15 27 39 38 26 3
3 15 16 27 
3 16 28 27 
3 16 17 28 
3 17 29 28 
3 17 18 29 
3 18 30 29 
3 19 32 31 
3 19 20 32 
5 20 21 33 44 32 3
3 21 22 33 
3 22 34 33 
3 22 35 34 
3 23 36 35 
3 23 24 36 
5 24 37 48 47 36 3
3 24 25 37 
3 25 26 37 
3 26 38 37 
3 27 40 39 
3 27 28 40 
5 28 29 41 51 40 3
3 29 30 41 
3 30 42 41 
3 30 31 42 
3 31 43 42 
3 31 32 43 
3 32 44 43 
3 33 45 44 
3 33 34 45 
5 34 46 55 54 45 3
3 34 35 46 
3 35 36 46 
3 36 47 46 
3 37 38 48 
3 38 49 48 
3 38 39 49 
3 39 50 49 
3 39 40 50 
3 40 51 50 
3 41 52 51 
3 41 42 52 
5 42 43 53 58 52 3
3 43 44 53 
3 44 45 53 
3 45 54 53 
3 46 47 55 
3 47 56 55 
3 47 48 56 
3 48 49 56 
5 49 50 57 59 56 3
3 50 51 57 
3 51 52 57 
3 52 58 57 
3 53 54 58 
3 54 59 58 
3 54 55 59 
3 55 56 59 
3 57 58 59 
5 4 0 1 2 3 
5 4 5 6 7 0 
5 7 8 9 1 0 
5 1 10 11 12 2 
5 12 13 14 3 2 
5 14 15 5 4 3 
5 15 16 17 6 5 
5 6 18 19 8 7 
5 19 20 21 9 8 
5 21 22 23 1 9 
5 23 24 25 10 1 
5 25 26 27 11 10 
5 27 28 13 12 11 
5 28 29 30 14 13 
5 14 31 32 16 15 
5 32 33 34 17 16 
5 34 35 36 6 17 
5 36 37 38 18 6 
5 38 39 20 19 18 
5 20 40 41 22 21 
5 41 42 24 23 22 
5 42 43 26 25 24 
5 43 44 45 27 26 
5 27 46 47 29 28 
5 47 48 49 30 29 
5 49 50 31 14 30 
5 50 51 33 32 31 
5 33 52 53 35 34 
5 53 54 37 36 35 
5 54 55 39 38 37 
5 55 56 57 20 39 
5 57 58 59 40 20 
5 59 60 42 41 40 
5 42 61 62 44 43 
5 62 63 64 45 44 
5 64 65 46 27 45 
5 65 66 48 47 46 
5 48 67 51 50 49 
5 67 68 69 33 51 
5 69 70 71 52 33 
5 71 72 54 53 52 
5 54 73 74 56 55 
5 74 75 58 57 56 
5 75 76 60 59 58 
5 76 77 61 42 60 
5 77 78 63 62 61 
5 63 79 66 65 64 
5 79 80 81 48 66 
5 81 82 68 67 48 
5 82 83 70 69 68 
5 83 84 72 71 70 
5 84 85 73 54 72 
5 85 86 75 74 73 
5 75 87 78 77 76 
5 87 88 89 63 78 
5 89 90 80 79 63 
5 90 83 82 81 80 
5 83 91 86 85 84 
5 91 88 87 75 86 
5 88 89 90 83 91 
great dodecahemidodecahedron
great dodecahemidodecacron
5/3 5/2|5/3
(10/3.5/3.10/3.5/2)
icosahedral group
A5
6{10/3}+6{5/2}+6{5/3}
74 30 60 18 30 0 1 1 -12 3 4 120 5 1 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9510565163  0.0000000000 -0.3090169944
-0.9510565163  0.0000000000 -0.3090169944
-0.4253254042  0.8506508084 -0.3090169944
 0.4253254042 -0.8506508084 -0.3090169944
-0.5877852523 -0.0000000000 -0.8090169944
-0.1624598481 -0.8506508084  0.5000000000
 0.1624598481  0.8506508084  0.5000000000
 0.5877852523 -0.0000000000 -0.8090169944
 0.2628655561 -0.5257311121 -0.8090169944
-0.6881909602 -0.5257311121  0.5000000000
 0.6881909602  0.5257311121  0.5000000000
-0.2628655561  0.5257311121 -0.8090169944
 0.5257311121  0.8506508084 -0.0000000000
-0.5877852523 -0.0000000000  0.8090169944
-0.8506508084  0.5257311121 -0.0000000000
 0.8506508084 -0.5257311121  0.0000000000
 0.5877852523  0.0000000000  0.8090169944
-0.5257311121 -0.8506508084 -0.0000000000
 0.2628655561 -0.5257311121  0.8090169944
-0.2628655561  0.5257311121  0.8090169944
 0.9510565163  0.0000000000  0.3090169944
-0.1624598481 -0.8506508084 -0.5000000000
 0.6881909602  0.5257311121 -0.5000000000
 0.1624598481  0.8506508084 -0.5000000000
-0.6881909602 -0.5257311121 -0.5000000000
-0.9510565163 -0.0000000000  0.3090169944
-0.4253254042  0.8506508084  0.3090169944
 0.4253254042 -0.8506508084  0.3090169944
 0.0000000000 -0.0000000000 -1.0000000000
 0.0000000000  1.0000000000  0.0000000000
-0.7236067977  0.4472135955  0.5257311121
-0.8944271910 -0.4472135955  0.0000000000
 0.7236067977 -0.4472135955  0.5257311121
-0.2763932023 -0.4472135955 -0.8506508084
 0.2763932023  0.4472135955 -0.8506508084
-0.2763932023 -0.4472135955 -0.8506508084
-0.2763932023 -0.4472135955  0.8506508084
 0.7236067977 -0.4472135955 -0.5257311121
-0.8944271910 -0.4472135955 -0.0000000000
 0.8944271910  0.4472135955 -0.0000000000
-0.7236067977  0.4472135955 -0.5257311121
 0.0000000000 -1.0000000000 -0.0000000000
-0.0000000000  1.0000000000 -0.0000000000
 0.2763932023  0.4472135955  0.8506508084
-0.2763932023 -0.4472135955  0.8506508084
 0.7236067977 -0.4472135955 -0.5257311121
-0.7236067977  0.4472135955 -0.5257311121
10 0 1 5 14 21 29 26 17 8 2 3
5 0 2 7 10 3 3
10 0 3 9 19 27 29 28 20 12 4 3
5 0 1 6 11 4 2
10 1 6 15 23 28 26 24 16 10 3 3
5 1 3 9 13 5 3
5 2 8 18 12 4 2
10 2 4 11 15 22 21 27 25 16 7 3
10 5 13 19 25 24 17 18 12 11 6 3
5 5 6 15 22 14 2
5 7 16 24 17 8 2
10 7 8 18 20 23 22 14 13 9 10 3
5 9 10 16 25 19 3
5 11 15 23 20 12 3
5 13 14 21 27 19 2
5 17 26 28 20 18 2
5 21 22 23 28 29 2
5 24 26 29 27 25 3
4 3 0 1 2 
4 3 4 5 0 
4 6 0 1 7 
4 1 4 5 2 
4 6 2 3 7 
4 5 8 9 0 
4 3 8 9 4 
4 10 7 1 11 
4 10 0 6 11 
4 5 11 12 2 
4 12 4 1 11 
4 13 7 3 8 
4 13 2 6 8 
4 14 11 5 8 
4 9 11 14 0 
4 9 7 13 4 
4 12 7 10 4 
4 15 0 10 8 
4 15 11 6 8 
4 12 8 14 2 
4 15 2 13 11 
4 14 7 16 0 
4 16 11 9 7 
4 16 4 13 11 
4 17 4 10 8 
4 17 7 12 8 
4 17 0 15 4 
4 17 2 14 7 
4 16 2 15 4 
4 16 0 17 2 
great icosihemidodecahedron
great icosihemidodecacron
3/2 3|5/3
(10/3.3/2.10/3.3)
icosahedral group
A5
6{10/3}+10{3}+10{3/2}
75 30 60 26 30 0 1 1 -4 3 4 120 5 1 -1
 0.0000000000  0.0000000000  1.0000000000
 0.9510565163  0.0000000000 -0.3090169944
-0.9510565163  0.0000000000 -0.3090169944
 0.4253254042  0.8506508084 -0.3090169944
-0.4253254042 -0.8506508084 -0.3090169944
-0.5877852523  0.0000000000 -0.8090169944
-0.1624598481  0.8506508084  0.5000000000
 0.1624598481 -0.8506508084  0.5000000000
 0.5877852523 -0.0000000000 -0.8090169944
-0.2628655561 -0.5257311121 -0.8090169944
 0.6881909602 -0.5257311121  0.5000000000
-0.6881909602  0.5257311121  0.5000000000
 0.2628655561  0.5257311121 -0.8090169944
 0.5257311121 -0.8506508084 -0.0000000000
-0.5877852523 -0.0000000000  0.8090169944
-0.8506508084 -0.5257311121 -0.0000000000
 0.8506508084  0.5257311121  0.0000000000
 0.5877852523  0.0000000000  0.8090169944
-0.5257311121  0.8506508084 -0.0000000000
-0.2628655561 -0.5257311121  0.8090169944
 0.2628655561  0.5257311121  0.8090169944
 0.9510565163  0.0000000000  0.3090169944
-0.1624598481  0.8506508084 -0.5000000000
 0.6881909602 -0.5257311121 -0.5000000000
-0.6881909602  0.5257311121 -0.5000000000
 0.1624598481 -0.8506508084 -0.5000000000
-0.9510565163 -0.0000000000  0.3090169944
 0.4253254042  0.8506508084  0.3090169944
-0.4253254042 -0.8506508084  0.3090169944
 0.0000000000 -0.0000000000 -1.0000000000
 0.0000000000  1.0000000000  0.0000000000
-0.4911234732  0.7946544723  0.3568220898
-0.8944271910  0.4472135955  0.0000000000
 0.4911234732 -0.7946544723  0.3568220898
-0.2763932023  0.4472135955 -0.8506508084
 0.1875924741  0.7946544723 -0.5773502692
-0.1875924741 -0.7946544723 -0.5773502692
-0.2763932023  0.4472135955  0.8506508084
 0.7946544723 -0.1875924741 -0.5773502692
-0.7946544723  0.1875924741 -0.5773502692
 0.7236067977  0.4472135955 -0.5257311121
-0.6070619982 -0.7946544723 -0.0000000000
-0.3035309991 -0.1875924741  0.9341723590
 0.7236067977  0.4472135955  0.5257311121
 0.3035309991  0.1875924741  0.9341723590
 0.6070619982  0.7946544723 -0.0000000000
-0.9822469464 -0.1875924741 -0.0000000000
 0.9822469464  0.1875924741 -0.0000000000
 0.1875924741  0.7946544723  0.5773502692
-0.3035309991 -0.1875924741 -0.9341723590
 0.3035309991  0.1875924741 -0.9341723590
-0.1875924741 -0.7946544723  0.5773502692
 0.7946544723 -0.1875924741  0.5773502692
-0.7946544723  0.1875924741  0.5773502692
 0.4911234732 -0.7946544723 -0.3568220898
-0.4911234732  0.7946544723 -0.3568220898
10 0 1 5 14 21 29 26 17 8 2 3
3 0 2 3 2
10 0 3 9 19 27 29 28 20 12 4 3
3 0 1 4 
10 1 4 11 16 25 26 27 23 15 6 3
3 1 6 5 2
3 2 8 7 
10 2 7 16 24 28 21 22 15 10 3 3
3 3 10 9 
3 4 12 11 2
10 5 6 10 9 18 17 25 24 20 13 3
3 5 13 14 
3 6 15 10 
10 7 8 18 19 23 22 14 13 12 11 3
3 7 11 16 2
3 8 17 18 2
3 9 18 19 2
3 12 20 13 
3 14 22 21 2
3 15 23 22 2
3 16 25 24 
3 17 26 25 
3 19 23 27 
3 20 28 24 2
3 21 28 29 
3 26 29 27 2
4 3 0 1 2 
4 3 4 5 0 
4 6 0 1 7 
4 8 7 1 2 
4 9 2 3 4 
4 5 10 11 0 
4 12 4 5 10 
4 6 13 14 7 
4 15 0 6 13 
4 8 10 16 2 
4 12 7 8 10 
4 9 13 14 4 
4 17 2 9 13 
4 17 10 11 13 
4 18 13 11 0 
4 19 4 12 7 
4 20 4 14 7 
4 21 0 15 10 
4 16 13 15 10 
4 22 13 16 2 
4 23 2 17 10 
4 18 7 24 0 
4 19 13 18 7 
4 22 4 19 13 
4 20 10 23 7 
4 21 4 20 10 
4 25 0 21 4 
4 25 2 22 4 
4 24 2 23 7 
4 24 0 25 2 
small retrosnub icosicosidodecahedron
small hexagrammic hexecontahedron
|3/2 3/2 5/2
(3.3/2.3.3/2.3.5/2)
icosahedral group
A5
60{3}+12{5/2}+40{3/2}
76 60 180 112 60 38 0 0 -8 3 6 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8757465433  0.0000000000 -0.4827711589
-0.8174044834 -0.3142959094 -0.4827711589
 0.6501517764  0.5867151573 -0.4827711589
-0.3962731062 -0.7809607118 -0.4827711589
 0.0895951656  0.8711513729 -0.4827711589
 0.2290203992 -0.8452701727 -0.4827711589
-0.3122207301 -0.8452701727  0.4336318148
-0.3795312117  0.8711513729  0.3115306484
-0.6140944004 -0.7809607118 -0.1139668111
-0.1089106471  0.5867151573  0.8024361627
 0.8534618594 -0.5085414639 -0.1139668111
 0.3122207301 -0.5085414639  0.8024361627
-0.9791144009  0.1683643544 -0.1139668111
 0.3018736703 -0.9010110667  0.3115306484
 0.9485998144 -0.0557408940  0.3115306484
-0.4185577901  0.9010110667 -0.1139668111
 0.5724942349 -0.1683643544  0.8024361627
 0.7140366257 -0.6907700508 -0.1139668111
-0.5947789188 -0.0483139995  0.8024361627
 0.5931883546  0.7969561732 -0.1139668111
-0.9400878225  0.1385046605  0.3115306484
 0.7342041525  0.5224056964  0.4336318148
-0.1810253991  0.1385046605 -0.9736766732
 0.1865681885  0.7969561732  0.5745025405
 0.4155885877 -0.0483139995 -0.9082686184
 0.2449102485 -0.6907700508  0.6803349963
 0.9791144009 -0.1683643544  0.1139668111
-0.3018736703  0.9010110667 -0.3115306484
 0.7307785202 -0.0557408940  0.6803349963
 0.4185577901 -0.9010110667  0.1139668111
-0.5724942349  0.1683643544 -0.8024361627
-0.4155885877  0.0483139995  0.9082686184
-0.2449102485  0.6907700508 -0.6803349963
-0.7204314604 -0.3884911091  0.5745025405
 0.1553150829 -0.3884911091 -0.9082686184
-0.7140366257  0.6907700508  0.1139668111
 0.5947789188  0.0483139995 -0.8024361627
 0.3795312117 -0.8711513729 -0.3115306484
 0.6140944004  0.7809607118  0.1139668111
-0.7307785202  0.0557408940 -0.6803349963
-0.5931883546 -0.7969561732  0.1139668111
 0.9400878225 -0.1385046605 -0.3115306484
 0.1089106471 -0.5867151573 -0.8024361627
-0.8534618594  0.5085414639  0.1139668111
-0.1553150829  0.3884911091  0.9082686184
-0.3122207301  0.5085414639 -0.8024361627
-0.9485998144  0.0557408940 -0.3115306484
 0.7204314604  0.3884911091 -0.5745025405
-0.6501517764 -0.5867151573  0.4827711589
 0.1810253991 -0.1385046605  0.9736766732
-0.1865681885 -0.7969561732 -0.5745025405
 0.3962731062  0.7809607118  0.4827711589
-0.0895951656 -0.8711513729  0.4827711589
 0.3122207301  0.8452701727 -0.4336318148
-0.2290203992  0.8452701727  0.4827711589
-0.8757465433  0.0000000000  0.4827711589
-0.7342041525 -0.5224056964 -0.4336318148
 0.8174044834  0.3142959094  0.4827711589
-0.0000000000 -0.0000000000 -1.0000000000
 0.1814588279 -0.9775412010  0.1071722635
-0.5201989819  0.8472940016  0.1071722635
 0.7896280312 -0.6041536876  0.1071722635
-0.9538473568  0.2805161775  0.1071722635
 0.9909764414  0.0804971962  0.1071722635
 0.1814588279 -0.1388362820  0.1071722635
 0.5722705843  0.0804971962  0.8161045152
-0.3666342546  0.2805161775 -0.8870682034
 0.4750653790 -0.6041536876  0.6397743410
-0.1572813261  0.8472940016 -0.5073021381
-0.2265924308 -0.7344008871  0.6397743410
-0.0257718743 -0.2505849906 -0.0152212496
 0.4508878772 -0.7344008871 -0.5073021381
-0.0520716024  0.7667968054  0.6397743410
-0.0842536226 -0.4538847096 -0.8870682034
 0.1572813261 -0.1203377912 -0.1564292618
 0.4160557770  0.2000189813 -0.8870682034
-0.7537294122 -0.1502689781  0.6397743410
 0.8267571157 -0.2431403140 -0.5073021381
 0.2351248029  0.0904066044 -0.0152212496
 0.6495862074  0.4107633769  0.6397743410
-0.8589391359 -0.0697717819 -0.5073021381
 0.7073653437 -0.3005379561  0.6397743410
-0.3666342546  0.2805161775 -0.8870682034
 0.0719611847 -0.5734064947  0.8161045152
 0.7494414927 -0.5734064947 -0.3309719638
-0.9538473568  0.2805161775  0.1071722635
 0.9017757544 -0.3005379561  0.3106081546
-0.8589391359 -0.0697717819 -0.5073021381
 0.8738816538  0.4107633769  0.2600082756
 0.1001815169  0.0904066044  0.2132581137
-0.0451336029 -0.2431403140  0.9689405274
 0.1964013458 -0.1502689781 -0.9689405274
-0.5759871832  0.2000189813  0.7926103532
-0.0610614972 -0.1203377912  0.2132581137
-0.8175221318 -0.4538847096  0.3544661259
 0.5351414998  0.7667968054 -0.3544661259
-0.4187058571 -0.9077694191 -0.0252999395
 0.6001646849  0.7170468022  0.3544661259
-0.3479751379 -0.6415295512 -0.6836323123
-0.7666809950 -0.6415295512  0.0252999395
 0.6001646849  0.7170468022  0.3544661259
-0.2242954464 -0.9077694191 -0.3544661259
-0.1001815169 -0.0904066044 -0.2132581137
 0.0451336029  0.2431403140 -0.9689405274
-0.1964013458  0.1502689781  0.9689405274
 0.5759871832 -0.2000189813 -0.7926103532
-0.7537294122 -0.1502689781  0.6397743410
 0.9561443412  0.1071476454 -0.2725938019
 0.1466267277 -0.9508907518 -0.2725938019
-0.0520716024  0.7667968054  0.6397743410
 0.3436872184 -0.5036347128 -0.7926103532
-0.1964013458  0.1502689781  0.9689405274
-0.2228758320 -0.1071476454 -0.9689405274
 0.0610614972  0.1203377912 -0.2132581137
 0.8175221318  0.4538847096 -0.3544661259
-0.5351414998 -0.7667968054  0.3544661259
 0.4187058571  0.9077694191  0.0252999395
 0.5282035002  0.5036347128 -0.6836323123
-0.5351414998 -0.7667968054  0.3544661259
 0.7666809950  0.6415295512 -0.0252999395
-0.6001646849 -0.7170468022 -0.3544661259
 0.2242954464  0.9077694191  0.3544661259
-0.3436872184  0.5036347128  0.7926103532
 0.1964013458 -0.1502689781 -0.9689405274
 0.2228758320  0.1071476454  0.9689405274
-0.1679359245 -0.9508907518  0.2600082756
-0.1572813261  0.8472940016 -0.5073021381
 0.5259065158 -0.7917985292  0.3106081546
-0.5201989819  0.8472940016  0.1071722635
-0.6001646849 -0.7170468022 -0.3544661259
 0.3479751379  0.6415295512  0.6836323123
 0.0520716024 -0.7667968054 -0.6397743410
 0.0520716024 -0.7667968054 -0.6397743410
 0.0842536226  0.4538847096  0.8870682034
-0.1572813261  0.1203377912  0.1564292618
-0.9561443412 -0.1071476454  0.2725938019
 0.7537294122  0.1502689781 -0.6397743410
-0.5282035002 -0.5036347128  0.6836323123
 0.5351414998  0.7667968054 -0.3544661259
-0.4160557770 -0.2000189813  0.8870682034
 0.7537294122  0.1502689781 -0.6397743410
-0.8267571157  0.2431403140  0.5073021381
-0.2351248029 -0.0904066044  0.0152212496
-0.9017757544  0.3005379561 -0.3106081546
 0.8589391359  0.0697717819  0.5073021381
-0.8738816538 -0.4107633769 -0.2600082756
-0.6495862074 -0.4107633769 -0.6397743410
 0.8589391359  0.0697717819  0.5073021381
-0.7073653437  0.3005379561 -0.6397743410
-0.5722705843 -0.0804971962 -0.8161045152
 0.3666342546 -0.2805161775  0.8870682034
-0.4750653790  0.6041536876 -0.6397743410
 0.1679359245  0.9508907518 -0.2600082756
 0.3666342546 -0.2805161775  0.8870682034
-0.0719611847  0.5734064947 -0.8161045152
 0.1572813261 -0.8472940016  0.5073021381
 0.1572813261 -0.8472940016  0.5073021381
 0.2265924308  0.7344008871 -0.6397743410
 0.0257718743  0.2505849906  0.0152212496
-0.5259065158  0.7917985292 -0.3106081546
-0.4508878772  0.7344008871  0.5073021381
-0.1466267277  0.9508907518  0.2725938019
 0.5201989819 -0.8472940016 -0.1071722635
 0.5201989819 -0.8472940016 -0.1071722635
-0.7896280312  0.6041536876 -0.1071722635
-0.7494414927  0.5734064947  0.3309719638
 0.9538473568 -0.2805161775 -0.1071722635
 0.9538473568 -0.2805161775 -0.1071722635
-0.9909764414 -0.0804971962 -0.1071722635
-0.1814588279  0.1388362820 -0.1071722635
-0.1814588279  0.9775412010 -0.1071722635
3 0 2 1 
3 0 3 2 2
3 0 4 3 
3 0 5 4 2
3 0 6 5 
5 0 1 7 22 6 2
3 1 8 7 
3 1 9 8 2
3 1 10 9 
3 1 2 10 2
3 2 11 10 
5 2 12 35 34 11 2
3 2 3 12 
3 3 13 12 2
3 3 14 13 
5 3 4 15 23 14 2
3 4 16 15 
3 4 17 16 2
3 4 5 17 
5 5 18 24 25 17 2
3 5 19 18 
3 5 6 19 2
3 6 20 19 
3 6 21 20 2
3 6 22 21 
3 7 23 22 
3 7 24 23 2
3 7 25 24 
3 7 8 25 2
3 8 26 25 
5 8 27 19 20 26 2
3 8 9 27 
3 9 28 27 2
3 9 29 28 
5 9 10 30 21 29 2
3 10 31 30 
3 10 11 31 2
3 11 32 31 
3 11 33 32 2
3 11 34 33 
3 12 36 35 
3 12 37 36 2
3 12 13 37 
5 13 38 33 41 37 2
3 13 39 38 
3 13 14 39 2
3 14 40 39 
3 14 24 40 2
3 14 23 24 
3 15 34 23 
3 15 33 34 2
3 15 41 33 
3 15 16 41 2
3 16 42 41 
5 16 43 39 40 42 2
3 16 17 43 
3 17 44 43 2
3 17 25 44 
3 18 40 24 
3 18 45 40 2
3 18 46 45 
3 18 19 46 2
3 19 27 46 
3 20 47 26 
3 20 30 47 2
3 20 21 30 
3 21 35 29 
3 21 22 35 2
3 22 34 35 
3 22 23 34 2
3 25 26 44 2
3 26 48 44 
3 26 47 48 2
3 27 49 46 2
3 27 28 49 
5 28 50 47 52 49 2
3 28 51 50 
3 28 29 51 2
3 29 36 51 
3 29 35 36 2
3 30 52 47 
3 30 31 52 2
3 31 53 52 
5 31 32 51 36 53 2
3 32 54 51 
3 32 38 54 2
3 32 33 38 
3 36 37 53 
3 37 55 53 2
3 37 41 55 
3 38 56 54 
3 38 39 56 2
3 39 43 56 
3 40 45 42 
3 41 42 55 2
3 42 57 55 
3 42 45 57 2
3 43 58 56 2
3 43 44 58 
5 44 48 45 46 58 2
3 45 48 57 
3 46 49 58 
3 47 50 48 
3 48 50 57 2
3 49 59 58 2
3 49 52 59 
3 50 54 57 
3 50 51 54 2
3 52 53 59 2
3 53 55 59 
5 54 56 59 55 57 2
3 56 58 59 
6 5 0 1 2 3 4 
6 5 6 7 8 9 0 
6 9 10 11 12 1 0 
6 12 13 14 15 2 1 
6 15 16 17 18 3 2 
6 18 19 20 21 4 3 
6 21 22 23 24 5 4 
6 5 25 26 27 28 6 
6 28 29 30 31 7 6 
6 31 32 33 34 8 7 
6 34 35 36 10 9 8 
6 36 37 38 39 11 10 
6 11 40 41 42 13 12 
6 42 43 44 45 14 13 
6 45 46 47 48 15 14 
6 15 49 50 51 52 16 
6 52 53 54 55 17 16 
6 55 56 57 19 18 17 
6 19 58 59 60 61 20 
6 61 62 30 22 21 20 
6 30 63 64 65 23 22 
6 65 34 66 67 24 23 
6 67 68 69 25 5 24 
6 69 49 15 48 26 25 
6 47 58 19 27 26 48 
6 57 70 29 28 27 19 
6 70 71 72 63 30 29 
6 62 73 74 32 31 30 
6 74 75 76 77 33 32 
6 77 78 79 66 34 33 
6 64 80 81 35 34 65 
6 81 82 83 37 36 35 
6 83 84 85 86 38 37 
6 86 43 51 50 39 38 
6 68 11 39 50 49 69 
6 79 40 11 68 67 66 
6 78 83 87 41 40 79 
6 87 88 89 43 42 41 
6 85 90 91 44 43 86 
6 91 92 54 46 45 44 
6 54 93 59 58 47 46 
6 89 94 53 52 51 43 
6 94 95 96 93 54 53 
6 92 97 98 56 55 54 
6 98 99 71 70 57 56 
6 96 100 99 60 59 93 
6 99 101 73 62 61 60 
6 72 102 75 80 64 63 
6 100 103 102 72 71 99 
6 101 104 105 75 74 73 
6 103 106 107 76 75 102 
6 107 84 83 78 77 76 
6 105 108 82 81 80 75 
6 108 109 88 87 83 82 
6 106 110 90 85 84 107 
6 109 110 95 94 89 88 
6 110 111 97 92 91 90 
6 95 96 100 103 106 110 
6 111 104 101 99 98 97 
6 104 105 108 109 110 111 
great rhombidodecahedron
great rhombidodecacron
3/2 5/3 2|
(4.10/3.4/3.10/7)
icosahedral group
A5
15{4}+6{10/3}+6{10/7}+15{4/3}
77 60 120 42 60 0 0 1 -18 4 4 120 5 0 2
 0.0000000000  0.0000000000  1.0000000000
 0.9996324920  0.0000000000  0.0271086873
-0.9468654869  0.3204853643  0.0271086873
 0.0263835025 -0.9992842588  0.0271086873
-0.3453645319  0.9380770007  0.0271086873
 0.0527670051  0.3204853643 -0.9457826254
 0.0364611038  0.9380770007 -0.3445027268
-0.3352869307 -0.8768697425 -0.3445027268
 0.2398305218  0.7400061526  0.6283885859
-0.3189810294 -0.0612072581 -0.9457826254
-0.9367878857 -0.0612072581 -0.3445027268
 0.8677149793  0.3583135302 -0.3445027268
-0.7334184677 -0.2592781062  0.6283885859
 0.6216561575  0.7400061526  0.2567771718
-0.3678987333  0.3583135302  0.8580570704
 0.6480396600 -0.2592781062 -0.7161141409
 0.8514090780 -0.4573489542  0.2567771718
 0.2336022217 -0.4573489542  0.8580570704
 0.5060445461  0.4807280465 -0.7161141409
-0.7233408665 -0.6409707286  0.2567771718
 0.2762916255 -0.6409707286 -0.7161141409
 0.4796610435 -0.8390415766  0.2567771718
 0.4633551422 -0.2214499403  0.8580570704
-0.4672044434 -0.5185562123 -0.7161141409
-0.7295691665  0.4807280465  0.4864456563
 0.2436798229 -0.8390415766  0.4864456563
 0.8451807779 -0.2214499403  0.4864456563
-0.7031856640 -0.5185562123 -0.4864456563
-0.4998162460 -0.7166270604  0.4864456563
 0.4998162460 -0.7166270604 -0.4864456563
-0.8451807779  0.2214499403 -0.4864456563
-0.4998162460  0.7166270604  0.4864456563
 0.4998162460  0.7166270604 -0.4864456563
 0.7031856640  0.5185562123  0.4864456563
 0.7295691665 -0.4807280465 -0.4864456563
-0.2436798229  0.8390415766 -0.4864456563
-0.4633551422  0.2214499403 -0.8580570704
 0.4672044434  0.5185562123  0.7161141409
-0.5060445461 -0.4807280465  0.7161141409
-0.4796610435  0.8390415766 -0.2567771718
-0.2762916255  0.6409707286  0.7161141409
 0.7233408665  0.6409707286 -0.2567771718
 0.3678987333 -0.3583135302 -0.8580570704
-0.2336022217  0.4573489542 -0.8580570704
-0.8514090780  0.4573489542 -0.2567771718
-0.6480396600  0.2592781062  0.7161141409
-0.6216561575 -0.7400061526 -0.2567771718
-0.8677149793 -0.3583135302  0.3445027268
 0.7334184677  0.2592781062 -0.6283885859
-0.2398305218 -0.7400061526 -0.6283885859
 0.9367878857  0.0612072581  0.3445027268
 0.3189810294  0.0612072581  0.9457826254
-0.0364611038 -0.9380770007  0.3445027268
 0.3352869307  0.8768697425  0.3445027268
-0.0527670051 -0.3204853643  0.9457826254
 0.3453645319 -0.9380770007 -0.0271086873
 0.9468654869 -0.3204853643 -0.0271086873
-0.0263835025  0.9992842588 -0.0271086873
-0.9996324920  0.0000000000 -0.0271086873
 0.0000000000  0.0000000000 -1.0000000000
 0.1602426822  0.9732489895  0.1646471601
-0.2254435660 -0.1662507751  0.1646471601
-0.9686806297 -0.1858740172  0.1646471601
 0.1602426822  0.2297529205  0.1646471601
 0.1908463112 -0.1858740172 -0.9638612635
 0.1706981301 -0.1662507751 -0.2208973453
-0.0716627060  0.3082458890 -0.0736324484
-0.2898817352 -0.4156269378  0.8621037224
-0.3100299164  0.0635021454 -0.0736324484
 0.4078312422  0.3007504775  0.8621037224
 0.8696452057 -0.4156269378 -0.2664047011
 0.8507311228  0.3007504775  0.4310518612
-0.0652008839  0.0635021454 -0.3119120569
-0.6904884406  0.6724985120 -0.2664047011
 0.0652008839 -0.0635021454  0.3119120569
 0.4384348713 -0.8583725292 -0.2664047011
-0.2781921891 -0.8583725292  0.4310518612
 0.3100299164 -0.0635021454  0.0736324484
-0.2475885600  0.6724985120 -0.6974565623
 0.0189140829 -0.7163774153 -0.6974565623
-0.6977129774 -0.7163774153 -0.0000000000
 0.0716627060 -0.3082458890  0.0736324484
-0.6787988945  0.2297529205 -0.6974565623
 0.7166270604  0.0000000000 -0.6974565623
 0.6977129774  0.7163774153 -0.0000000000
-0.7166270604  0.0000000000  0.6974565623
-0.0189140829  0.7163774153  0.6974565623
 0.6787988945 -0.2297529205  0.6974565623
-0.1602426822 -0.2297529205 -0.1646471601
 0.2781921891  0.8583725292 -0.4310518612
 0.2475885600 -0.6724985120  0.6974565623
 0.2254435660  0.1662507751 -0.1646471601
-0.8507311228 -0.3007504775 -0.4310518612
-0.4384348713  0.8583725292  0.2664047011
-0.1706981301  0.1662507751  0.2208973453
 0.6904884406 -0.6724985120  0.2664047011
-0.4078312422 -0.3007504775 -0.8621037224
-0.8696452057  0.4156269378  0.2664047011
 0.2898817352  0.4156269378 -0.8621037224
-0.1908463112  0.1858740172  0.9638612635
 0.9686806297  0.1858740172 -0.1646471601
-0.1602426822 -0.9732489895 -0.1646471601
4 0 2 5 1 
10 0 3 10 14 25 27 24 17 7 2 3
4 0 4 9 3 3
10 0 1 6 14 26 32 31 22 11 4 7
4 1 3 10 6 3
10 1 5 7 16 18 23 21 11 9 3 3
10 2 8 18 30 40 41 36 24 13 5 7
4 2 7 16 8 3
10 4 12 23 35 45 46 43 31 19 9 3
4 4 11 21 12 
4 5 13 17 7 3
4 6 15 25 14 
10 6 10 20 32 44 49 48 39 27 15 3
4 8 12 23 18 
10 8 16 28 40 50 52 45 33 21 12 3
4 9 19 22 11 
4 10 20 26 14 3
10 13 15 25 37 48 55 51 41 29 17 3
4 13 24 27 15 
4 16 18 30 28 
4 17 24 36 29 3
10 19 20 26 38 49 56 54 46 34 22 7
4 19 31 32 20 3
4 21 23 35 33 3
4 22 31 43 34 
4 25 37 39 27 3
4 26 38 44 32 
4 28 29 41 40 3
10 28 30 42 52 58 59 55 47 36 29 7
4 30 42 50 40 
4 33 34 46 45 
10 33 35 42 50 57 59 56 53 43 34 3
4 35 42 52 45 3
4 36 41 51 47 
10 37 38 44 53 54 58 57 51 47 39 3
4 37 48 49 38 
4 39 48 55 47 3
4 43 46 54 53 3
4 44 49 56 53 
4 50 57 58 52 3
4 51 57 59 55 
4 54 58 59 56 3
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 1 4 5 2 
4 2 8 9 3 
4 5 10 6 0 
4 3 11 12 4 
4 7 5 10 1 
4 6 13 14 7 
4 5 15 8 2 
4 1 16 12 4 
4 9 5 15 3 
4 8 13 14 9 
4 10 17 18 6 
4 3 16 1 11 
4 11 17 18 12 
4 14 19 5 7 
4 17 20 1 10 
4 6 19 5 13 
4 15 21 22 8 
4 16 21 22 12 
4 14 23 5 9 
4 21 24 3 15 
4 8 23 5 13 
4 18 1 20 6 
4 1 25 17 11 
4 3 26 21 16 
4 25 12 18 1 
4 14 27 28 19 
4 17 27 28 20 
4 6 29 28 19 
4 22 3 24 8 
4 26 12 22 3 
4 14 30 31 23 
4 21 30 31 24 
4 8 32 31 23 
4 28 33 6 20 
4 25 34 35 17 
4 26 34 35 21 
4 34 36 12 25 
4 14 29 6 27 
4 17 33 6 27 
4 29 31 32 28 
4 31 37 8 24 
4 34 38 12 26 
4 14 32 8 30 
4 21 37 8 30 
4 28 36 34 33 
4 35 12 36 17 
4 38 21 35 12 
4 14 39 31 29 
4 17 40 34 33 
4 39 28 32 14 
4 31 38 34 37 
4 21 41 34 37 
4 28 40 17 36 
4 31 41 21 38 
4 39 34 40 31 
4 41 28 39 34 
4 28 40 31 41 
great retrosnub icosidodecahedron
great pentagrammic hexecontahedron
|3/2 5/3 2
(3.3/2.3.5/3.3)
icosahedral group
A5
60{3}+12{5/3}+20{3/2}
78 60 150 92 60 37 0 0 2 3 5 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.8737818460  0.0000000000 -0.4863180910
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3 0 2 1 
3 0 3 2 2
3 0 4 3 
5 0 5 13 12 4 3
3 0 1 5 
3 1 6 5 2
3 1 7 6 
5 1 2 8 17 7 3
3 2 9 8 
3 2 3 9 
5 3 10 21 20 9 3
3 3 4 10 
3 4 11 10 2
3 4 12 11 
3 5 14 13 
3 5 6 14 
5 6 15 27 26 14 3
3 6 7 15 
3 7 16 15 2
3 7 17 16 
3 8 18 17 
3 8 19 18 
3 8 9 19 2
3 9 20 19 
3 10 22 21 
3 10 11 22 
5 11 23 35 34 22 3
3 11 12 23 
3 12 24 23 2
3 12 13 24 
3 13 25 24 
3 13 14 25 2
3 14 26 25 
3 15 28 27 
3 15 16 28 
5 16 29 41 40 28 3
3 16 17 29 
3 17 18 29 2
3 18 30 29 
5 18 19 31 43 30 3
3 19 20 31 
3 20 32 31 2
3 20 21 32 
3 21 33 32 
3 21 22 33 2
3 22 34 33 
3 23 36 35 
3 23 24 36 
5 24 25 37 48 36 3
3 25 26 37 
3 26 38 37 2
3 26 27 38 
3 27 39 38 
3 27 28 39 2
3 28 40 39 
3 29 30 41 
3 30 42 41 2
3 30 43 42 
3 31 44 43 
3 31 32 44 
5 32 33 45 53 44 3
3 33 34 45 
3 34 46 45 2
3 34 35 46 
3 35 47 46 
3 35 36 47 2
3 36 48 47 
3 37 49 48 
3 37 38 49 
5 38 39 50 56 49 3
3 39 40 50 
3 40 51 50 2
3 40 41 51 
3 41 42 51 
5 42 52 58 57 51 3
3 42 43 52 
3 43 44 52 2
3 44 53 52 
3 45 54 53 
3 45 46 54 
5 46 47 55 59 54 3
3 47 48 55 
3 48 49 55 2
3 49 56 55 
3 50 57 56 
3 50 51 57 
3 52 53 58 
3 53 54 58 2
3 54 59 58 
3 55 56 59 
3 56 57 59 2
3 57 58 59 
5 4 0 1 2 3 
5 4 5 6 7 0 
5 7 8 9 1 0 
5 9 10 11 2 1 
5 11 12 13 3 2 
5 3 14 15 5 4 
5 15 16 17 6 5 
5 17 18 19 7 6 
5 7 20 21 22 8 
5 22 23 10 9 8 
5 10 24 25 12 11 
5 25 26 27 13 12 
5 27 28 29 3 13 
5 29 30 31 14 3 
5 31 32 16 15 14 
5 16 33 34 18 17 
5 34 35 36 19 18 
5 36 37 20 7 19 
5 37 38 39 21 20 
5 39 40 23 22 21 
5 40 41 42 10 23 
5 42 43 44 24 10 
5 44 45 26 25 24 
5 26 46 47 28 27 
5 47 48 30 29 28 
5 48 49 32 31 30 
5 49 50 51 16 32 
5 51 52 53 33 16 
5 53 54 35 34 33 
5 35 55 38 37 36 
5 55 56 57 39 38 
5 39 58 59 41 40 
5 59 60 43 42 41 
5 60 61 45 44 43 
5 61 62 63 26 45 
5 63 64 65 46 26 
5 65 66 48 47 46 
5 48 67 68 50 49 
5 68 69 52 51 50 
5 69 70 54 53 52 
5 70 71 72 35 54 
5 72 73 56 55 35 
5 73 74 75 57 56 
5 75 76 58 39 57 
5 76 77 60 59 58 
5 60 78 79 62 61 
5 79 80 64 63 62 
5 80 81 66 65 64 
5 81 82 67 48 66 
5 82 83 69 68 67 
5 69 84 85 71 70 
5 85 74 73 72 71 
5 74 86 77 76 75 
5 86 87 78 60 77 
5 87 88 80 79 78 
5 80 89 83 82 81 
5 89 90 84 69 83 
5 90 91 74 85 84 
5 91 88 87 86 74 
5 88 80 89 90 91 
great dirhombicosidodecahedron
great dirhombicosidodecacron
|3/2 5/3 3 5/2
(4.5/3.4.3.4.5/2.4.3/2)
icosahedral group
A5
60{4}+20{3}+12{5/2}+12{5/3}+20{3/2}
79 60 240 124 60 0 1 0 -56 5 8 120 5 1 -1
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 0.0000000000 -1.0000000000  0.0000000000
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