ref: 600bbfe4aaa9ad0f73d8d73eef1b7670e5f7d3a3
dir: /lib/polyhedra.all/
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
-0.5896684388 0.2849096099 0.7557232605
-0.0503237759 0.6529547237 0.7557232605
0.1620948777 -0.5955095034 0.7868250644
-0.5109791130 -0.4096128656 0.7557232605
0.8403525023 0.2849096099 0.4611227451
0.3449242913 0.6529547237 0.6742976806
0.7680705005 -0.4096128656 0.4922245490
-0.6439521587 0.5856966883 0.4922245490
-0.7337650345 -0.0831355038 0.6742976806
-0.3106188254 0.8131610779 0.4922245490
0.1014038338 -0.8645416449 0.4922245490
-0.5716701569 -0.6786450072 0.4611227451
0.7860687824 0.5856966883 0.1976240336
0.9405326461 -0.0831355038 0.3293733893
0.4798773090 0.8131610779 0.3293733893
0.7073794566 -0.6786450072 0.1976240336
-0.8423324743 0.5184386529 0.1473002577
-0.9321453501 -0.1503935392 0.3293733893
-0.1756658076 0.9733674322 0.1473002577
0.3740461233 -0.9061093968 0.1976240336
-0.2654786835 -0.9061093968 0.3293733893
-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
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0.2227859215 -0.3264773618 -0.9185744202
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0.1884917927 -0.2762216876 0.9149583817
0.7299680182 -0.0454313035 0.6819697127
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0.6262353286 0.5524433752 0.5016094570
0.4751441987 -0.6962909658 0.5379747963
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0.3769835855 -0.5524433752 -0.7082839194
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0.4009827382 0.0454313035 -0.9149583817
-0.1884917927 0.2762216876 -0.9149583817
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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
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-0.4170113787 0.4408282437 0.7948408455
0.1357750258 -0.5914331516 0.7948408455
0.8183499926 0.1506049079 0.5546363234
0.6572159007 0.4408282437 0.6113409191
-0.7899976948 -0.0465394760 0.6113409191
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-0.0663908970 -0.7885775354 0.6113409191
0.2655635881 -0.7885775354 0.5546363234
0.9481385550 -0.0465394760 0.3144318014
0.5262840256 0.7132750815 0.4628863603
-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
0.5009249595 -0.8063540334 0.3144318014
0.9227794888 -0.3477492917 0.1659772426
0.9970067683 -0.0753024539 -0.0175226837
0.4755658933 0.8638799894 0.1659772426
0.2402045220 0.8816564874 0.4061817646
-0.6542226690 -0.6379726275 0.4061817646
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-0.5244341067 -0.8351170114 0.1659772426
0.5497931728 -0.8351170114 -0.0175226837
0.7519590956 -0.6379726275 0.1659772426
0.9462886360 0.0753024539 -0.3144318014
0.5244341067 0.8351170114 -0.1659772426
-0.9481385550 0.0465394760 -0.3144318014
-0.9227794888 0.3477492917 -0.1659772426
-0.7519590956 0.6379726275 -0.1659772426
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-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
0.3681431654 0.8063540334 -0.4628863603
-0.8183499926 -0.1506049079 -0.5546363234
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0.0917499632 -0.8816564874 -0.4628863603
0.3427840993 -0.7132750815 -0.6113409191
0.5878317720 -0.1506049079 -0.7948408455
0.0663908970 0.7885775354 -0.6113409191
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-0.5829886213 -0.1683814059 -0.7948408455
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0.4170113787 -0.4408282437 -0.7948408455
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
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-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
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0.3158300191 -0.8717156832 0.3746507262
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0.6130206997 0.7884742426 0.0501397095
0.9847687342 -0.1664828812 0.0501397095
0.9617292448 0.2693749604 -0.0501397095
0.8197341309 -0.5705453218 -0.0501397095
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0.2182331759 0.9746077624 -0.0501397095
-0.8197341309 0.5705453218 0.0501397095
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-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
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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
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-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
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-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
-0.9500077743 0.0000000000 0.2182670607
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-0.8890012226 0.3323929240 0.1237389298
0.0501474947 -0.9486832981 0.2182670607
-0.8091426096 -0.5435471629 -0.0000000000
0.4686190076 0.8278950396 -0.3081980354
0.8890012226 -0.3323929240 -0.1237389298
0.9500077743 0.0000000000 -0.2182670607
0.8538605757 0.3323929240 -0.2766886585
0.7280022588 -0.5435471629 -0.3531635228
-0.0501474947 0.9486832981 -0.2182670607
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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
-0.6874320834 0.4108602493 -0.5241665181
-0.6313654799 -0.4743416490 -0.5714305835
-0.6623583361 0.1119768737 -0.7063270456
-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
-0.2192156342 -0.1411140222 0.9654177015
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snub dodecahedron
pentagonal hexecontahedron
|2 3 5
(3.3.3.3.5)
icosahedral group
A5
12{5}+80{3}
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-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
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0.2560622612 0.5610323550 0.7871942677
0.0961864071 0.8472940016 0.5223418899
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-0.6496432409 -0.6041536876 0.4614780399
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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
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-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
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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
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0.7029212391 0.2650636348 -0.3651134768
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0.1488707758 -0.9634937711 -0.2225247069
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0.0746433386 -0.8214200499 0.1317661698
0.5432565786 -0.3645767609 0.5192503492
0.4402662939 0.7076735504 -0.0550325933
0.0484747550 0.8295519246 -0.0846088198
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0.0243625739 -0.6670600099 0.5020978570
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0.3299109277 -0.6618755327 -0.3882581729
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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
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0.1326479105 -0.9732489895 0.1875924741
0.2146288278 -0.0877578066 -0.0442845760
0.4799246488 0.3717480345 -0.7946544723
0.1833149038 0.1419951139 0.0442845760
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0.0313139240 -0.2297529205 0.0442845760
0.0819809172 -0.6015009550 -0.7946544723
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-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
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0.8545497448 0.4993361296 -0.1428571429
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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
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0.9787751202 0.1102640897 0.1727457514
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0.5849197102 -0.1159385250 0.1624598481
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0.3825657108 -0.2262386491 0.5129472562
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0.3615002616 0.4911234732 0.1004057079
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0.5923004729 -0.2262386491 -0.2421808427
0.7008582352 0.1875924741 -0.6881909602
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0.9464199718 -0.1875924741 0.2628655561
0.2677040246 -0.4911234732 -0.2628655561
0.4359734112 -0.5058849985 0.1210904213
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0.0000000000 0.6787159473 -0.0000000000
0.0937962370 -0.4911234732 0.3632712640
0.1131193245 0.5058849985 0.4381092601
0.4331542107 -0.7946544723 -0.4253254042
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0.2455617366 0.1875924741 0.9510565163
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0.4331542107 0.1159385250 -0.4253254042
0.0864154744 0.2262386491 -0.6340376775
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0.6355082101 0.2262386491 -0.0748379961
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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
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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
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0.5199990010 -0.0881350076 0.8496077091
-0.1358666171 0.5096145631 0.8496077091
0.2176453044 -0.3004779764 0.9286245243
0.8327355166 -0.4593916847 0.3090482801
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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
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0.1385433541 0.9344550281 0.3280236873
0.6152755562 0.6750955630 0.4070405025
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0.8765539540 -0.0526433046 -0.4784159782
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-0.5860128319 -0.5802507864 -0.5655952490
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0.7441167318 -0.4021954364 -0.5334127111
0.1582993033 -0.2824850577 -0.9461202475
0.4809752902 0.7416267119 -0.4676030266
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0.1610261654 0.0935730734 -0.9825042768
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0.3247276953 0.2183102780 0.6558852870
0.2330291401 0.2556853380 0.6558852870
0.1873305537 0.3435327018 0.6558852870
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0.3505745987 0.6723073767 0.0916144386
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0.7357021020 0.0410148862 0.2008809586
0.4787409949 0.8779303974 -0.0067288271
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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
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-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
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0.3142555466 0.3448089608 0.8845056427
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-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
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-0.2510608506 -0.3497687395 -0.6308115736
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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
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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
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-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
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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
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0.9910042312 0.0000000000 0.1338305414
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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
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3 17 29 6
3 19 18 10
3 18 24 0
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3 21 20 11
3 20 31 7
3 27 21 2
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3 14 20 25
3 25 36 4
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3 5 38 26
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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
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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
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3 40 35 28
3 29 39 41
3 41 36 6
3 19 45 42
3 42 23 18
3 18 50 35
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3 21 22 43
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3 14 38 31
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3 23 45 44
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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
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3 15 53 47
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3 16 18 48
3 49 45 29
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3 38 40 35
3 35 28 50
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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
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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
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-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
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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
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-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
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0.4998162460 0.7166270604 -0.4864456563
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0.4672044434 0.5185562123 0.7161141409
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0.3678987333 -0.3583135302 -0.8580570704
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0.7334184677 0.2592781062 -0.6283885859
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0.9367878857 0.0612072581 0.3445027268
-0.0364611038 -0.9380770007 0.3445027268
0.3189810294 0.0612072581 0.9457826254
0.3352869307 0.8768697425 0.3445027268
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0.3453645319 -0.9380770007 -0.0271086873
0.9468654869 -0.3204853643 -0.0271086873
-0.0263835025 0.9992842588 -0.0271086873
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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
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0.7166270604 0.0000000000 -0.6974565623
0.6977129774 0.7163774153 0.0000000000
0.2532120777 -0.0227699753 -0.1118423604
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0.6787988945 -0.2297529205 0.6974565623
-0.2532120777 0.0227699753 0.1118423604
0.2781921891 0.8583725292 -0.4310518612
0.1186655045 0.0227699753 -0.2500871207
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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
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0.0894953255 -0.9958974583 0.0133730803
0.7289964592 0.5008783463 -0.4665672992
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0.2360757152 0.7797588398 -0.5798658539
0.3476955019 -0.5446593410 -0.7631867663
0.8391011449 -0.2292402645 0.4933134598
0.8347157954 -0.5505185752 0.0133730803
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0.0922056206 0.9462572293 0.3099925474
0.6766544115 -0.3460984252 -0.6498882116
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0.2168215026 0.9462572293 0.2399701898
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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
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0.9069896296 0.3460984252 -0.2399701898
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0.3172191052 -0.0591206691 0.9465076787
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0.0404422899 0.9498784352 -0.3099925474
0.7550875064 -0.3059386363 0.5798658539
0.6434677197 -0.0591206691 0.7631867663
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0.3948146729 0.7914773082 0.4665672992
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0.0351205564 0.9958974583 -0.0833954380
0.7776307312 -0.5008783463 -0.3800149051
0.1931819403 0.7914773082 0.5798658539
0.0150288165 0.2292402645 -0.9732538393
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0.7539911690 -0.6556582674 -0.0401192410
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0.8090435119 0.3898794199 0.4398211385
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0.8315867367 0.1949397099 -0.5200596205
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0.1125484940 0.1027486297 0.2002978807
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0.1125484940 -0.9732489895 0.2002978807
0.2465918377 0.1262614479 -0.0198507936
0.2605224485 0.6488326596 -0.7149435178
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0.1224008564 0.0175515613 -0.2192114469
0.2245940980 -0.1148764603 0.1162085697
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-0.0175451002 -0.1148764603 0.2522679329
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0.1014417091 -0.2122013592 -0.0895759354
0.2339533531 0.8785855802 0.4163570665
-0.0072045220 -0.2042953142 -0.1880294155
0.7912222885 -0.3536689320 -0.4988843319
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0.1425004198 -0.1239160115 0.9820073587
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0.7646531932 -0.1239160115 0.6324162524
0.2285438474 -0.1490314232 -0.0519700523
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0.0063908288 -0.0552638910 -0.2721187265
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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
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-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
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0.1348570368 -0.0368425940 0.2399994678
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-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
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-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
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0.3170419295 -0.8949249348 0.3139964587
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0.2582173913 -0.1829926907 0.9485976249
-0.9980199890 0.0131730113 0.0615026278
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0.4846651202 0.2204107171 0.8464743570
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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
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0.2099866077 0.9742658140 -0.0819252605
0.1401812208 -0.3162174531 -0.9382727469
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0.5310965183 0.7818292322 0.3266183398
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0.4802495600 0.5116505870 0.7124423043
0.8209889390 -0.3458563213 0.4542692670
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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
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0.5471106816 -0.7084162097 0.4458882998
0.2705130889 -0.3502689009 -0.8967353934
0.3101487853 -0.0000000000 -0.7043410035
0.2705130889 0.3502689009 -0.8967353934
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0.3573599567 0.5114170284 0.7815027091
0.9224380568 -0.3187513710 -0.2179577823
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0.6473614019 0.2164780859 -0.7307943990
0.6473614019 -0.2164780859 -0.7307943990
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0.2461720631 -0.7517075429 0.6118292942
0.8671240119 -0.1070352996 -0.4864559514
0.2454877182 0.9396111859 0.2384671877
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0.4577817420 -0.8362546538 -0.3018510074
0.5750948931 -0.4964545016 -0.1228304115
0.5632615562 -0.8178589961 0.1176566270
0.1797689355 0.2646385431 0.9474437035
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0.3153129089 -0.0541128280 0.9474437035
0.4814093527 -0.1213684016 0.5880503928
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0.0376080229 -0.0000000000 -0.9992925681
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0.7334393435 0.4281941574 0.5279360691
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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
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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
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0.4078312422 0.3007504775 0.8621037224
0.8696452057 -0.4156269378 -0.2664047011
0.8507311228 0.3007504775 0.4310518612
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-0.6904884406 0.6724985120 -0.2664047011
0.0652008839 -0.0635021454 0.3119120569
0.4384348713 -0.8583725292 -0.2664047011
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0.3100299164 -0.0635021454 0.0736324484
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0.0189140829 -0.7163774153 -0.6974565623
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0.0716627060 -0.3082458890 0.0736324484
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0.6977129774 0.7163774153 -0.0000000000
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0.6787988945 -0.2297529205 0.6974565623
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0.2781921891 0.8583725292 -0.4310518612
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0.2254435660 0.1662507751 -0.1646471601
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0.6904884406 -0.6724985120 0.2664047011
-0.4078312422 -0.3007504775 -0.8621037224
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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
-0.8272355164 -0.2813825063 -0.4863180910
0.6925555704 0.5327865392 -0.4863180910
-0.4840908004 -0.7274275300 -0.4863180910
-0.8272355164 0.2813825063 -0.4863180910
-0.0881336164 -0.5327865392 0.8416477703
-0.6603580332 0.7274275300 -0.1864844676
0.3909285122 0.9013314827 -0.1864844676
0.2550110996 -0.4760234971 0.8416477703
-0.3947197174 0.3685449435 0.8416477703
0.9714370516 0.1467433071 -0.1864844676
-0.5280509481 0.7309574441 0.4322770073
0.0271688654 -0.9013314827 0.4322770073
0.8594330536 0.4760234971 -0.1864844676
0.5434572030 -0.3685449435 -0.7542074602
0.3094806701 -0.1467433071 0.9395148305
0.1209150724 -0.7309574441 -0.6716254612
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0.9269841826 -0.3745166086 0.0209197322
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0.7014236118 0.2385878386 -0.6716254612
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0.4690884602 0.3745166086 0.7998083060
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0.6370715704 -0.5866558879 -0.4999746827
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0.6206411698 -0.6903443834 0.3717918378
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0.4019596432 0.6682227370 0.6260246154
0.1702647736 0.0891832664 -0.9813542948
0.7353106948 0.2151178849 0.6426838084
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0.6721432584 0.7404097257 -0.0041083120
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0.0900414998 -0.1398813892 -0.1531621544
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0.6999311915 0.2380801948 0.6733603404
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0.1224786701 0.3441803374 0.9308806963
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0.3826352213 0.6557130703 -0.6508691550
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0.7641147853 -0.3812005018 0.5203986667
0.0231391970 0.2214684501 -0.0393601759
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0.5067407650 -0.0146004527 -0.8619748395
-0.7623950866 -0.1395273955 0.6318906850
0.6968507713 0.4935425313 -0.5203986667
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0.1674404903 0.4465908350 -0.8789313445
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0.6354632109 -0.1224416147 0.7623611733
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0.4989740095 -0.3819252966 -0.7779190226
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0.8394638530 0.4913219899 -0.2321705015
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0.6639956781 0.6539122663 0.3626409897
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0.9751746089 0.1224416147 0.1845061871
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0.6304789864 -0.5559875283 -0.5416402091
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0.2053800891 -0.4913219899 0.8464169902
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0.6397822240 -0.6539122663 0.4038284955
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0.1940488224 0.0660053188 -0.0955053542
0.0485023878 -0.0191231611 0.9986399867
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0.4594979286 0.4223387451 0.7813396432
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0.3697500488 0.9182285161 -0.1419200256
0.0109186081 -0.0660053188 0.2160023198
0.8961810797 0.0191231611 -0.4432761860
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0.9061825512 -0.4223387451 0.0215213446
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0.0558089959 -0.9182285161 0.3920991561
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0.1451481861 0.8774517931 0.4571765031
0.1583802720 -0.7508056718 -0.6412538753
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0.4700607175 -0.8774517931 -0.0955053542
-0.4832928034 0.7508056718 0.4502431669
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
0.0000000000 0.0000000000 1.0000000000
1.0000000000 0.0000000000 0.0000000000
-1.0000000000 0.0000000000 0.0000000000
-0.6180339887 0.7861513778 0.0000000000
0.6180339887 -0.7861513778 0.0000000000
0.7861513778 0.6180339887 0.0000000000
-0.7861513778 -0.6180339887 0.0000000000
0.0000000000 -1.0000000000 0.0000000000
-0.0000000000 1.0000000000 0.0000000000
-0.0000000000 -0.6180339887 0.7861513778
0.0000000000 0.6180339887 -0.7861513778
-0.0000000000 0.7861513778 0.6180339887
0.0000000000 -0.7861513778 -0.6180339887
0.0000000000 -0.0000000000 -1.0000000000
-0.6180339887 -0.4858682718 0.6180339887
0.6180339887 0.4858682718 -0.6180339887
-0.4858682718 -0.3819660113 -0.7861513778
0.4858682718 0.3819660113 0.7861513778
-0.3819660113 0.4858682718 0.7861513778
0.3819660113 -0.4858682718 -0.7861513778
0.4858682718 -0.6180339887 0.6180339887
-0.4858682718 0.6180339887 -0.6180339887
-0.7861513778 -0.0000000000 0.6180339887
0.7861513778 -0.0000000000 -0.6180339887
-0.6180339887 -0.0000000000 -0.7861513778
0.6180339887 -0.0000000000 0.7861513778
0.6180339887 -0.6180339887 -0.4858682718
-0.6180339887 0.6180339887 0.4858682718
-0.7861513778 -0.4858682718 -0.3819660113
0.7861513778 0.4858682718 0.3819660113
0.7861513778 -0.3819660113 0.4858682718
-0.7861513778 0.3819660113 -0.4858682718
-0.8678342830 0.3177508827 0.3819660113
0.8678342830 -0.3177508827 -0.3819660113
0.1039022605 0.8678342830 -0.4858682718
-0.1039022605 -0.8678342830 0.4858682718
-0.9183170948 -0.1039022605 -0.3819660113
0.9183170948 0.1039022605 0.3819660113
0.3819660113 0.7861513778 0.4858682718
-0.3819660113 -0.7861513778 -0.4858682718
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0.4858682718 0.7861513778 -0.3819660113
0.3819660113 -0.8678342830 0.3177508827
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0.4858682718 -0.1039022605 -0.8678342830
-0.3819660113 -0.9183170948 -0.1039022605
0.3819660113 0.9183170948 0.1039022605
0.3177508827 -0.2360679775 0.9183170948
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0.2360679775 -0.9183170948 -0.3177508827
-0.3177508827 -0.3819660113 0.8678342830
0.3177508827 0.3819660113 -0.8678342830
-0.8678342830 0.4858682718 -0.1039022605
0.8678342830 -0.4858682718 0.1039022605
0.1039022605 0.3819660113 0.9183170948
-0.1039022605 -0.3819660113 -0.9183170948
0.9183170948 0.3177508827 -0.2360679775
-0.9183170948 -0.3177508827 0.2360679775
0.0000000000 1.0000000000 0.0000000000
-0.5773502692 0.2805161775 0.5773502692
-0.7861513778 -0.6180339887 -0.0000000000
0.8107067993 -0.0970626198 0.5773502692
-0.6180339887 0.7861513778 0.0000000000
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1.0000000000 0.0000000000 0.0000000000
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