shithub: purgatorio

ref: a8083462e62459b2ae8a243dc4ba88416eba03b1

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# data generated by kaleido written by Dr. Zvi Har'El (rl@math.technion.ac.il)
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 
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 
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 
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
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 0.3740461233 -0.9061093968  0.1976240336
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-0.8319652063 -0.5184386529  0.1976240336
 0.8319652063  0.5184386529 -0.1976240336
 0.9864290700 -0.1503935392 -0.0658746779
 0.2195822596  0.9733674322  0.0658746779
 0.8423324743 -0.5184386529 -0.1473002577
-0.7073794566  0.6786450072 -0.1976240336
-0.9864290700  0.1503935392  0.0658746779
-0.3740461233  0.9061093968 -0.1976240336
 0.1756658076 -0.9733674322 -0.1473002577
-0.2195822596 -0.9733674322 -0.0658746779
-0.7860687824 -0.5856966883 -0.1976240336
 0.5716701569  0.6786450072 -0.4611227451
 0.9321453501  0.1503935392 -0.3293733893
 0.2654786835  0.9061093968 -0.3293733893
 0.6439521587 -0.5856966883 -0.4922245490
-0.7680705005  0.4096128656 -0.4922245490
-0.9405326461  0.0831355038 -0.3293733893
-0.1014038338  0.8645416449 -0.4922245490
 0.3106188254 -0.8131610779 -0.4922245490
-0.4798773090 -0.8131610779 -0.3293733893
-0.8403525023 -0.2849096099 -0.4611227451
 0.5109791130  0.4096128656 -0.7557232605
 0.7337650345  0.0831355038 -0.6742976806
 0.5896684388 -0.2849096099 -0.7557232605
-0.4954282110  0.3680451137 -0.7868250644
-0.1620948777  0.5955095034 -0.7868250644
 0.0503237759 -0.6529547237 -0.7557232605
-0.3449242913 -0.6529547237 -0.6742976806
-0.5677102129 -0.3264773618 -0.7557232605
 0.1440965957  0.3680451137 -0.9185744202
 0.2227859215 -0.3264773618 -0.9185744202
-0.3952480672 -0.0000000000 -0.9185744202
-0.0000000000 -0.0000000000 -1.0000000000
 0.1884917927  0.3568220898  0.9149583817
-0.4009827382 -0.0454313035  0.9149583817
 0.1884917927 -0.2762216876  0.9149583817
 0.7299680182 -0.0454313035  0.6819697127
-0.3769835855  0.5524433752  0.7082839194
-0.2238218084 -0.6962909658  0.6819697127
 0.6262353286  0.5524433752  0.5016094570
 0.4751441987 -0.6962909658  0.5379747963
-0.8612946448  0.2378813932  0.4489810437
 0.0924951818  0.8887410555  0.4489810437
-0.7427296631 -0.3817289838  0.5016094570
 0.9686221187  0.2378813932  0.0719974582
 0.8805126380 -0.3817289838  0.1672031523
-0.5563085176  0.8152316624  0.1609912108
 0.0344457437 -0.9590792530  0.1672031523
-0.5746422389 -0.8152316624  0.0719974582
 0.5746422389  0.8152316624 -0.0719974582
 0.5563085176 -0.8152316624 -0.1609912108
-0.8805126380  0.3817289838 -0.1672031523
-0.9686221187 -0.2378813932 -0.0719974582
-0.0344457437  0.9590792530 -0.1672031523
 0.7427296631  0.3817289838 -0.5016094570
 0.8612946448 -0.2378813932 -0.4489810437
-0.4751441987  0.6962909658 -0.5379747963
-0.0924951818 -0.8887410555 -0.4489810437
-0.6262353286 -0.5524433752 -0.5016094570
 0.2238218084  0.6962909658 -0.6819697127
 0.3769835855 -0.5524433752 -0.7082839194
-0.7299680182  0.0454313035 -0.6819697127
 0.4009827382  0.0454313035 -0.9149583817
-0.1884917927  0.2762216876 -0.9149583817
-0.1884917927 -0.3568220898 -0.9149583817
6 0 2 7 11 4 1 
6 0 3 9 14 6 2 
5 0 1 5 8 3 
6 1 4 10 19 12 5 
5 2 6 13 15 7 
6 3 8 16 26 17 9 
5 4 11 20 18 10 
6 5 12 21 25 16 8 
6 6 14 23 33 22 13 
6 7 15 24 30 20 11 
5 9 17 27 23 14 
6 10 18 28 39 29 19 
5 12 19 29 31 21 
6 13 22 32 34 24 15 
5 16 25 35 36 26 
6 17 26 36 46 37 27 
6 18 20 30 40 38 28 
6 21 31 41 45 35 25 
5 22 33 43 42 32 
6 23 27 37 47 43 33 
5 24 34 44 40 30 
5 28 38 48 49 39 
6 29 39 49 50 41 31 
6 32 42 51 52 44 34 
6 35 45 53 54 46 36 
5 37 46 54 55 47 
6 38 40 44 52 56 48 
5 41 50 57 53 45 
6 42 43 47 55 58 51 
6 48 56 59 57 50 49 
5 51 58 59 56 52 
6 53 57 59 58 55 54 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 6 0 
3 2 7 3 
3 4 8 1 
3 0 9 4 
3 5 7 2 
3 1 10 5 
3 3 11 6 
3 6 9 0 
3 7 12 3 
3 4 13 8 
3 8 10 1 
3 9 13 4 
3 5 14 7 
3 10 15 5 
3 11 16 6 
3 12 11 3 
3 16 9 6 
3 7 17 12 
3 13 18 8 
3 8 19 10 
3 9 20 13 
3 14 17 7 
3 15 14 5 
3 19 15 10 
3 11 21 16 
3 12 22 11 
3 16 20 9 
3 17 22 12 
3 13 23 18 
3 18 19 8 
3 20 23 13 
3 14 24 17 
3 15 24 14 
3 19 25 15 
3 21 26 16 
3 22 21 11 
3 26 20 16 
3 17 27 22 
3 23 28 18 
3 28 19 18 
3 26 23 20 
3 24 27 17 
3 25 24 15 
3 28 25 19 
3 21 29 26 
3 22 29 21 
3 27 29 22 
3 23 30 28 
3 26 30 23 
3 24 31 27 
3 25 31 24 
3 28 31 25 
3 29 30 26 
3 31 29 27 
3 30 31 28 
3 29 30 31 
truncated dodecahedron
triakisicosahedron
2 3|5
(10.10.3)
icosahedral group
A5
12{10}+20{3}
30 60 90 32 60 1 0 0 2 2 3 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.3319544852  0.0000000000  0.9432954043
-0.2860795036  0.1683814059  0.9432954043
 0.1611340919 -0.2902233358  0.9432954043
 0.5829886213  0.1683814059  0.7948408455
-0.5878317720  0.1506049079  0.7948408455
-0.4170113787  0.4408282437  0.7948408455
 0.1357750258 -0.5914331516  0.7948408455
 0.8183499926  0.1506049079  0.5546363234
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-0.7899976948 -0.0465394760  0.6113409191
-0.3427840993  0.7132750815  0.6113409191
-0.0663908970 -0.7885775354  0.6113409191
 0.2655635881 -0.7885775354  0.5546363234
 0.9481385550 -0.0465394760  0.3144318014
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-0.8153567609 -0.3477492917  0.4628863603
-0.9462886360 -0.0753024539  0.3144318014
-0.3935022315  0.8638799894  0.3144318014
-0.0917499632  0.8816564874  0.4628863603
-0.3681431654 -0.8063540334  0.4628863603
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 0.9227794888 -0.3477492917  0.1659772426
 0.9970067683 -0.0753024539 -0.0175226837
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-0.6542226690 -0.6379726275  0.4061817646
-0.9970067683  0.0753024539  0.0175226837
-0.5497931728  0.8351170114  0.0175226837
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-0.9481385550  0.0465394760 -0.3144318014
-0.9227794888  0.3477492917 -0.1659772426
-0.7519590956  0.6379726275 -0.1659772426
-0.5009249595  0.8063540334 -0.3144318014
-0.4755658933 -0.8638799894 -0.1659772426
 0.3935022315 -0.8638799894 -0.3144318014
 0.7899976948  0.0465394760 -0.6113409191
 0.8153567609  0.3477492917 -0.4628863603
 0.6542226690  0.6379726275 -0.4061817646
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-0.8183499926 -0.1506049079 -0.5546363234
-0.2655635881  0.7885775354 -0.5546363234
-0.5262840256 -0.7132750815 -0.4628863603
-0.2402045220 -0.8816564874 -0.4061817646
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 0.3427840993 -0.7132750815 -0.6113409191
 0.5878317720 -0.1506049079 -0.7948408455
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-0.6572159007 -0.4408282437 -0.6113409191
-0.5829886213 -0.1683814059 -0.7948408455
-0.1357750258  0.5914331516 -0.7948408455
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 0.2860795036 -0.1683814059 -0.9432954043
-0.3319544852  0.0000000000 -0.9432954043
-0.1611340919  0.2902233358 -0.9432954043
-0.0000000000 -0.0000000000 -1.0000000000
 0.1432337790  0.5257311121  0.8385051474
-0.3901124942 -0.3804226065  0.8385051474
 0.1432337790 -0.0843049040  0.8385051474
 0.6463368675 -0.3804226065  0.6614584599
-0.3749909018  0.2207131041  0.7357864254
 0.5979747984  0.2207131041  0.5695840419
-0.7989163046  0.4702282018  0.3749909018
 0.0972965700 -0.6299377043  0.5695840419
 0.8780939903  0.4702282018  0.0885233438
-0.7412085774 -0.1364082001  0.4033816583
-0.2405303491  0.7142426083  0.4033816583
 0.0151215924 -0.9959593140  0.0885233438
 0.8330829954 -0.1364082001  0.1344605528
 0.3607955236  0.7142426083  0.3006629363
-0.8780939903 -0.4702282018 -0.0885233438
-0.0151215924  0.9959593140 -0.0885233438
-0.4493188674 -0.6621393122  0.3006629363
 0.5236468329 -0.6621393122  0.1344605528
 0.7989163046 -0.4702282018 -0.3749909018
-0.8330829954  0.1364082001 -0.1344605528
-0.5236468329  0.6621393122 -0.1344605528
 0.7412085774  0.1364082001 -0.4033816583
 0.4493188674  0.6621393122 -0.3006629363
-0.6463368675  0.3804226065 -0.6614584599
-0.3607955236 -0.7142426083 -0.3006629363
 0.2405303491 -0.7142426083 -0.4033816583
 0.3901124942  0.3804226065 -0.8385051474
-0.5979747984 -0.2207131041 -0.5695840419
-0.0972965700  0.6299377043 -0.5695840419
-0.1432337790 -0.5257311121 -0.8385051474
 0.3749909018 -0.2207131041 -0.7357864254
-0.1432337790  0.0843049040 -0.8385051474
10 0 2 6 11 19 25 15 9 4 1 
10 0 3 7 12 20 26 16 10 5 2 
3 0 1 3 
10 1 4 8 14 22 31 21 13 7 3 
3 2 5 6 
3 4 9 8 
10 5 10 17 27 35 36 28 18 11 6 
3 7 13 12 
10 8 9 15 24 33 42 41 32 23 14 
3 10 16 17 
3 11 18 19 
10 12 13 21 30 39 48 47 38 29 20 
3 14 23 22 
3 15 25 24 
10 16 26 29 38 46 52 44 34 27 17 
10 18 28 37 45 51 43 33 24 25 19 
3 20 29 26 
3 21 31 30 
10 22 23 32 40 50 55 49 39 30 31 
3 27 34 35 
3 28 36 37 
3 32 41 40 
3 33 43 42 
10 34 44 53 57 58 54 45 37 36 35 
3 38 47 46 
3 39 49 48 
10 40 41 42 43 51 54 58 59 56 50 
3 44 52 53 
3 45 54 51 
10 46 47 48 49 55 56 59 57 53 52 
3 50 56 55 
3 57 59 58 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 3 2 
3 3 5 0 
3 4 6 1 
3 0 6 4 
3 1 7 3 
3 3 8 5 
3 8 0 5 
3 6 9 1 
3 0 10 6 
3 1 11 7 
3 11 3 7 
3 3 12 8 
3 8 13 0 
3 9 14 1 
3 6 14 9 
3 10 15 6 
3 0 15 10 
3 1 16 11 
3 11 17 3 
3 3 18 12 
3 18 8 12 
3 8 15 13 
3 13 0 15 
3 14 16 1 
3 6 19 14 
3 15 20 6 
3 14 11 16 
3 11 18 17 
3 17 3 18 
3 18 21 8 
3 8 22 15 
3 19 23 14 
3 6 23 19 
3 20 23 6 
3 15 23 20 
3 14 24 11 
3 11 25 18 
3 18 26 21 
3 26 8 21 
3 26 22 8 
3 26 15 22 
3 23 27 14 
3 15 28 23 
3 14 29 24 
3 29 11 24 
3 29 25 11 
3 29 18 25 
3 18 30 26 
3 26 28 15 
3 27 29 14 
3 23 29 27 
3 26 23 28 
3 29 30 18 
3 29 26 30 
3 23 31 29 
3 26 31 23 
3 29 26 31 
rhombicosidodecahedron
deltoidal hexecontahedron
3 5|2
(4.3.4.5)
icosahedral group
A5
12{5}+30{4}+20{3}
31 60 120 62 60 1 0 0 2 3 4 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.4364663517  0.0000000000  0.8997205810
-0.0230394894  0.4358578416  0.8997205810
-0.3947875239  0.1861335198  0.8997205810
-0.1650346033 -0.4040624406  0.8997205810
 0.4134268623  0.4358578416  0.7994411620
 0.7478962199  0.1861335198  0.6371856536
 0.5411827887 -0.4040624406  0.7374650726
-0.2253527696  0.7370282030  0.6371856536
-0.5598221272 -0.2179289208  0.7994411620
-0.5971008041  0.4873038812  0.6371856536
 0.1694347542 -0.6537867624  0.7374650726
-0.4551056902 -0.6219913614  0.6371856536
 0.4808646224  0.7370282030  0.4749301452
 0.8526126568 -0.2179289208  0.4749301452
 0.8153339799  0.4873038812  0.3126746369
 0.6875780535 -0.6219913614  0.3746507262
 0.0860770985  0.9231617228  0.3746507262
-0.5296630440  0.7884742426  0.3126746369
-0.8641324015 -0.1664828812  0.4749301452
-0.8871718909  0.2693749604  0.3746507262
-0.1206363326 -0.8717156832  0.4749301452
 0.3158300191 -0.8717156832  0.3746507262
-0.7594159645 -0.5705453218  0.3126746369
 0.6130206997  0.7884742426  0.0501397095
 0.9847687342 -0.1664828812  0.0501397095
 0.9617292448  0.2693749604 -0.0501397095
 0.8197341309 -0.5705453218 -0.0501397095
-0.2182331759  0.9746077624  0.0501397095
 0.2182331759  0.9746077624 -0.0501397095
-0.8197341309  0.5705453218  0.0501397095
-0.9617292448 -0.2693749604  0.0501397095
-0.9847687342  0.1664828812 -0.0501397095
-0.2182331759 -0.9746077624  0.0501397095
 0.2182331759 -0.9746077624 -0.0501397095
-0.6130206997 -0.7884742426 -0.0501397095
 0.7594159645  0.5705453218 -0.3126746369
 0.8871718909 -0.2693749604 -0.3746507262
 0.8641324015  0.1664828812 -0.4749301452
 0.5296630440 -0.7884742426 -0.3126746369
-0.3158300191  0.8717156832 -0.3746507262
 0.1206363326  0.8717156832 -0.4749301452
-0.6875780535  0.6219913614 -0.3746507262
-0.8153339799 -0.4873038812 -0.3126746369
-0.8526126568  0.2179289208 -0.4749301452
-0.0860770985 -0.9231617228 -0.3746507262
-0.4808646224 -0.7370282030 -0.4749301452
 0.4551056902  0.6219913614 -0.6371856536
 0.5971008041 -0.4873038812 -0.6371856536
 0.5598221272  0.2179289208 -0.7994411620
 0.2253527696 -0.7370282030 -0.6371856536
-0.1694347542  0.6537867624 -0.7374650726
-0.5411827887  0.4040624406 -0.7374650726
-0.7478962199 -0.1861335198 -0.6371856536
-0.4134268623 -0.4358578416 -0.7994411620
 0.1650346033  0.4040624406 -0.8997205810
 0.3947875239 -0.1861335198 -0.8997205810
 0.0230394894 -0.4358578416 -0.8997205810
-0.4364663517 -0.0000000000 -0.8997205810
 0.0000000000  0.0000000000 -1.0000000000
 0.2124281962  0.2239537475  0.9245941063
-0.1379991118  0.2054301247  0.9245941063
-0.2876494382 -0.1119768737  0.9245941063
 0.2124281962 -0.3162277660  0.9245941063
 0.6623583361 -0.1119768737  0.7063270456
 0.5277148574  0.2054301247  0.7716443776
 0.1583346290  0.7071067812  0.6891517578
-0.3186422944  0.4743416490  0.7896976442
-0.7144788670  0.1207882584  0.6891517578
-0.3897157456 -0.4108602493  0.7716443776
-0.1467842735 -0.6555240367  0.7063270456
 0.6313654799  0.4743416490  0.5714305835
 0.9436228948  0.1207882584  0.3081980354
 0.4403528206 -0.6555240367  0.5714305835
 0.6874320834 -0.4108602493  0.5241665181
-0.2279246243  0.8794777841  0.3531635228
-0.4465745066  0.6647858481  0.5241665181
-0.6778547641 -0.4051361351  0.5714305835
-0.7280022588  0.5435471629  0.3531635228
 0.1204287884 -0.7917486474  0.5241665181
-0.4686190076 -0.8278950396  0.3081980354
 0.6305733224  0.6647858481  0.2766886585
 0.3592124698  0.8794777841  0.2182670607
 0.8592901042 -0.4051361351  0.2182670607
 0.8091426096  0.5435471629 -0.0000000000
 0.5561442379 -0.8278950396  0.0727556869
 0.0284293805  0.9486832981  0.1237389298
-0.5561442379  0.8278950396 -0.0727556869
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 0.0501474947 -0.9486832981  0.2182670607
-0.8091426096 -0.5435471629 -0.0000000000
 0.4686190076  0.8278950396 -0.3081980354
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-0.3592124698 -0.8794777841 -0.2182670607
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 0.2279246243 -0.8794777841 -0.3531635228
-0.6305733224 -0.6647858481 -0.2766886585
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-0.4403528206  0.6555240367 -0.5714305835
 0.1467842735  0.6555240367 -0.7063270456
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-0.1583346290 -0.7071067812 -0.6891517578
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-0.2124281962  0.3162277660 -0.9245941063
-0.5277148574 -0.2054301247 -0.7716443776
-0.2124281962 -0.2239537475 -0.9245941063
 0.1379991118 -0.2054301247 -0.9245941063
4 0 2 5 1 
3 0 3 2 
4 0 4 9 3 
5 0 1 7 11 4 
4 1 6 14 7 
3 1 5 6 
5 2 8 17 13 5 
4 2 3 10 8 
5 3 9 19 20 10 
3 4 12 9 
4 4 11 21 12 
4 5 13 15 6 
5 6 15 26 25 14 
4 7 16 22 11 
3 7 14 16 
4 8 18 28 17 
3 8 10 18 
4 9 12 23 19 
4 10 20 30 18 
3 11 22 21 
5 12 21 33 35 23 
3 13 24 15 
4 13 17 29 24 
4 14 25 27 16 
4 15 24 36 26 
5 16 27 39 34 22 
3 17 28 29 
5 18 30 42 40 28 
4 19 31 32 20 
3 19 23 31 
3 20 32 30 
4 21 22 34 33 
4 23 35 43 31 
5 24 29 41 47 36 
3 25 37 27 
4 25 26 38 37 
3 26 36 38 
4 27 37 48 39 
4 28 40 41 29 
4 30 32 44 42 
5 31 43 53 44 32 
4 33 45 46 35 
3 33 34 45 
4 34 39 50 45 
3 35 46 43 
4 36 47 49 38 
5 37 38 49 56 48 
3 39 48 50 
3 40 51 41 
4 40 42 52 51 
4 41 51 55 47 
3 42 44 52 
4 43 46 54 53 
4 44 53 58 52 
5 45 50 57 54 46 
3 47 55 49 
4 48 56 57 50 
4 49 55 59 56 
5 51 52 58 59 55 
3 53 54 58 
4 54 57 59 58 
3 56 59 57 
4 3 0 1 2 
4 3 4 5 0 
4 0 6 7 1 
4 7 8 2 1 
4 2 9 10 3 
4 5 11 6 0 
4 4 12 11 5 
4 3 13 14 4 
4 6 15 16 7 
4 8 17 9 2 
4 16 18 8 7 
4 10 19 13 3 
4 17 20 10 9 
4 11 21 22 6 
4 14 23 12 4 
4 12 24 21 11 
4 13 25 23 14 
4 22 26 15 6 
4 15 27 18 16 
4 8 28 29 17 
4 18 30 28 8 
4 20 31 19 10 
4 31 25 13 19 
4 29 32 20 17 
4 24 33 22 21 
4 23 34 35 12 
4 35 36 24 12 
4 25 37 34 23 
4 26 38 27 15 
4 33 38 26 22 
4 27 39 30 18 
4 28 40 32 29 
4 39 40 28 30 
4 20 41 42 31 
4 42 43 25 31 
4 32 44 41 20 
4 36 45 33 24 
4 37 46 35 34 
4 46 45 36 35 
4 43 47 37 25 
4 38 48 49 27 
4 33 50 48 38 
4 49 51 39 27 
4 40 52 44 32 
4 51 53 40 39 
4 41 54 43 42 
4 52 54 41 44 
4 45 55 50 33 
4 47 56 46 37 
4 46 57 55 45 
4 54 56 47 43 
4 50 58 49 48 
4 58 53 51 49 
4 53 59 52 40 
4 59 60 54 52 
4 57 58 50 55 
4 56 61 57 46 
4 60 61 56 54 
4 58 60 59 53 
4 57 58 60 61 
truncated icosidodecahedron
disdyakistriacontahedron
2 3 5|
(4.6.10)
icosahedral group
A5
12{10}+20{6}+30{4}
32 120 180 62 120 1 0 0 2 3 3 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.2607080006  0.0000000000  0.9654177015
-0.0045873783  0.2606676380  0.9654177015
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 0.2561208549  0.2606676380  0.9308353722
 0.4633267724 -0.1411140222  0.8748800687
-0.2283903908  0.3802212538  0.8962531046
-0.3132059807 -0.3694413065  0.8748800687
-0.4430186467 -0.0215604065  0.8962531046
 0.4541524811  0.3802212538  0.8057154101
 0.5304628314 -0.3694413065  0.7629694001
 0.6613583986 -0.0215604065  0.7497601066
-0.3298032754  0.5736633003  0.7497601066
-0.4476060250  0.2391072316  0.8616708061
-0.5370090771 -0.2498878945  0.8057153910
-0.2460699217 -0.5977685908  0.7629694001
 0.5138663784  0.5736633003  0.6378493263
 0.6567712529  0.2391072316  0.7151777773
 0.7284945175 -0.2498878945  0.6378493381
 0.4364724850 -0.5977685908  0.6724317673
-0.5490190001  0.4325494506  0.7151776775
-0.2700897570  0.7671054904  0.5818940537
-0.6936761144 -0.3586617667  0.6246400447
-0.0434511498 -0.7388826131  0.6724317673
-0.4027369590 -0.7065424630  0.5818940537
 0.7164852035  0.4325494506  0.5473115438
 0.4124538677  0.7671054904  0.4913562594
 0.8325358571 -0.3586617667  0.4221916434
 0.2172568508 -0.7388826131  0.6378494688
 0.5405138246 -0.7065424630  0.4567740725
-0.7085212064  0.4848777911  0.5127291954
-0.0720583700  0.8866594825  0.4567740725
-0.4295919633  0.8194338309  0.3794455716
-0.8531785590 -0.3063341981  0.4221915508
-0.6265400554 -0.5869890510  0.5127293760
-0.2001180064 -0.8476566112  0.4913563402
 0.8176915179  0.4848777911  0.3102806942
 0.1886510811  0.8866594825  0.4221915817
 0.5136601821  0.8194338309  0.2543254098
 0.9337423985 -0.3063341981  0.1851607203
 0.7385455107 -0.5869890510  0.3316540106
 0.3212979948 -0.8476566112  0.4221917432
-0.8651885085  0.3761046523  0.3316536375
-0.6488076880  0.6783199813  0.3448631425
-0.2315603996  0.9389879297  0.2543254788
-0.7860426423 -0.5346614357  0.3102807015
-0.9545918983 -0.1128925413  0.2756983531
-0.0960768624 -0.9564306093  0.2756986145
 0.9217330580  0.3761046523  0.0946227263
 0.7162790072  0.6783199813  0.1637876273
 0.2898571959  0.9389879297  0.1851606704
 0.8397521423 -0.5346614357  0.0946228761
 0.9934566827 -0.1128925413  0.0172943252
 0.1646311382 -0.9564306093  0.2411163161
-0.8054751299  0.5695467454  0.1637874231
-0.9591793219  0.1477776761  0.2411157125
-0.1303544328  0.9913166095  0.0172945558
-0.8203200648 -0.5695470165  0.0518766546
-0.9888693637 -0.1477781439  0.0172916663
-0.1303536668 -0.9913167102  0.0172945558
 0.8203206401  0.5695467454 -0.0518705331
 0.9888694917  0.1477776761 -0.0172883463
 0.1303553059  0.9913166095 -0.0172879732
 0.8054761704 -0.5695470165 -0.1637813633
 0.9591800640 -0.1477781439 -0.2411124739
 0.1303545664 -0.9913167102 -0.0172877735
-0.8397525647  0.5346618623 -0.0946167165
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-0.7162795951 -0.6783208443 -0.1637814823
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-0.2898558028 -0.9389895580 -0.1851545936
 0.7860446559  0.5346618623 -0.3102748651
 0.9545928720  0.1128921245 -0.2756951522
 0.0960787036  0.9564322465 -0.2756922934
 0.6488098576 -0.6783208443 -0.3448573632
 0.8651904546 -0.3761053597 -0.3316477584
 0.2315606390 -0.9389895580 -0.2543192490
-0.7385472639  0.5869902473 -0.3316479890
-0.9337433781  0.3063348862 -0.1851546415
-0.3212992842  0.8476584134 -0.4221871436
-0.8176928415 -0.4848792845 -0.3102748723
-0.5136611563 -0.8194350139 -0.2543196306
-0.1886494644 -0.8866613987 -0.4221882798
 0.6265433179  0.5869902473 -0.5127240198
 0.8531810896  0.3063348862 -0.4221859376
 0.2001204504  0.8476584134 -0.4913522358
 0.7085240020 -0.4848792845 -0.5127239199
 0.4295944104 -0.8194350139 -0.3794402462
 0.0720576700 -0.8866613987 -0.4567704634
-0.8325379870  0.3586633178 -0.4221861255
-0.5405162125  0.7065442357 -0.4567685048
-0.2172590958  0.7388844270 -0.6378466030
-0.7164876491 -0.4325518944 -0.5473064108
-0.4124548660 -0.7671068289 -0.4913533317
 0.6936796092  0.3586633178 -0.6246352729
 0.4027407159  0.7065442357 -0.5818893011
 0.0434540643  0.7388844270 -0.6724295858
 0.5490226993 -0.4325518944 -0.7151733596
 0.2700914841 -0.7671068289 -0.5818914876
-0.7284976588  0.2498903768 -0.6378447779
-0.4364761587  0.5977701626 -0.6724279854
-0.6567747682 -0.2391103983 -0.7151734903
-0.5138692103 -0.5736660641 -0.6378445591
 0.5370132986  0.2498903768 -0.8057118075
 0.2460744543  0.5977701626 -0.7629667067
 0.4476105365 -0.2391103983 -0.8616675838
 0.3298072522 -0.5736660641 -0.7497562426
-0.6613622562  0.0215634725 -0.7497566156
-0.5304666075  0.3694443652 -0.7629652937
-0.4541562762 -0.3802243954 -0.8057117884
 0.4430232811  0.0215634725 -0.8962507401
 0.3132106967  0.3694443652 -0.8748770888
 0.2283949989 -0.3802243954 -0.8962505976
-0.4633311450  0.1411172572 -0.8748772313
-0.2561255056 -0.2606708670 -0.9308331883
 0.2192205953  0.1411172572 -0.9654161022
 0.0045924376 -0.2606708670 -0.9654168056
-0.2607129987  0.0000032913 -0.9654163518
 0.0000051771  0.0000032912 -0.9999999999
 0.1200387571  0.1221698550  0.9049446030
-0.2175780247  0.1162282816  0.9049446030
 0.1200387571 -0.4082474279  0.9049446030
 0.4459799746  0.1162282816  0.8169252068
 0.1016985225  0.6339220449  0.7666817889
-0.3544276914 -0.1832548434  0.8300952867
 0.5585832497 -0.1832548434  0.7089865490
-0.3643565320  0.3809295903  0.7552459704
-0.4568036952 -0.4649138222  0.6745068322
-0.7747432361  0.0697368203  0.6284189748
 0.5486549126  0.3809295903  0.6341371659
 0.6168557011 -0.4649138222  0.5320884576
 0.9117846887  0.0697368203  0.4047050422
-0.4756956529  0.6085799433  0.5320883790
-0.2091195905 -0.6774423865  0.5878778112
 0.5979647013  0.6085799433  0.3896698773
 0.3551522032 -0.6774423865  0.5130284950
-0.2351136470  0.7996124516  0.3919196492
-0.6935150612 -0.4186830921  0.4381790039
 0.0589047087 -0.8240793946  0.4440690614
-0.5063278658 -0.8431340489  0.1809911096
 0.3291594648  0.7996124516  0.3170701581
 0.7837684883 -0.4186830921  0.2422208418
 0.5360037147 -0.8431340489  0.0427282955
-0.7095802914  0.4941881267  0.3170700500
 0.0283375922  0.9128709077  0.2136305953
-0.5360037809  0.8431342740 -0.0427230226
-0.8627717620 -0.3317288924  0.1592318224
 0.7677040727  0.4941881267  0.1211117799
 0.5063293044  0.8431342740 -0.1809860363
 0.8744481415 -0.3317288924 -0.0712062810
-0.8744476717  0.3317288831  0.0712120936
-0.9130127824 -0.0000002089  0.1211105323
 0.0160652247 -0.9128709077  0.1211120373
 0.8627728239  0.3317288831 -0.1592260883
 0.9130131866 -0.0000002089 -0.1211074853
-0.0160644264  0.9128718312 -0.1211060185
-0.7677045094 -0.4941888273 -0.1211061534
-0.9117856757 -0.0697383469 -0.4047106460
-0.0283368549 -0.9128720729 -0.2136250368
 0.7095821798 -0.4941888273 -0.3170647319
 0.7747427279 -0.0697383469 -0.6284246421
-0.7837697662  0.4186839017 -0.2422153076
-0.0589041897  0.8240821079 -0.4440651491
-0.5979663637 -0.6085817063 -0.3896645730
-0.3291594183 -0.7996144008 -0.3170661961
 0.6935177376  0.4186839017 -0.4381739942
 0.4756986407 -0.6085817063 -0.5320836915
 0.2351146351 -0.7996144008 -0.3919158121
-0.6168583888  0.4649158905 -0.5320835344
-0.3551545140  0.6774441676 -0.5130247732
-0.1016986410 -0.6339226751 -0.7666826828
 0.4568075735  0.4649158905 -0.6745027800
 0.2091227917  0.6774441676 -0.5878748207
-0.1200394924  0.4082445693 -0.9049501465
-0.5486577777 -0.3809323480 -0.6341330304
 0.3643603762 -0.3809323480 -0.7552427249
-0.5585867166  0.1832576685 -0.7089830873
-0.4459830958 -0.1162285368 -0.8169244453
 0.3544319409  0.1832576685 -0.8300928486
 0.2175812365 -0.1162285368 -0.9049446815
-0.1200388929 -0.1221699932 -0.9049456265
4 0 2 4 1 
6 0 3 8 13 6 2 
10 0 1 5 10 19 28 23 15 7 3 
6 1 4 9 17 11 5 
10 2 6 12 21 31 37 26 16 9 4 
4 3 7 14 8 
4 5 11 18 10 
4 6 13 20 12 
6 7 15 24 34 22 14 
10 8 14 22 33 46 55 42 30 20 13 
4 9 16 25 17 
6 10 18 27 40 29 19 
10 11 17 25 36 48 61 52 39 27 18 
6 12 20 30 43 32 21 
4 15 23 35 24 
6 16 26 38 49 36 25 
4 19 29 41 28 
4 21 32 44 31 
4 22 34 45 33 
6 23 28 41 53 47 35 
10 24 35 47 59 71 82 69 57 45 34 
4 26 37 50 38 
4 27 39 51 40 
10 29 40 51 63 75 88 77 65 53 41 
4 30 42 54 43 
6 31 44 56 62 50 37 
10 32 43 54 66 78 91 80 68 56 44 
6 33 45 57 70 58 46 
4 36 49 60 48 
10 38 50 62 74 86 96 84 72 60 49 
6 39 52 64 76 63 51 
6 42 55 67 79 66 54 
4 46 58 67 55 
4 47 53 65 59 
6 48 60 72 85 73 61 
4 52 61 73 64 
4 56 68 74 62 
4 57 69 81 70 
10 58 70 81 93 102 108 100 90 79 67 
6 59 65 77 89 83 71 
4 63 76 87 75 
10 64 73 85 95 104 111 106 98 87 76 
4 66 79 90 78 
6 68 80 92 97 86 74 
6 69 82 94 103 93 81 
4 71 83 94 82 
4 72 84 95 85 
6 75 87 98 107 99 88 
4 77 88 99 89 
6 78 90 100 109 101 91 
4 80 91 101 92 
10 83 89 99 107 113 117 115 110 103 94 
6 84 96 105 112 104 95 
4 86 97 105 96 
10 92 101 109 114 118 119 116 112 105 97 
4 93 103 110 102 
4 98 106 113 107 
4 100 108 114 109 
6 102 110 115 118 114 108 
4 104 112 116 111 
6 106 111 116 119 117 113 
4 115 117 119 118 
3 2 0 1 
3 2 3 0 
3 0 4 1 
3 1 5 2 
3 3 4 0 
3 2 6 3 
3 4 7 1 
3 5 8 2 
3 1 9 5 
3 3 10 4 
3 2 11 6 
3 6 12 3 
3 4 13 7 
3 7 9 1 
3 9 8 5 
3 8 14 2 
3 10 15 4 
3 12 10 3 
3 11 12 6 
3 2 16 11 
3 13 9 7 
3 4 17 13 
3 9 18 8 
3 14 19 2 
3 8 20 14 
3 12 15 10 
3 15 21 4 
3 11 22 12 
3 19 16 2 
3 16 23 11 
3 13 24 9 
3 4 25 17 
3 17 26 13 
3 9 27 18 
3 18 20 8 
3 20 19 14 
3 12 28 15 
3 21 25 4 
3 15 29 21 
3 22 30 12 
3 23 22 11 
3 19 23 16 
3 24 31 9 
3 26 24 13 
3 25 26 17 
3 27 20 18 
3 9 32 27 
3 20 33 19 
3 12 34 28 
3 28 29 15 
3 29 25 21 
3 23 30 22 
3 30 35 12 
3 33 23 19 
3 26 31 24 
3 31 32 9 
3 25 36 26 
3 27 37 20 
3 32 38 27 
3 20 39 33 
3 34 29 28 
3 35 34 12 
3 29 36 25 
3 23 40 30 
3 30 41 35 
3 39 23 33 
3 26 42 31 
3 31 38 32 
3 36 43 26 
3 37 44 20 
3 38 37 27 
3 20 45 39 
3 34 46 29 
3 41 34 35 
3 29 43 36 
3 23 47 40 
3 40 41 30 
3 39 48 23 
3 26 49 42 
3 42 38 31 
3 43 50 26 
3 38 44 37 
3 44 45 20 
3 45 51 39 
3 46 52 29 
3 41 46 34 
3 29 53 43 
3 47 41 40 
3 48 47 23 
3 51 48 39 
3 49 38 42 
3 50 49 26 
3 43 54 50 
3 38 55 44 
3 44 51 45 
3 41 52 46 
3 52 53 29 
3 53 54 43 
3 47 56 41 
3 51 47 48 
3 49 57 38 
3 54 49 50 
3 38 58 55 
3 55 51 44 
3 41 59 52 
3 52 54 53 
3 56 60 41 
3 51 56 47 
3 57 58 38 
3 54 57 49 
3 58 51 55 
3 60 59 41 
3 59 54 52 
3 51 60 56 
3 54 58 57 
3 58 61 51 
3 60 54 59 
3 61 60 51 
3 54 61 58 
3 60 54 61 
snub dodecahedron
pentagonal hexecontahedron
|2 3 5
(3.3.3.3.5)
icosahedral group
A5
12{5}+80{3}
33 60 150 92 60 1 0 0 2 2 5 120 5 0 -1
 0.0000000000  0.0000000000  1.0000000000
 0.4512088258  0.0000000000  0.8924183971
 0.2127790861  0.3978875029  0.8924183971
-0.2505259628  0.3752680994  0.8924183971
-0.4490629634 -0.0439529224  0.8924183971
-0.1730083366 -0.4167223535  0.8924183971
 0.5570628795 -0.4167223535  0.7183477071
 0.8034191070 -0.0439529224  0.5937894232
 0.6262410352  0.3752680994  0.6833710701
 0.3401140582  0.7292026799  0.5937894232
-0.4095292581  0.6926037162  0.5937894232
-0.6598181766  0.3124803264  0.6833710701
-0.5867073299 -0.4344864666  0.6833710701
-0.2674638242 -0.7588657481  0.5937894232
 0.1712754568 -0.6742709318  0.7183477071
 0.5066126656 -0.7588657481  0.4092265672
 0.8319314730 -0.4344864666  0.3451253896
 0.9853200794 -0.0345183587  0.1671909808
 0.6986399371  0.6437955034  0.3121371303
 0.3534611035  0.9196768661  0.1710546996
-0.0444936500  0.9113473168  0.4092265672
-0.4413672010  0.8808718883  0.1710546996
-0.7580304168  0.5726781810  0.3121371303
-0.9277164283  0.1422346447  0.3451253896
-0.8825314401 -0.3194162218  0.3451253896
-0.6326042630 -0.7087892905  0.3121371303
 0.0822881568 -0.9349423109  0.3451253896
 0.3841470954 -0.9232462719 -0.0068797092
 0.9105239830 -0.3983895691 -0.1105975932
 0.9561362417  0.0261888093 -0.2917492648
 0.9205629910  0.3905335442 -0.0068797092
 0.6521763631  0.7453882542 -0.1380664403
-0.0487110154  0.9977300839 -0.0464964156
-0.4177242369  0.8604584989 -0.2917492648
-0.9300960831  0.3617906055 -0.0634730968
-0.9941677927 -0.0973061317 -0.0464964156
-0.8422948163 -0.5352668572 -0.0634730968
-0.5085214838 -0.8539169004 -0.1105975932
-0.0666936701 -0.9936871537 -0.0902097278
 0.2171184410 -0.8730158634 -0.4366954143
 0.6337780180 -0.7004597412 -0.3281487085
 0.7752228621 -0.3165232566 -0.5466649267
 0.7846911652  0.4275505711 -0.4488432737
 0.4346204276  0.7157251860 -0.5466649267
 0.0014482055  0.8716810135 -0.4900715391
-0.3439002478  0.6359394784 -0.6908788601
-0.7197752973  0.5396486232 -0.4366954143
-0.8871554693  0.1072142198 -0.4488432737
-0.6414198315 -0.6014211198 -0.4763121208
-0.2422737833 -0.8373370292 -0.4900715391
 0.4183769714 -0.5607792259 -0.7144839884
 0.4919671680 -0.1269691999 -0.8613054788
 0.4978189011  0.3328937158 -0.8008483725
 0.0947401619  0.5614556665 -0.8220655912
-0.5854826930  0.2482988995 -0.7717238319
-0.6691452398 -0.2043459771 -0.7144839884
-0.3249352618 -0.5030496595 -0.8008483725
 0.0833693593 -0.3321275372 -0.9395428936
 0.1242523988  0.1277815601 -0.9839884218
-0.2961484454 -0.0657599657 -0.9528755035
 0.2190839064  0.1312836377  0.9188614921
-0.0124546442  0.2551039658  0.9188614921
-0.2308305197  0.1093179889  0.9188614921
-0.2052534511 -0.1520005669  0.9188614921
 0.2190839064 -0.3281703830  0.9188614921
 0.5977703708 -0.1520005669  0.7273967313
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