ref: d916a4c3823f55227ffae35738c2497256e307b5
dir: /lib/polyhedra/
# 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
-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
-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
0.6572159007 0.4408282437 0.6113409191
-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
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
-0.9970067683 0.0753024539 0.0175226837
-0.5497931728 0.8351170114 0.0175226837
-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
-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
0.3681431654 0.8063540334 -0.4628863603
-0.8183499926 -0.1506049079 -0.5546363234
-0.2655635881 0.7885775354 -0.5546363234
-0.5262840256 -0.7132750815 -0.4628863603
-0.2402045220 -0.8816564874 -0.4061817646
0.0917499632 -0.8816564874 -0.4628863603
0.3427840993 -0.7132750815 -0.6113409191
0.5878317720 -0.1506049079 -0.7948408455
0.0663908970 0.7885775354 -0.6113409191
-0.6572159007 -0.4408282437 -0.6113409191
-0.5829886213 -0.1683814059 -0.7948408455
-0.1357750258 0.5914331516 -0.7948408455
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
-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
-0.9500077743 0.0000000000 0.2182670607
-0.8538605757 -0.3323929240 0.2766886585
-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
-0.8592901042 0.4051361351 -0.2182670607
-0.9436228948 -0.1207882584 -0.3081980354
-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
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
-0.9934567883 0.1128921245 -0.0172909812
-0.1646312678 0.9564322465 -0.2411097335
-0.7162795951 -0.6783208443 -0.1637814823
-0.9217334041 -0.3761053597 -0.0946165431
-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
0.6205958173 0.1093179889 0.7158561322
0.4257131685 0.2551039658 0.8143892546
0.3890572668 0.4957055924 0.7158561322
-0.0330094857 0.6761213397 0.7360504792
-0.4354944038 0.4554494653 0.7158561322
-0.4485386151 0.2124213879 0.8143892546
-0.7630826557 -0.0746882186 0.6419708175
-0.3988385021 -0.2953600929 0.8143892546
-0.3389195666 -0.5312467586 0.7158561322
-0.0888218963 -0.6103640383 0.7273967313
0.4074741194 -0.6103640383 0.6090650015
0.6254586613 -0.5312467586 0.4859196824
0.7233904360 -0.2953600929 0.5468165011
0.8646946053 -0.1692512546 0.3649614304
0.8780829721 0.2897337362 0.3808210291
0.5493678557 0.5768433427 0.5243913714
0.4593636674 0.7564719129 0.3553517403
0.2141655150 0.8447510749 0.3873865601
-0.2954354429 0.8198714201 0.3873865601
-0.5308680756 0.7081269803 0.3553517403
-0.6029463352 0.5205852472 0.5243913714
-0.7739230465 0.3389900646 0.4423442636
-0.6935065744 -0.4826176302 0.4423442636
-0.4905640004 -0.6276147261 0.5243913714
-0.3032002312 -0.9251016481 0.2285969389
-0.0045863974 -0.7813515677 0.5468165011
0.2508214168 -0.7813515677 0.4859196824
0.3210587649 -0.8635013917 0.2466297006
0.7110959079 -0.6998764938 0.0671974935
0.9000340357 -0.2861982107 0.1325477729
0.9410156039 -0.1341976438 -0.0775900694
0.9443279912 0.1261088383 -0.0433681826
0.7494453424 0.5872206583 0.0551649398
0.5623291395 0.7618123698 0.1138746914
0.3032002312 0.9251016481 -0.2285969389
0.0858720409 0.9333521346 0.1761231918
-0.1763828687 0.9205483682 0.1761231918
-0.2995309163 0.9037575188 -0.0551649398
-0.7110959079 0.6998764938 -0.0671974935
-0.8631016874 0.3552600725 0.1959217993
-0.9410156039 0.1341976438 0.0775900694
-0.9253215715 -0.0905676721 0.2124078137
-0.8971365698 -0.3141104098 0.0775900694
-0.7778380870 -0.5158702863 0.1959217993
-0.6544328852 -0.6922296665 0.0455552496
0.1318953941 -0.9409811017 0.0818398716
0.1763828687 -0.9205483682 -0.1761231918
0.4075046572 -0.8237974999 -0.2546315508
0.7653310532 -0.4670045122 -0.3251380596
0.8716936806 -0.2272456248 -0.3131280032
0.7630826557 0.0746882186 -0.6419708175
0.8781301501 0.2785692436 -0.2466297006
0.7778380870 0.5158702863 -0.1959217993
0.6175005369 0.6231678047 -0.3740248218
-0.1534232428 0.9007249745 -0.2733046324
-0.2508214168 0.7813515677 -0.4859196824
-0.4887903007 0.6717969331 -0.4683081420
-0.8370961923 0.3328068685 -0.3131280032
-0.9276324486 0.1226425968 -0.1843812002
-0.8780829721 -0.2897337362 -0.3808210291
-0.6573415966 -0.6568033615 -0.2145948808
-0.4593636674 -0.7564719129 -0.3553517403
-0.2697318228 -0.8859007376 -0.2279566191
-0.0303057331 -0.8922024719 -0.3355531328
0.0330094857 -0.6761213397 -0.7360504792
0.4187988612 -0.7042009004 -0.4881067495
0.6029463352 -0.5205852472 -0.5243913714
0.5561556114 -0.3313610975 -0.7003073269
0.5665700378 0.4870645516 -0.5927108132
0.3389195666 0.5312467586 -0.7158561322
0.1751412372 0.7090205159 -0.6133148036
-0.0817329434 0.6826950901 -0.6608984288
-0.2190839064 0.3281703830 -0.9188614921
-0.5441424799 0.4698138638 -0.6266765419
-0.7233904360 0.2953600929 -0.5468165011
-0.7066849651 0.0498778478 -0.6384732991
-0.5396360317 -0.4318462468 -0.6571463807
-0.3987890908 -0.6407026882 -0.5831011230
0.3278774074 -0.3365097556 -0.8299380599
0.2308305197 -0.1093179889 -0.9188614921
0.3675788294 0.1101068700 -0.8730990062
0.2365131238 0.3372537898 -0.8601517406
-0.5116812230 -0.0071952699 -0.8047795644
-0.4257131685 -0.2551039658 -0.8143892546
-0.1774197357 -0.2972657023 -0.8886478115
-0.0292095264 -0.0891219012 -0.9490751728
3 0 2 1
3 0 3 2
3 0 4 3
3 0 5 4
5 0 1 6 14 5
3 1 7 6
3 1 8 7
3 1 2 8
3 2 9 8
5 2 3 10 20 9
3 3 11 10
3 3 4 11
5 4 12 24 23 11
3 4 5 12
3 5 13 12
3 5 14 13
3 6 15 14
3 6 16 15
3 6 7 16
3 7 17 16
5 7 8 18 30 17
3 8 9 18
3 9 19 18
3 9 20 19
3 10 21 20
3 10 22 21
3 10 11 22
3 11 23 22
3 12 25 24
3 12 13 25
5 13 26 38 37 25
3 13 14 26
3 14 15 26
3 15 27 26
5 15 16 28 40 27
3 16 17 28
3 17 29 28
3 17 30 29
3 18 31 30
3 18 19 31
5 19 32 44 43 31
3 19 20 32
3 20 21 32
3 21 33 32
5 21 22 34 46 33
3 22 23 34
3 23 35 34
3 23 24 35
3 24 36 35
3 24 25 36
3 25 37 36
3 26 27 38
3 27 39 38
3 27 40 39
3 28 41 40
3 28 29 41
5 29 42 52 51 41
3 29 30 42
3 30 31 42
3 31 43 42
3 32 33 44
3 33 45 44
3 33 46 45
3 34 47 46
3 34 35 47
5 35 36 48 55 47
3 36 37 48
3 37 49 48
3 37 38 49
3 38 39 49
5 39 50 57 56 49
3 39 40 50
3 40 41 50
3 41 51 50
3 42 43 52
3 43 53 52
3 43 44 53
3 44 45 53
5 45 54 59 58 53
3 45 46 54
3 46 47 54
3 47 55 54
3 48 56 55
3 48 49 56
3 50 51 57
3 51 58 57
3 51 52 58
3 52 53 58
3 54 55 59
3 55 56 59
3 56 57 59
3 57 58 59
5 4 0 1 2 3
5 4 5 6 7 0
5 7 8 9 1 0
5 9 10 11 2 1
5 11 12 13 3 2
5 13 14 15 4 3
5 4 16 17 18 5
5 18 19 20 6 5
5 20 21 8 7 6
5 21 22 23 9 8
5 9 24 25 26 10
5 26 27 12 11 10
5 12 28 29 14 13
5 29 30 31 15 14
5 31 32 16 4 15
5 32 33 34 17 16
5 34 35 19 18 17
5 35 36 37 20 19
5 20 38 39 22 21
5 39 40 41 23 22
5 41 42 24 9 23
5 42 43 44 25 24
5 44 45 27 26 25
5 45 46 47 12 27
5 47 48 49 28 12
5 49 50 30 29 28
5 30 51 33 32 31
5 51 52 53 34 33
5 34 54 55 36 35
5 55 56 57 37 36
5 57 58 38 20 37
5 58 59 40 39 38
5 40 60 43 42 41
5 60 61 62 44 43
5 44 63 64 46 45
5 64 65 48 47 46
5 65 66 50 49 48
5 66 67 68 30 50
5 68 69 52 51 30
5 69 70 71 53 52
5 71 72 54 34 53
5 72 73 56 55 54
5 56 74 59 58 57
5 74 75 76 40 59
5 76 77 61 60 40
5 77 78 79 62 61
5 79 80 63 44 62
5 80 81 65 64 63
5 65 82 83 67 66
5 83 70 69 68 67
5 70 84 73 72 71
5 84 85 86 56 73
5 86 87 75 74 56
5 87 78 77 76 75
5 78 88 81 80 79
5 88 89 82 65 81
5 89 90 70 83 82
5 90 91 85 84 70
5 91 78 87 86 85
5 78 88 89 90 91