ref: 600bbfe4aaa9ad0f73d8d73eef1b7670e5f7d3a3
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
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6 0 2 7 11 4 1
6 0 3 9 14 6 2
5 0 1 5 8 3
6 1 4 10 19 12 5
5 2 6 13 15 7
6 3 8 16 26 17 9
5 4 11 20 18 10
6 5 12 21 25 16 8
6 6 14 23 33 22 13
6 7 15 24 30 20 11
5 9 17 27 23 14
6 10 18 28 39 29 19
5 12 19 29 31 21
6 13 22 32 34 24 15
5 16 25 35 36 26
6 17 26 36 46 37 27
6 18 20 30 40 38 28
6 21 31 41 45 35 25
5 22 33 43 42 32
6 23 27 37 47 43 33
5 24 34 44 40 30
5 28 38 48 49 39
6 29 39 49 50 41 31
6 32 42 51 52 44 34
6 35 45 53 54 46 36
5 37 46 54 55 47
6 38 40 44 52 56 48
5 41 50 57 53 45
6 42 43 47 55 58 51
6 48 56 59 57 50 49
5 51 58 59 56 52
6 53 57 59 58 55 54
3 2 0 1
3 2 3 0
3 0 4 1
3 1 5 2
3 3 6 0
3 2 7 3
3 4 8 1
3 0 9 4
3 5 7 2
3 1 10 5
3 3 11 6
3 6 9 0
3 7 12 3
3 4 13 8
3 8 10 1
3 9 13 4
3 5 14 7
3 10 15 5
3 11 16 6
3 12 11 3
3 16 9 6
3 7 17 12
3 13 18 8
3 8 19 10
3 9 20 13
3 14 17 7
3 15 14 5
3 19 15 10
3 11 21 16
3 12 22 11
3 16 20 9
3 17 22 12
3 13 23 18
3 18 19 8
3 20 23 13
3 14 24 17
3 15 24 14
3 19 25 15
3 21 26 16
3 22 21 11
3 26 20 16
3 17 27 22
3 23 28 18
3 28 19 18
3 26 23 20
3 24 27 17
3 25 24 15
3 28 25 19
3 21 29 26
3 22 29 21
3 27 29 22
3 23 30 28
3 26 30 23
3 24 31 27
3 25 31 24
3 28 31 25
3 29 30 26
3 31 29 27
3 30 31 28
3 29 30 31
truncated dodecahedron
triakisicosahedron
2 3|5
(10.10.3)
icosahedral group
A5
12{10}+20{3}
30 60 90 32 60 1 0 0 2 2 3 120 5 0 -1
0.0000000000 0.0000000000 1.0000000000
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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
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0.4134268623 0.4358578416 0.7994411620
0.7478962199 0.1861335198 0.6371856536
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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
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0.2175812365 -0.1162285368 -0.9049446815
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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
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