pentagonal prism pentagonal dipyramid 2 5|2 (4.4.5) dihedral group D 2{5}+5{4} 0 10 15 7 10 1 0 0 2 2 3 20 2 0 -1 0.0000000000 0.0000000000 1.0000000000 0.8737108351 0.0000000000 0.4864456563 -0.3018596695 0.8199093629 0.4864456563 -0.6651309335 -0.5665434359 0.4864456563 0.5718511657 0.8199093629 -0.0271086873 0.7485628941 -0.5665434359 -0.3445027268 -0.9669906029 0.2533659270 -0.0271086873 -0.2024936222 -0.9166865354 -0.3445027268 0.4467032247 0.2533659270 -0.8580570704 -0.5043532916 -0.0967771725 -0.8580570704 0.2978495106 0.4270509831 0.5067318540 -0.5036584607 0.1319660113 0.5067318540 0.2978495106 -0.8090169944 0.5067318540 0.6877395818 0.1319660113 -0.1935543450 -0.2978495106 0.8090169944 -0.5067318540 -0.6091275581 -0.3454915028 -0.1935543450 0.1271969263 -0.3454915028 -0.6263550179 4 0 2 4 1 4 0 3 6 2 5 0 1 5 7 3 4 1 4 8 5 5 2 6 9 8 4 4 3 7 9 6 4 5 8 9 7 3 2 0 1 3 2 3 0 3 0 4 1 3 1 5 2 3 3 4 0 3 2 6 3 3 4 5 1 3 5 6 2 3 6 4 3 3 4 5 6 pentagonal antiprism pentagonal deltohedron |2 2 5 (3.3.3.5) dihedral group D 2{5}+10{3} 1 10 20 12 10 1 0 0 2 2 4 20 2 0 -1 0.0000000000 0.0000000000 1.0000000000 0.8944271910 0.0000000000 0.4472135955 0.2763932023 0.8506508084 0.4472135955 -0.7236067977 0.5257311121 0.4472135955 -0.7236067977 -0.5257311121 0.4472135955 0.7236067977 -0.5257311121 -0.4472135955 0.7236067977 0.5257311121 -0.4472135955 -0.8944271910 -0.0000000000 -0.4472135955 -0.2763932023 -0.8506508084 -0.4472135955 -0.0000000000 -0.0000000000 -1.0000000000 0.2763932023 0.2008114159 0.4472135955 -0.1055728090 0.3249196962 0.4472135955 -0.3416407865 -0.0000000000 0.4472135955 0.2763932023 -0.8506508084 0.4472135955 0.5527864045 0.0000000000 -0.1055728090 0.4472135955 0.3249196962 0.1055728090 -0.2763932023 0.8506508084 -0.4472135955 -0.5527864045 -0.0000000000 0.1055728090 -0.4472135955 -0.3249196962 -0.1055728090 0.1055728090 -0.3249196962 -0.4472135955 0.3416407865 0.0000000000 -0.4472135955 -0.2763932023 -0.2008114159 -0.4472135955 3 0 2 1 3 0 3 2 3 0 4 3 5 0 1 5 8 4 3 1 6 5 3 1 2 6 5 2 3 7 9 6 3 3 4 7 3 4 8 7 3 5 9 8 3 5 6 9 3 7 8 9 4 3 0 1 2 4 3 4 5 0 4 5 6 1 0 4 6 7 2 1 4 7 8 3 2 4 3 9 10 4 4 10 6 5 4 4 6 11 8 7 4 11 9 3 8 4 9 10 6 11 pentagrammic prism pentagrammic dipyramid 2 5/2|2 (4.4.5/2) dihedral group D 5{4}+2{5/2} 2 10 15 7 10 2 0 0 2 2 3 20 2 0 -1 0.0000000000 0.0000000000 1.0000000000 0.9987422138 0.0000000000 0.0501397095 -0.9033708188 0.4259192097 0.0501397095 0.6354709497 -0.7704950886 0.0501397095 0.0953713949 0.4259192097 -0.8997205810 0.0182143157 -0.7704950886 0.6371856536 -0.2678998691 -0.3445758789 -0.8997205810 0.6059995679 0.4761921529 0.6371856536 -0.8851565032 -0.3445758789 -0.3126746369 -0.2973712509 0.9021113626 -0.3126746369 0.2129596049 0.9510565163 0.2239189798 -0.5982071492 -0.7694208843 0.2239189798 0.2129596049 -0.1004057079 0.2239189798 0.2536312703 -0.7694208843 -0.5862274998 -0.2129596049 0.1004057079 -0.2239189798 0.7549598948 0.2938926261 -0.5862274998 -0.6233436208 0.2938926261 0.7246170401 4 0 2 4 1 4 0 3 6 2 5 0 1 5 7 3 2 4 1 4 8 5 5 2 6 9 8 4 2 4 3 7 9 6 4 5 8 9 7 3 2 0 1 3 2 3 0 3 0 4 1 3 1 5 2 3 3 4 0 3 2 6 3 3 4 5 1 3 5 6 2 3 6 4 3 3 4 5 6 pentagrammic antiprism pentagrammic deltohedron |2 2 5/2 (3.3.3.5/2) dihedral group D 10{3}+2{5/2} 3 10 20 12 10 2 0 0 2 2 4 20 2 0 -1 0.0000000000 0.0000000000 1.0000000000 0.9870590084 0.0000000000 -0.1603574566 -0.1885114962 0.9688905521 -0.1603574566 -0.9150540242 -0.3700832595 -0.1603574566 0.5380310318 -0.8275313256 -0.1603574566 -0.0720049843 -0.8275313256 0.5567828907 -0.3050180081 -0.3700832595 -0.8774978039 0.1440099685 0.4574480661 -0.8774978039 0.6545375437 0.5114424860 0.5567828907 -0.8430490399 0.4574480661 0.2828596527 0.5593892211 0.6787159473 0.4758448931 -0.7730568906 0.4194695241 0.4758448931 -0.2641077641 -0.8389390482 0.4758448931 0.5593892211 -0.3035309991 0.4758448931 0.4273353390 -0.8389390482 -0.3369952245 0.3457215516 0.4194695241 -0.8393580447 -0.5593892211 0.3035309991 -0.4758448931 -0.1632275749 -0.5184928463 -0.8393580447 0.9362844655 0.0990233222 -0.3369952245 -0.1824939766 0.0990233222 0.9782077132 -0.8546706780 -0.5184928463 -0.0265179270 -0.0311736929 0.9991621492 -0.0265179270 3 0 2 1 3 0 3 2 3 0 4 3 5 0 1 5 8 4 2 3 1 6 5 3 1 2 6 5 2 3 7 9 6 2 3 3 4 7 3 4 8 7 3 5 9 8 3 5 6 9 3 7 8 9 4 3 0 1 2 4 3 4 5 0 4 5 6 1 0 4 6 7 2 1 4 7 8 3 2 4 3 9 10 4 4 10 6 5 4 4 6 11 8 7 4 11 9 3 8 4 9 10 6 11 pentagrammic crossed antiprism pentagrammic concave deltohedron |2 2 5/3 (3.3.3.5/3) dihedral group D 10{3}+2{5/3} 4 10 20 12 10 3 0 0 2 2 4 20 2 0 -1 0.0000000000 0.0000000000 1.0000000000 0.8944271910 0.0000000000 -0.4472135955 -0.7236067977 0.5257311121 -0.4472135955 0.2763932023 -0.8506508084 -0.4472135955 0.2763932023 0.8506508084 -0.4472135955 -0.2763932023 0.8506508084 0.4472135955 -0.2763932023 -0.8506508084 0.4472135955 -0.8944271910 0.0000000000 0.4472135955 0.7236067977 -0.5257311121 0.4472135955 -0.0000000000 0.0000000000 -1.0000000000 0.3035309991 0.9341723590 0.1875924741 -0.7946544723 -0.5773502692 0.1875924741 0.9822469464 0.0000000000 0.1875924741 0.3035309991 0.2205281794 0.1875924741 0.6070619982 -0.0000000000 0.7946544723 -0.1875924741 -0.5773502692 -0.7946544723 -0.3035309991 -0.2205281794 -0.1875924741 -0.6070619982 -0.0000000000 -0.7946544723 0.1875924741 0.5773502692 0.7946544723 0.7946544723 0.5773502692 -0.1875924741 -0.9822469464 0.0000000000 -0.1875924741 -0.3035309991 -0.9341723590 -0.1875924741 3 0 2 1 3 0 3 2 3 0 4 3 5 0 1 5 8 4 3 3 1 6 5 3 1 2 6 5 2 3 7 9 6 3 3 3 4 7 3 4 8 7 3 5 9 8 3 5 6 9 3 7 8 9 4 3 0 1 2 4 3 4 5 0 4 5 6 1 0 4 6 7 2 1 4 7 8 3 2 4 3 9 10 4 4 10 6 5 4 4 6 11 8 7 4 11 9 3 8 4 9 10 6 11 tetrahedron tetrahedron 3|2 3 (3.3.3) tetrahedral group A4 4{3} 5 4 6 4 4 1 0 0 2 1 3 24 3 0 -1 0.0000000000 0.0000000000 1.0000000000 0.9428090416 0.0000000000 -0.3333333333 -0.4714045208 0.8164965809 -0.3333333333 -0.4714045208 -0.8164965809 -0.3333333333 0.4714045208 0.8164965809 0.3333333333 -0.9428090416 0.0000000000 0.3333333333 0.4714045208 -0.8164965809 0.3333333333 -0.0000000000 0.0000000000 -1.0000000000 3 0 2 1 3 0 3 2 3 0 1 3 3 1 2 3 3 2 0 1 3 2 3 0 3 3 1 0 3 1 2 3 truncated tetrahedron triakistetrahedron 2 3|3 (6.6.3) tetrahedral group A4 4{6}+4{3} 6 12 18 8 12 1 0 0 2 2 3 24 3 0 -1 0.0000000000 0.0000000000 1.0000000000 0.7713892158 0.0000000000 0.6363636364 -0.6428243465 0.4264014327 0.6363636364 0.2999846950 -0.7106690545 0.6363636364 0.8999540851 0.4264014327 -0.0909090909 -0.9856639980 0.1421338109 -0.0909090909 -0.5142594772 0.8528028654 -0.0909090909 -0.0428549564 -0.9949366763 -0.0909090909 0.5571144337 0.1421338109 -0.8181818182 0.2571297386 0.8528028654 -0.4545454545 -0.6856793030 -0.5685352436 -0.4545454545 0.0857099129 -0.5685352436 -0.8181818182 0.2461829820 0.8164965809 0.5222329679 -0.6564879519 -0.5443310540 0.5222329679 0.2461829820 -0.1632993162 0.5222329679 0.8206099399 -0.5443310540 -0.1740776560 -0.4923659639 0.3265986324 0.1044465936 0.3938927711 0.3265986324 -0.3133397807 -0.4103049699 0.2721655270 -0.8703882798 -0.1477097892 -0.4898979486 -0.3133397807 6 0 2 6 9 4 1 6 0 3 7 10 5 2 3 0 1 3 6 1 4 8 11 7 3 3 2 5 6 3 4 9 8 6 5 10 11 8 9 6 3 7 11 10 3 2 0 1 3 2 3 0 3 0 4 1 3 1 3 2 3 3 5 0 3 4 6 1 3 0 6 4 3 1 7 3 3 3 6 5 3 5 0 6 3 6 7 1 3 7 3 6 octahemioctahedron octahemioctacron 3/2 3|3 (6.3/2.6.3) tetrahedral group A4 4{6}+4{3}+4{3/2} 7 12 24 12 12 0 1 0 0 3 4 24 3 1 -1 0.0000000000 0.0000000000 1.0000000000 0.8660254038 0.0000000000 0.5000000000 -0.8660254038 0.0000000000 0.5000000000 -0.2886751346 0.8164965809 0.5000000000 0.2886751346 -0.8164965809 0.5000000000 0.8660254038 0.0000000000 -0.5000000000 0.5773502692 0.8164965809 0.0000000000 -0.5773502692 -0.8164965809 0.0000000000 -0.8660254038 -0.0000000000 -0.5000000000 -0.2886751346 0.8164965809 -0.5000000000 0.2886751346 -0.8164965809 -0.5000000000 -0.0000000000 0.0000000000 -1.0000000000 0.0000000000 1.0000000000 0.0000000000 -0.4714045208 0.3333333333 0.8164965809 -0.9428090416 -0.3333333333 0.0000000000 0.4714045208 -0.3333333333 0.8164965809 0.4714045208 -0.3333333333 -0.8164965809 0.9428090416 0.3333333333 0.0000000000 -0.9428090416 -0.3333333333 0.0000000000 0.4714045208 -0.3333333333 0.8164965809 0.0000000000 1.0000000000 0.0000000000 -0.0000000000 -1.0000000000 0.0000000000 0.4714045208 -0.3333333333 -0.8164965809 -0.4714045208 0.3333333333 -0.8164965809 6 0 1 5 11 8 2 3 0 2 3 2 6 0 3 9 11 10 4 3 0 1 4 6 1 4 7 8 9 6 3 1 6 5 2 3 2 8 7 6 2 7 10 5 6 3 3 3 6 9 3 4 10 7 2 3 5 10 11 3 8 11 9 2 4 3 0 1 2 4 3 4 5 0 4 6 0 1 7 4 8 7 1 2 4 9 2 3 4 4 5 7 10 0 4 8 4 5 7 4 6 4 9 7 4 11 0 6 4 4 11 2 8 4 4 10 2 9 7 4 10 0 11 2 tetrahemihexahedron tetrahemihexacron 3/2 3|2 (4.3/2.4.3) tetrahedral group A4 3{4}+2{3}+2{3/2} 8 6 12 7 6 0 1 1 1 3 4 24 3 1 -1 0.0000000000 0.0000000000 1.0000000000 1.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 -0.0000000000 1.0000000000 0.0000000000 -0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 1.0000000000 0.0000000000 -0.5773502692 0.5773502692 0.5773502692 -1.0000000000 0.0000000000 0.0000000000 0.5773502692 -0.5773502692 0.5773502692 -0.0000000000 0.0000000000 -1.0000000000 0.5773502692 0.5773502692 -0.5773502692 -0.5773502692 -0.5773502692 -0.5773502692 4 0 1 5 2 3 0 2 3 2 4 0 3 5 4 3 0 1 4 4 1 4 2 3 3 1 3 5 2 3 2 5 4 4 3 0 1 2 4 3 4 5 0 4 6 0 1 4 4 5 2 1 4 4 6 2 3 4 4 5 0 6 2 octahedron hexahedron 4|2 3 (3.3.3.3) octahedral group S4 8{3} 9 6 12 8 6 1 0 0 2 1 4 48 4 0 -1 0.0000000000 0.0000000000 1.0000000000 1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.0000000000 0.0000000000 0.0000000000 -1.0000000000 0.5773502692 0.5773502692 0.5773502692 -0.5773502692 0.5773502692 0.5773502692 -0.5773502692 -0.5773502692 0.5773502692 0.5773502692 -0.5773502692 0.5773502692 0.5773502692 -0.5773502692 -0.5773502692 0.5773502692 0.5773502692 -0.5773502692 -0.5773502692 0.5773502692 -0.5773502692 -0.5773502692 -0.5773502692 -0.5773502692 3 0 2 1 3 0 3 2 3 0 4 3 3 0 1 4 3 1 5 4 3 1 2 5 3 2 3 5 3 3 4 5 4 3 0 1 2 4 3 4 5 0 4 5 6 1 0 4 6 7 2 1 4 7 4 3 2 4 4 5 6 7 hexahedron octahedron 3|2 4 (4.4.4) octahedral group S4 6{4} 10 8 12 6 8 1 0 0 2 1 3 48 4 0 -1 0.0000000000 0.0000000000 1.0000000000 0.9428090416 0.0000000000 0.3333333333 -0.4714045208 0.8164965809 0.3333333333 -0.4714045208 -0.8164965809 0.3333333333 0.4714045208 0.8164965809 -0.3333333333 0.4714045208 -0.8164965809 -0.3333333333 -0.9428090416 0.0000000000 -0.3333333333 0.0000000000 0.0000000000 -1.0000000000 0.4082482905 0.7071067812 0.5773502692 -0.8164965809 0.0000000000 0.5773502692 0.4082482905 -0.7071067812 0.5773502692 0.8164965809 0.0000000000 -0.5773502692 -0.4082482905 0.7071067812 -0.5773502692 -0.4082482905 -0.7071067812 -0.5773502692 4 0 2 4 1 4 0 3 6 2 4 0 1 5 3 4 1 4 7 5 4 2 6 7 4 4 3 5 7 6 3 2 0 1 3 2 3 0 3 0 4 1 3 1 5 2 3 3 4 0 3 5 3 2 3 4 5 1 3 3 4 5 cuboctahedron rhombic dodecahedron 2|3 4 (3.4.3.4) octahedral group S4 6{4}+8{3} 11 12 24 14 12 1 0 0 2 2 4 48 4 0 -1 0.0000000000 0.0000000000 1.0000000000 0.8660254038 0.0000000000 0.5000000000 0.2886751346 0.8164965809 0.5000000000 -0.8660254038 0.0000000000 0.5000000000 -0.2886751346 -0.8164965809 0.5000000000 0.8660254038 0.0000000000 -0.5000000000 0.5773502692 -0.8164965809 0.0000000000 -0.5773502692 0.8164965809 0.0000000000 0.2886751346 0.8164965809 -0.5000000000 -0.8660254038 0.0000000000 -0.5000000000 -0.2886751346 -0.8164965809 -0.5000000000 0.0000000000 0.0000000000 -1.0000000000 0.4082482905 0.2886751346 0.7071067812 -0.4082482905 0.5773502692 0.7071067812 -0.4082482905 -0.2886751346 0.7071067812 0.4082482905 -0.5773502692 0.7071067812 0.8164965809 -0.2886751346 0.0000000000 0.8164965809 0.5773502692 0.0000000000 0.0000000000 0.8660254038 0.0000000000 -0.8164965809 0.2886751346 -0.0000000000 -0.8164965809 -0.5773502692 0.0000000000 -0.0000000000 -0.8660254038 -0.0000000000 0.4082482905 -0.5773502692 -0.7071067812 0.4082482905 0.2886751346 -0.7071067812 -0.4082482905 0.5773502692 -0.7071067812 -0.4082482905 -0.2886751346 -0.7071067812 3 0 2 1 4 0 3 7 2 3 0 4 3 4 0 1 6 4 3 1 5 6 4 1 2 8 5 3 2 7 8 3 3 9 7 4 3 4 10 9 3 4 6 10 4 5 11 10 6 3 5 8 11 4 7 9 11 8 3 9 10 11 4 3 0 1 2 4 3 4 5 0 4 5 6 1 0 4 1 7 8 2 4 8 9 3 2 4 4 10 11 5 4 9 10 4 3 4 6 12 7 1 4 11 12 6 5 4 12 13 8 7 4 13 10 9 8 4 10 11 12 13 truncated octahedron tetrakishexahedron 2 4|3 (6.6.4) octahedral group S4 8{6}+6{4} 12 24 36 14 24 1 0 0 2 2 3 48 4 0 -1 0.0000000000 0.0000000000 1.0000000000 0.6000000000 0.0000000000 0.8000000000 -0.4000000000 0.4472135955 0.8000000000 -0.0666666667 -0.5962847940 0.8000000000 0.8000000000 0.4472135955 0.4000000000 0.5333333333 -0.5962847940 0.6000000000 -0.8666666667 0.2981423970 0.4000000000 -0.2000000000 0.8944271910 0.4000000000 -0.5333333333 -0.7453559925 0.4000000000 0.9333333333 0.2981423970 -0.2000000000 0.4000000000 0.8944271910 0.2000000000 0.6666666667 -0.7453559925 0.0000000000 -0.6666666667 0.7453559925 0.0000000000 -0.9333333333 -0.2981423970 0.2000000000 -0.4000000000 -0.8944271910 -0.2000000000 0.5333333333 0.7453559925 -0.4000000000 0.8666666667 -0.2981423970 -0.4000000000 0.2000000000 -0.8944271910 -0.4000000000 -0.5333333333 0.5962847940 -0.6000000000 -0.8000000000 -0.4472135955 -0.4000000000 0.0666666667 0.5962847940 -0.8000000000 0.4000000000 -0.4472135955 -0.8000000000 -0.6000000000 -0.0000000000 -0.8000000000 0.0000000000 -0.0000000000 -1.0000000000 0.2581988897 0.5773502692 0.7745966692 -0.6024640761 -0.1924500897 0.7745966692 0.2581988897 -0.2886751346 0.7745966692 0.9467292624 -0.1924500897 0.2581988897 -0.5163977795 0.5773502692 0.3872983346 0.0860662966 -0.9622504486 0.2581988897 0.6454972244 0.5773502692 0.0000000000 -0.9467292624 0.1924500897 -0.2581988897 -0.0860662966 0.9622504486 -0.2581988897 -0.6454972244 -0.5773502692 -0.0000000000 0.6024640761 0.1924500897 -0.7745966692 0.5163977795 -0.5773502692 -0.3872983346 -0.2581988897 -0.5773502692 -0.7745966692 -0.2581988897 0.2886751346 -0.7745966692 6 0 2 7 10 4 1 6 0 3 8 13 6 2 4 0 1 5 3 6 1 4 9 16 11 5 4 2 6 12 7 6 3 5 11 17 14 8 4 4 10 15 9 6 6 13 19 22 18 12 6 7 12 18 20 15 10 4 8 14 19 13 6 9 15 20 23 21 16 4 11 16 21 17 6 14 17 21 23 22 19 4 18 22 23 20 3 2 0 1 3 2 3 0 3 0 4 1 3 1 5 2 3 3 6 0 3 5 3 2 3 4 7 1 3 0 8 4 3 1 9 5 3 3 10 6 3 6 8 0 3 5 11 3 3 8 7 4 3 7 9 1 3 9 12 5 3 10 8 6 3 11 10 3 3 12 11 5 3 8 13 7 3 7 12 9 3 10 13 8 3 12 10 11 3 13 12 7 3 10 13 12 truncated hexahedron triakisoctahedron 2 3|4 (8.8.3) octahedral group S4 6{8}+8{3} 13 24 36 14 24 1 0 0 2 2 3 48 4 0 -1 0.0000000000 0.0000000000 1.0000000000 0.5395042868 0.0000000000 0.8419828529 -0.4604957132 0.2810846377 0.8419828529 0.2466110680 -0.4798414911 0.8419828529 0.8419828529 0.2810846377 0.4604957132 -0.8651239283 0.1987568534 0.4604957132 -0.5722307095 0.6785983445 0.4604957132 0.1348760717 -0.8773551980 0.4604957132 0.9768589246 0.1987568534 -0.0790085736 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9 16 18 21 19 13 14 10 4 11 15 21 18 3 13 20 14 2 3 16 22 18 2 4 17 22 23 20 3 19 21 23 2 4 3 0 1 2 4 3 4 5 0 4 0 6 7 1 4 7 8 2 1 4 2 9 10 3 4 5 7 11 0 4 4 8 7 5 4 10 12 4 3 4 6 10 9 7 4 0 13 14 6 4 8 14 13 2 4 2 15 7 9 4 7 12 10 11 4 11 14 16 0 4 4 16 14 8 4 15 4 12 7 4 14 17 10 6 4 0 18 2 13 4 2 17 14 15 4 10 19 14 11 4 4 18 0 16 4 19 4 15 14 4 18 10 17 2 4 10 19 4 18 great cubicuboctahedron great hexacronic icositetrahedron 3 4|4/3 (8/3.3.8/3.4) octahedral group S4 6{4}+8{3}+6{8/3} 18 24 48 20 24 4 0 0 -4 3 4 48 4 0 -1 0.0000000000 0.0000000000 1.0000000000 0.9968739365 0.0000000000 0.0790085736 0.4556778364 0.8866314650 0.0790085736 -0.8508851285 0.5193766874 0.0790085736 -0.8508851285 -0.5193766874 0.0790085736 0.0427591319 0.8866314650 0.4604957132 0.1459888080 0.5193766874 -0.8419828529 0.1459888080 -0.5193766874 -0.8419828529 -0.3952072921 0.3672547776 -0.8419828529 0.8081259966 -0.3672547776 0.4604957132 -0.4984369683 -0.7345095553 0.4604957132 -0.4984369683 0.7345095553 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3 4 2 8 10 4 6 2 4 6 5 9 7 4 5 6 10 11 4 7 9 11 8 4 3 0 1 2 4 3 4 5 0 4 6 0 1 7 4 1 4 5 2 4 6 2 3 7 4 5 7 8 0 4 8 4 3 7 4 9 7 1 4 4 9 0 6 4 4 9 2 5 7 4 8 2 6 4 4 8 0 9 2 cubitruncated cuboctahedron tetradyakishexahedron 4/3 3 4| (8/3.6.8) octahedral group S4 6{8}+8{6}+6{8/3} 20 48 72 20 48 4 0 0 -4 3 3 48 4 0 -1 0.0000000000 0.0000000000 1.0000000000 0.6998542122 0.0000000000 0.7142857143 0.4607079005 0.5268245902 0.7142857143 -0.6939926379 -0.0903888097 0.7142857143 0.1708187941 0.5268245902 0.8326324464 0.9956048929 -0.0903888097 0.0245104108 0.2274231631 0.9632603706 0.1428571429 0.5090227516 -0.2182178902 0.8326324464 -0.9755922264 -0.2182178902 0.0245104108 -0.9272773753 0.3460469708 0.1428571429 -0.0624659433 0.9632603706 0.2612038750 0.2191336452 -0.2182178902 0.9509791785 0.7140053045 -0.2182178902 -0.6652648928 0.7623201555 0.3460469708 -0.5469181607 -0.0541764254 0.8354312901 -0.5469181607 -0.4665694748 0.8728715609 -0.1428571429 -0.0200126666 0.3086066999 0.9509791785 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3 4 5 10 11 0 4 9 12 4 3 4 7 13 4 1 4 6 9 8 7 4 0 13 4 6 4 10 14 2 5 4 2 12 4 8 4 10 12 9 11 4 11 2 14 0 4 7 14 10 13 4 4 15 9 6 4 15 7 8 4 4 0 16 10 13 4 2 17 10 12 4 9 17 2 11 4 7 16 0 14 4 15 10 16 9 4 17 7 15 10 4 9 17 7 16 stellated truncated hexahedron great triakisoctahedron 2 3|4/3 (8/3.8/3.3) octahedral group S4 8{3}+6{8/3} 23 24 36 14 24 7 0 0 2 2 3 48 4 0 -1 0.0000000000 0.0000000000 1.0000000000 0.8722604191 0.0000000000 -0.4890416764 -0.1277395809 0.8628562095 -0.4890416764 -0.8348463621 -0.2527247326 -0.4890416764 -0.4890416764 0.8628562095 0.1277395809 -0.7819348952 -0.6101314769 0.1277395809 0.9251718860 -0.3574067443 0.1277395809 0.2180651048 0.9675382212 0.1277395809 -0.2709765716 -0.6101314769 -0.7445208382 0.5638697904 -0.3574067443 0.7445208382 0.2709765716 0.6101314769 0.7445208382 -0.4361302096 0.5054494651 0.7445208382 -0.4361302096 -0.5054494651 0.7445208382 0.4361302096 -0.5054494651 -0.7445208382 0.7819348952 0.6101314769 -0.1277395809 0.4361302096 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5 6 3 4 9 8 8 5 10 17 21 22 18 11 6 3 3 7 13 12 8 8 9 15 18 22 23 20 14 3 3 10 16 17 3 11 18 15 8 12 13 19 20 23 21 17 16 3 3 14 20 19 3 21 23 22 3 2 0 1 3 2 3 0 3 0 4 1 3 1 3 2 3 3 5 0 3 4 6 1 3 0 6 4 3 1 7 3 3 3 8 5 3 8 0 5 3 6 9 1 3 0 10 6 3 1 11 7 3 11 3 7 3 3 12 8 3 8 10 0 3 9 11 1 3 6 11 9 3 8 6 10 3 11 12 3 3 11 8 12 3 6 13 11 3 8 13 6 3 11 8 13 great truncated cuboctahedron great disdyakisdodecahedron 4/3 2 3| (8/3.4.6) octahedral group S4 8{6}+12{4}+6{8/3} 24 48 72 26 48 1 0 0 2 3 3 48 4 0 -1 0.0000000000 0.0000000000 1.0000000000 0.8305094692 0.0000000000 0.5570045077 0.5180497550 0.6491305182 0.5570045077 -0.7696968212 0.3119499667 0.5570045077 0.1740414692 0.6491305182 0.7404992487 0.8913221171 0.3119499667 -0.3289864768 -0.2516470662 0.9610804849 0.1140090155 0.6159262346 -0.2688786644 0.7404992487 -0.7088841733 0.6238999334 -0.3289864768 0.2348541172 0.9610804849 -0.1454917358 0.2719179488 -0.2688786644 0.9239939897 0.1216252958 0.6238999334 -0.7719819690 -0.9234674078 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