pentagonal prismpentagonal dipyramid2 5|2(4.4.5)dihedral groupD2{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 -0.62635501794 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 antiprismpentagonal deltohedron|2 2 5(3.3.3.5)dihedral groupD2{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 -0.44721359553 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 prismpentagrammic dipyramid2 5/2|2(4.4.5/2)dihedral groupD5{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  0.72461704014 0 2 4 1 4 0 3 6 2 5 0 1 5 7 3 24 1 4 8 5 5 2 6 9 8 4 24 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 antiprismpentagrammic deltohedron|2 2 5/2(3.3.3.5/2)dihedral groupD10{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 -0.02651792703 0 2 1 3 0 3 2 3 0 4 3 5 0 1 5 8 4 23 1 6 5 3 1 2 6 5 2 3 7 9 6 23 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 antiprismpentagrammic concave deltohedron|2 2 5/3(3.3.3.5/3)dihedral groupD10{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 -0.18759247413 0 2 1 3 0 3 2 3 0 4 3 5 0 1 5 8 4 33 1 6 5 3 1 2 6 5 2 3 7 9 6 33 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 tetrahedrontetrahedron3|2 3(3.3.3)tetrahedral groupA44{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 -1.00000000003 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 tetrahedrontriakistetrahedron2 3|3(6.6.3)tetrahedral groupA44{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 -0.31333978076 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 octahemioctahedronoctahemioctacron3/2 3|3(6.3/2.6.3)tetrahedral groupA44{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 -0.81649658096 0 1 5 11 8 2 3 0 2 3 26 0 3 9 11 10 4 3 0 1 4 6 1 4 7 8 9 6 3 1 6 5 23 2 8 7 6 2 7 10 5 6 3 3 3 6 9 3 4 10 7 23 5 10 11 3 8 11 9 24 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 tetrahemihexahedrontetrahemihexacron3/2 3|2(4.3/2.4.3)tetrahedral groupA43{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 -0.57735026924 0 1 5 2 3 0 2 3 24 0 3 5 4 3 0 1 4 4 1 4 2 3 3 1 3 5 23 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 octahedronhexahedron4|2 3(3.3.3.3)octahedral groupS48{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 -0.57735026923 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 hexahedronoctahedron3|2 4(4.4.4)octahedral groupS46{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 -0.57735026924 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 cuboctahedronrhombic dodecahedron2|3 4(3.4.3.4)octahedral groupS46{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

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