1# data generated by kaleido written by Dr. Zvi Har'El (rl@math.technion.ac.il) 2pentagonal prism 3pentagonal dipyramid 42 5|2 5(4.4.5) 6dihedral group 7D 82{5}+5{4} 90 10 15 7 10 1 0 0 2 2 3 20 2 0 -1 10 0.0000000000 0.0000000000 1.0000000000 11 0.8737108351 0.0000000000 0.4864456563 12-0.3018596695 0.8199093629 0.4864456563 13-0.6651309335 -0.5665434359 0.4864456563 14 0.5718511657 0.8199093629 -0.0271086873 15 0.7485628941 -0.5665434359 -0.3445027268 16-0.9669906029 0.2533659270 -0.0271086873 17-0.2024936222 -0.9166865354 -0.3445027268 18 0.4467032247 0.2533659270 -0.8580570704 19-0.5043532916 -0.0967771725 -0.8580570704 20 0.2978495106 0.4270509831 0.5067318540 21-0.5036584607 0.1319660113 0.5067318540 22 0.2978495106 -0.8090169944 0.5067318540 23 0.6877395818 0.1319660113 -0.1935543450 24-0.2978495106 0.8090169944 -0.5067318540 25-0.6091275581 -0.3454915028 -0.1935543450 26 0.1271969263 -0.3454915028 -0.6263550179 274 0 2 4 1 284 0 3 6 2 295 0 1 5 7 3 304 1 4 8 5 315 2 6 9 8 4 324 3 7 9 6 334 5 8 9 7 343 2 0 1 353 2 3 0 363 0 4 1 373 1 5 2 383 3 4 0 393 2 6 3 403 4 5 1 413 5 6 2 423 6 4 3 433 4 5 6 44pentagonal antiprism 45pentagonal deltohedron 46|2 2 5 47(3.3.3.5) 48dihedral group 49D 502{5}+10{3} 511 10 20 12 10 1 0 0 2 2 4 20 2 0 -1 52 0.0000000000 0.0000000000 1.0000000000 53 0.8944271910 0.0000000000 0.4472135955 54 0.2763932023 0.8506508084 0.4472135955 55-0.7236067977 0.5257311121 0.4472135955 56-0.7236067977 -0.5257311121 0.4472135955 57 0.7236067977 -0.5257311121 -0.4472135955 58 0.7236067977 0.5257311121 -0.4472135955 59-0.8944271910 -0.0000000000 -0.4472135955 60-0.2763932023 -0.8506508084 -0.4472135955 61-0.0000000000 -0.0000000000 -1.0000000000 62 0.2763932023 0.2008114159 0.4472135955 63-0.1055728090 0.3249196962 0.4472135955 64-0.3416407865 -0.0000000000 0.4472135955 65 0.2763932023 -0.8506508084 0.4472135955 66 0.5527864045 0.0000000000 -0.1055728090 67 0.4472135955 0.3249196962 0.1055728090 68-0.2763932023 0.8506508084 -0.4472135955 69-0.5527864045 -0.0000000000 0.1055728090 70-0.4472135955 -0.3249196962 -0.1055728090 71 0.1055728090 -0.3249196962 -0.4472135955 72 0.3416407865 0.0000000000 -0.4472135955 73-0.2763932023 -0.2008114159 -0.4472135955 743 0 2 1 753 0 3 2 763 0 4 3 775 0 1 5 8 4 783 1 6 5 793 1 2 6 805 2 3 7 9 6 813 3 4 7 823 4 8 7 833 5 9 8 843 5 6 9 853 7 8 9 864 3 0 1 2 874 3 4 5 0 884 5 6 1 0 894 6 7 2 1 904 7 8 3 2 914 3 9 10 4 924 10 6 5 4 934 6 11 8 7 944 11 9 3 8 954 9 10 6 11 96tetrahedron 97tetrahedron 983|2 3 99(3.3.3) 100tetrahedral group 101A4 1024{3} 1035 4 6 4 4 1 0 0 2 1 3 24 3 0 -1 104 0.0000000000 0.0000000000 1.0000000000 105 0.9428090416 0.0000000000 -0.3333333333 106-0.4714045208 0.8164965809 -0.3333333333 107-0.4714045208 -0.8164965809 -0.3333333333 108 0.4714045208 0.8164965809 0.3333333333 109-0.9428090416 -0.0000000000 0.3333333333 110 0.4714045208 -0.8164965809 0.3333333333 111-0.0000000000 0.0000000000 -1.0000000000 1123 0 2 1 1133 0 3 2 1143 0 1 3 1153 1 2 3 1163 2 0 1 1173 2 3 0 1183 3 1 0 1193 1 2 3 120truncated tetrahedron 121triakistetrahedron 1222 3|3 123(6.6.3) 124tetrahedral group 125A4 1264{6}+4{3} 1276 12 18 8 12 1 0 0 2 2 3 24 3 0 -1 128 0.0000000000 0.0000000000 1.0000000000 129 0.7713892158 0.0000000000 0.6363636364 130-0.6428243465 0.4264014327 0.6363636364 131 0.2999846950 -0.7106690545 0.6363636364 132 0.8999540851 0.4264014327 -0.0909090909 133-0.9856639980 0.1421338109 -0.0909090909 134-0.5142594772 0.8528028654 -0.0909090909 135-0.0428549564 -0.9949366763 -0.0909090909 136 0.5571144337 0.1421338109 -0.8181818182 137 0.2571297386 0.8528028654 -0.4545454545 138-0.6856793030 -0.5685352436 -0.4545454545 139 0.0857099129 -0.5685352436 -0.8181818182 140 0.2461829820 0.8164965809 0.5222329679 141-0.6564879519 -0.5443310540 0.5222329679 142 0.2461829820 -0.1632993162 0.5222329679 143 0.8206099399 -0.5443310540 -0.1740776560 144-0.4923659639 0.3265986324 0.1044465936 145 0.3938927711 0.3265986324 -0.3133397807 146-0.4103049699 0.2721655270 -0.8703882798 147-0.1477097892 -0.4898979486 -0.3133397807 1486 0 2 6 9 4 1 1496 0 3 7 10 5 2 1503 0 1 3 1516 1 4 8 11 7 3 1523 2 5 6 1533 4 9 8 1546 5 10 11 8 9 6 1553 7 11 10 1563 2 0 1 1573 2 3 0 1583 0 4 1 1593 1 3 2 1603 3 5 0 1613 4 6 1 1623 0 6 4 1633 1 7 3 1643 3 6 5 1653 5 0 6 1663 6 7 1 1673 7 3 6 168octahedron 169hexahedron 1704|2 3 171(3.3.3.3) 172octahedral group 173S4 1748{3} 1759 6 12 8 6 1 0 0 2 1 4 48 4 0 -1 176 0.0000000000 0.0000000000 1.0000000000 177 1.0000000000 0.0000000000 -0.0000000000 178-0.0000000000 1.0000000000 -0.0000000000 179-1.0000000000 -0.0000000000 -0.0000000000 180 0.0000000000 -1.0000000000 -0.0000000000 181-0.0000000000 -0.0000000000 -1.0000000000 182 0.5773502692 0.5773502692 0.5773502692 183-0.5773502692 0.5773502692 0.5773502692 184-0.5773502692 -0.5773502692 0.5773502692 185 0.5773502692 -0.5773502692 0.5773502692 186 0.5773502692 -0.5773502692 -0.5773502692 187 0.5773502692 0.5773502692 -0.5773502692 188-0.5773502692 0.5773502692 -0.5773502692 189-0.5773502692 -0.5773502692 -0.5773502692 1903 0 2 1 1913 0 3 2 1923 0 4 3 1933 0 1 4 1943 1 5 4 1953 1 2 5 1963 2 3 5 1973 3 4 5 1984 3 0 1 2 1994 3 4 5 0 2004 5 6 1 0 2014 6 7 2 1 2024 7 4 3 2 2034 4 5 6 7 204hexahedron 205octahedron 2063|2 4 207(4.4.4) 208octahedral group 209S4 2106{4} 21110 8 12 6 8 1 0 0 2 1 3 48 4 0 -1 212 0.0000000000 0.0000000000 1.0000000000 213 0.9428090416 0.0000000000 0.3333333333 214-0.4714045208 0.8164965809 0.3333333333 215-0.4714045208 -0.8164965809 0.3333333333 216 0.4714045208 0.8164965809 -0.3333333333 217 0.4714045208 -0.8164965809 -0.3333333333 218-0.9428090416 -0.0000000000 -0.3333333333 219-0.0000000000 -0.0000000000 -1.0000000000 220 0.4082482905 0.7071067812 0.5773502692 221-0.8164965809 -0.0000000000 0.5773502692 222 0.4082482905 -0.7071067812 0.5773502692 223 0.8164965809 -0.0000000000 -0.5773502692 224-0.4082482905 0.7071067812 -0.5773502692 225-0.4082482905 -0.7071067812 -0.5773502692 2264 0 2 4 1 2274 0 3 6 2 2284 0 1 5 3 2294 1 4 7 5 2304 2 6 7 4 2314 3 5 7 6 2323 2 0 1 2333 2 3 0 2343 0 4 1 2353 1 5 2 2363 3 4 0 2373 5 3 2 2383 4 5 1 2393 3 4 5 240cuboctahedron 241rhombic dodecahedron 2422|3 4 243(3.4.3.4) 244octahedral group 245S4 2466{4}+8{3} 24711 12 24 14 12 1 0 0 2 2 4 48 4 0 -1 248 0.0000000000 0.0000000000 1.0000000000 249 0.8660254038 0.0000000000 0.5000000000 250 0.2886751346 0.8164965809 0.5000000000 251-0.8660254038 -0.0000000000 0.5000000000 252-0.2886751346 -0.8164965809 0.5000000000 253 0.8660254038 -0.0000000000 -0.5000000000 254 0.5773502692 -0.8164965809 -0.0000000000 255-0.5773502692 0.8164965809 -0.0000000000 256 0.2886751346 0.8164965809 -0.5000000000 257-0.8660254038 0.0000000000 -0.5000000000 258-0.2886751346 -0.8164965809 -0.5000000000 259-0.0000000000 -0.0000000000 -1.0000000000 260 0.4082482905 0.2886751346 0.7071067812 261-0.4082482905 0.5773502692 0.7071067812 262-0.4082482905 -0.2886751346 0.7071067812 263 0.4082482905 -0.5773502692 0.7071067812 264 0.8164965809 -0.2886751346 -0.0000000000 265 0.8164965809 0.5773502692 -0.0000000000 266 0.0000000000 0.8660254038 -0.0000000000 267-0.8164965809 0.2886751346 -0.0000000000 268-0.8164965809 -0.5773502692 -0.0000000000 269-0.0000000000 -0.8660254038 -0.0000000000 270 0.4082482905 -0.5773502692 -0.7071067812 271 0.4082482905 0.2886751346 -0.7071067812 272-0.4082482905 0.5773502692 -0.7071067812 273-0.4082482905 -0.2886751346 -0.7071067812 2743 0 2 1 2754 0 3 7 2 2763 0 4 3 2774 0 1 6 4 2783 1 5 6 2794 1 2 8 5 2803 2 7 8 2813 3 9 7 2824 3 4 10 9 2833 4 6 10 2844 5 11 10 6 2853 5 8 11 2864 7 9 11 8 2873 9 10 11 2884 3 0 1 2 2894 3 4 5 0 2904 5 6 1 0 2914 1 7 8 2 2924 8 9 3 2 2934 4 10 11 5 2944 9 10 4 3 2954 6 12 7 1 2964 11 12 6 5 2974 12 13 8 7 2984 13 10 9 8 2994 10 11 12 13 300truncated octahedron 301tetrakishexahedron 3022 4|3 303(6.6.4) 304octahedral group 305S4 3068{6}+6{4} 30712 24 36 14 24 1 0 0 2 2 3 48 4 0 -1 308 0.0000000000 0.0000000000 1.0000000000 309 0.6000000000 0.0000000000 0.8000000000 310-0.4000000000 0.4472135955 0.8000000000 311-0.0666666667 -0.5962847940 0.8000000000 312 0.8000000000 0.4472135955 0.4000000000 313 0.5333333333 -0.5962847940 0.6000000000 314-0.8666666667 0.2981423970 0.4000000000 315-0.2000000000 0.8944271910 0.4000000000 316-0.5333333333 -0.7453559925 0.4000000000 317 0.9333333333 0.2981423970 -0.2000000000 318 0.4000000000 0.8944271910 0.2000000000 319 0.6666666667 -0.7453559925 -0.0000000000 320-0.6666666667 0.7453559925 -0.0000000000 321-0.9333333333 -0.2981423970 0.2000000000 322-0.4000000000 -0.8944271910 -0.2000000000 323 0.5333333333 0.7453559925 -0.4000000000 324 0.8666666667 -0.2981423970 -0.4000000000 325 0.2000000000 -0.8944271910 -0.4000000000 326-0.5333333333 0.5962847940 -0.6000000000 327-0.8000000000 -0.4472135955 -0.4000000000 328 0.0666666667 0.5962847940 -0.8000000000 329 0.4000000000 -0.4472135955 -0.8000000000 330-0.6000000000 0.0000000000 -0.8000000000 331-0.0000000000 0.0000000000 -1.0000000000 332 0.2581988897 0.5773502692 0.7745966692 333-0.6024640761 -0.1924500897 0.7745966692 334 0.2581988897 -0.2886751346 0.7745966692 335 0.9467292624 -0.1924500897 0.2581988897 336-0.5163977795 0.5773502692 0.3872983346 337 0.0860662966 -0.9622504486 0.2581988897 338 0.6454972244 0.5773502692 -0.0000000000 339-0.9467292624 0.1924500897 -0.2581988897 340-0.0860662966 0.9622504486 -0.2581988897 341-0.6454972244 -0.5773502692 -0.0000000000 342 0.6024640761 0.1924500897 -0.7745966692 343 0.5163977795 -0.5773502692 -0.3872983346 344-0.2581988897 -0.5773502692 -0.7745966692 345-0.2581988897 0.2886751346 -0.7745966692 3466 0 2 7 10 4 1 3476 0 3 8 13 6 2 3484 0 1 5 3 3496 1 4 9 16 11 5 3504 2 6 12 7 3516 3 5 11 17 14 8 3524 4 10 15 9 3536 6 13 19 22 18 12 3546 7 12 18 20 15 10 3554 8 14 19 13 3566 9 15 20 23 21 16 3574 11 16 21 17 3586 14 17 21 23 22 19 3594 18 22 23 20 3603 2 0 1 3613 2 3 0 3623 0 4 1 3633 1 5 2 3643 3 6 0 3653 5 3 2 3663 4 7 1 3673 0 8 4 3683 1 9 5 3693 3 10 6 3703 6 8 0 3713 5 11 3 3723 8 7 4 3733 7 9 1 3743 9 12 5 3753 10 8 6 3763 11 10 3 3773 12 11 5 3783 8 13 7 3793 7 12 9 3803 10 13 8 3813 12 10 11 3823 13 12 7 3833 10 13 12 384truncated hexahedron 385triakisoctahedron 3862 3|4 387(8.8.3) 388octahedral group 389S4 3906{8}+8{3} 39113 24 36 14 24 1 0 0 2 2 3 48 4 0 -1 392 0.0000000000 0.0000000000 1.0000000000 393 0.5395042868 0.0000000000 0.8419828529 394-0.4604957132 0.2810846377 0.8419828529 395 0.2466110680 -0.4798414911 0.8419828529 396 0.8419828529 0.2810846377 0.4604957132 397-0.8651239283 0.1987568534 0.4604957132 398-0.5722307095 0.6785983445 0.4604957132 399 0.1348760717 -0.8773551980 0.4604957132 400 0.9768589246 0.1987568534 -0.0790085736 401 0.7302478566 0.6785983445 0.0790085736 402-0.9768589246 -0.1987568534 0.0790085736 403-0.2697521434 0.9596829823 0.0790085736 404-0.2697521434 -0.9596829823 0.0790085736 405 0.2697521434 -0.9596829823 -0.0790085736 406 0.8651239283 -0.1987568534 -0.4604957132 407 0.2697521434 0.9596829823 -0.0790085736 408-0.7302478566 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2 4323 0 1 3 4338 1 4 8 14 19 13 7 3 4343 2 5 6 4353 4 9 8 4368 5 10 17 21 22 18 11 6 4373 7 13 12 4388 8 9 15 18 22 23 20 14 4393 10 16 17 4403 11 18 15 4418 12 13 19 20 23 21 17 16 4423 14 20 19 4433 21 23 22 4443 2 0 1 4453 2 3 0 4463 0 4 1 4473 1 3 2 4483 3 5 0 4493 4 6 1 4503 0 6 4 4513 1 7 3 4523 3 8 5 4533 8 0 5 4543 6 9 1 4553 0 10 6 4563 1 11 7 4573 11 3 7 4583 3 12 8 4593 8 10 0 4603 9 11 1 4613 6 11 9 4623 8 6 10 4633 11 12 3 4643 11 8 12 4653 6 13 11 4663 8 13 6 4673 11 8 13 468small rhombicuboctahedron 469deltoidal icositetrahedron 4703 4|2 471(4.3.4.4) 472octahedral group 473S4 47418{4}+8{3} 47514 24 48 26 24 1 0 0 2 2 4 48 4 0 -1 476 0.0000000000 0.0000000000 1.0000000000 477 0.6675992222 0.0000000000 0.7445208382 478-0.0977676425 0.6604015517 0.7445208382 479-0.6389637427 0.1934271362 0.7445208382 480-0.0977676425 -0.6604015517 0.7445208382 481 0.5698315797 0.6604015517 0.4890416764 482 0.9727633538 0.1934271362 0.1277395809 483 0.5698315797 -0.6604015517 0.4890416764 484-0.3337996111 0.9339488311 0.1277395809 485-0.7367313852 -0.4669744155 0.4890416764 486-0.8749957112 0.4669744155 0.1277395809 487-0.3337996111 -0.9339488311 0.1277395809 488 0.3337996111 0.9339488311 -0.1277395809 489 0.8749957112 -0.4669744155 -0.1277395809 490 0.7367313852 0.4669744155 -0.4890416764 491 0.3337996111 -0.9339488311 -0.1277395809 492-0.5698315797 0.6604015517 -0.4890416764 493-0.9727633538 -0.1934271362 -0.1277395809 494-0.5698315797 -0.6604015517 -0.4890416764 495 0.0977676425 0.6604015517 -0.7445208382 496 0.6389637427 -0.1934271362 -0.7445208382 497 0.0977676425 -0.6604015517 -0.7445208382 498-0.6675992222 0.0000000000 -0.7445208382 499-0.0000000000 0.0000000000 -1.0000000000 500 0.3302007759 0.3826834324 0.8628562095 501-0.2553967884 0.2959899757 0.8628562095 502-0.4269143440 -0.2705980501 0.8628562095 503 0.3302007759 -0.3826834324 0.8628562095 504 0.8938887595 -0.2705980501 0.3574067443 505 0.7661903653 0.2959899757 0.4719117310 506 0.1367736397 0.9238795325 0.3574067443 507-0.5636879836 0.6532814824 0.5054494651 508-0.9339488311 -0.0000000000 0.3574067443 509-0.4050047633 -0.7145830136 0.4719117310 510 0.1367736397 -0.9238795325 0.3574067443 511 0.7571151198 0.6532814824 -0.0000000000 512 0.9339488311 -0.0000000000 -0.3574067443 513 0.6165823904 -0.7145830136 0.0809672526 514-0.1367736397 0.9238795325 -0.3574067443 515-0.6165823904 0.7145830136 -0.0809672526 516-0.7571151198 -0.6532814824 -0.0000000000 517-0.8938887595 0.2705980501 -0.3574067443 518-0.1367736397 -0.9238795325 -0.3574067443 519 0.4050047633 0.7145830136 -0.4719117310 520 0.5636879836 -0.6532814824 -0.5054494651 521 0.4269143440 0.2705980501 -0.8628562095 522-0.3302007759 0.3826834324 -0.8628562095 523-0.7661903653 -0.2959899757 -0.4719117310 524-0.3302007759 -0.3826834324 -0.8628562095 525 0.2553967884 -0.2959899757 -0.8628562095 5264 0 2 5 1 5273 0 3 2 5284 0 4 9 3 5294 0 1 7 4 5304 1 6 13 7 5313 1 5 6 5324 2 8 12 5 5334 2 3 10 8 5344 3 9 17 10 5353 4 11 9 5364 4 7 15 11 5374 5 12 14 6 5384 6 14 20 13 5393 7 13 15 5404 8 16 19 12 5413 8 10 16 5424 9 11 18 17 5434 10 17 22 16 5444 11 15 21 18 5453 12 19 14 5464 13 20 21 15 5474 14 19 23 20 5484 16 22 23 19 5493 17 18 22 5504 18 21 23 22 5513 20 23 21 5524 3 0 1 2 5534 3 4 5 0 5544 0 6 7 1 5554 7 8 2 1 5564 2 9 10 3 5574 5 11 6 0 5584 4 12 11 5 5594 10 13 4 3 5604 6 14 15 7 5614 8 16 9 2 5624 15 17 8 7 5634 16 18 10 9 5644 11 19 14 6 5654 13 20 12 4 5664 12 21 19 11 5674 18 20 13 10 5684 14 22 17 15 5694 17 23 16 8 5704 23 24 18 16 5714 21 22 14 19 5724 20 25 21 12 5734 24 25 20 18 5744 22 24 23 17 5754 21 22 24 25 576truncated cuboctahedron 577disdyakisdodecahedron 5782 3 4| 579(4.6.8) 580octahedral group 581S4 5826{8}+8{6}+12{4} 58315 48 72 26 48 1 0 0 2 3 3 48 4 0 -1 584 0.0000000000 0.0000000000 1.0000000000 585 0.4213179058 0.0000000000 0.9069130180 586-0.0205668596 0.4208156152 0.9069130180 587-0.3330265737 -0.2580737859 0.9069130180 588 0.4007510462 0.4208156152 0.8138260361 589 0.6841248285 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