Group : Held

Order : 4,030,387,200

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Total number of polytopes : 1264

Number of polytopes of rank 3 : 1188

Polytopes References
[ 3 , 12 ] [ 5, 8, 9 ]
[ 3 , 17 ] [ 2, 4, 7, 12, 13 ]
[ 3 , 21 ] [ 1, 3, 6, 10, 11, 14, 15, 16 ]
[ 4 , 8 ] [ 507 ]
[ 4 , 10 ] [ 474, 480, 501 ]
[ 4 , 12 ] [ 470, 473, 476, 478, 481, 482, 483, 487, 490, 493, 494, 498, 510, 513 ]
[ 4 , 15 ] [ 506, 512, 514 ]
[ 4 , 17 ] [ 93, 158, 175, 193, 202, 228, 232, 257, 280, 343, 390, 392, 406, 429, 439, 443 ]
[ 4 , 21 ] [ 469, 471, 472, 475, 477, 479, 484, 485, 486, 488, 489, 491, 492, 495, 496, 497, 499, 500, 502, 503, 504, 505, 508, 509, 511, 515, 516, 517 ]
[ 5 , 8 ] [ 29 ]
[ 5 , 12 ] [ 17, 18, 23, 24, 25, 26 ]
[ 5 , 15 ] [ 27, 31 ]
[ 5 , 17 ] [ 22, 28, 32 ]
[ 5 , 21 ] [ 19, 20, 21, 30, 33, 34 ]
[ 6 , 6 ] [ 520, 522, 538 ]
[ 6 , 7 ] [ 50, 63 ]
[ 6 , 8 ] [ 525, 563, 598, 617, 636, 637, 653, 660 ]
[ 6 , 10 ] [ 518, 526, 532, 537, 549, 550, 557, 570, 586, 604, 608, 609, 634 ]
[ 6 , 12 ] [ 519, 521, 523, 524, 527, 530, 531, 534, 535, 539, 540, 541, 542, 544, 546, 547, 552, 554, 556, 565, 566, 567, 568, 569, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 583, 591, 592, 594, 602, 605, 620, 622, 624, 627, 628, 638, 642, 644, 647, 656, 659, 664, 666 ]
[ 6 , 15 ] [ 536, 555, 560, 562, 581, 584, 595, 603, 612, 616, 621, 626, 641, 658, 661 ]
[ 6 , 17 ] [ 99, 100, 108, 118, 126, 131, 136, 144, 153, 169, 174, 178, 191, 215, 219, 227, 239, 248, 253, 256, 258, 271, 273, 286, 287, 302, 306, 320, 345, 349, 351, 370, 371, 373, 374, 386, 395, 405, 438, 444, 448, 449, 451, 456, 461 ]
[ 6 , 21 ] [ 528, 529, 533, 543, 545, 548, 551, 553, 558, 559, 561, 564, 582, 585, 587, 588, 589, 590, 593, 596, 597, 599, 600, 601, 606, 607, 610, 611, 613, 614, 615, 618, 619, 623, 625, 629, 630, 631, 632, 633, 635, 639, 640, 643, 645, 646, 648, 649, 650, 651, 652, 654, 655, 657, 662, 663, 665, 667, 668, 669, 670 ]
[ 7 , 8 ] [ 39, 49, 59 ]
[ 7 , 10 ] [ 48, 51, 62 ]
[ 7 , 12 ] [ 43, 46, 54, 56, 57 ]
[ 7 , 15 ] [ 41, 42, 53, 61 ]
[ 7 , 17 ] [ 36, 40, 44, 45, 52, 55, 65, 66 ]
[ 7 , 21 ] [ 35, 37, 38, 47, 58, 60, 64 ]
[ 8 , 8 ] [ 1094, 1102, 1107 ]
[ 8 , 10 ] [ 672, 676, 705, 719, 730, 740, 744, 753 ]
[ 8 , 12 ] [ 1095, 1096, 1097, 1098, 1099, 1100, 1101, 1103, 1104, 1105, 1106, 1108, 1109, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117 ]
[ 8 , 15 ] [ 784, 785, 791, 805, 817, 832, 853, 854, 856, 863, 864 ]
[ 8 , 17 ] [ 68, 75, 87, 94, 104, 121, 132, 146, 150, 211, 217, 224, 230, 259, 278, 292, 310, 311, 312, 316, 324, 333, 338, 342, 401, 428, 434, 462 ]
[ 8 , 21 ] [ 878, 883, 906, 907, 919, 923, 925, 967, 978, 988, 990, 991, 999, 1000, 1018, 1031, 1032, 1034, 1047, 1054, 1057, 1061, 1066, 1067, 1070, 1077, 1088 ]
[ 10 , 10 ] [ 674, 694, 706, 722, 771 ]
[ 10 , 12 ] [ 671, 675, 678, 682, 683, 684, 689, 690, 692, 696, 697, 701, 710, 711, 714, 716, 720, 721, 723, 729, 733, 737, 739, 742, 745, 746, 747, 748, 750, 751, 752, 755, 757, 759, 761, 765, 767, 768, 769, 770, 772, 773, 774, 775, 776, 777, 778 ]
[ 10 , 15 ] [ 685, 688, 702, 704, 709, 724, 734, 756, 758 ]
[ 10 , 17 ] [ 67, 77, 92, 109, 139, 156, 160, 164, 171, 172, 197, 201, 206, 216, 231, 250, 255, 276, 294, 307, 313, 321, 335, 344, 359, 394, 417 ]
[ 10 , 21 ] [ 673, 677, 679, 680, 681, 686, 687, 691, 693, 695, 698, 699, 700, 703, 707, 708, 712, 713, 715, 717, 718, 725, 726, 727, 728, 731, 732, 735, 736, 738, 741, 743, 749, 754, 760, 762, 763, 764, 766 ]
[ 12 , 12 ] [ 1118, 1119, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188 ]
[ 12 , 15 ] [ 779, 783, 788, 790, 792, 794, 795, 796, 800, 802, 803, 807, 810, 811, 819, 822, 824, 828, 830, 833, 837, 838, 842, 844, 845, 846, 849, 852, 857, 861, 862, 866, 868, 870, 874 ]
[ 12 , 17 ] [ 74, 78, 81, 82, 96, 98, 105, 110, 112, 116, 119, 122, 123, 128, 133, 145, 147, 149, 151, 152, 155, 157, 161, 162, 177, 179, 189, 190, 199, 200, 203, 204, 210, 226, 229, 243, 249, 252, 260, 268, 275, 281, 282, 283, 285, 293, 295, 296, 298, 301, 308, 318, 319, 325, 328, 329, 341, 350, 353, 363, 364, 369, 376, 377, 378, 379, 383, 385, 388, 389, 398, 399, 402, 404, 409, 411, 412, 421, 422, 425, 431, 436, 437, 441, 442, 445, 450, 452, 454, 455, 458, 464, 466, 467 ]
[ 12 , 21 ] [ 875, 879, 880, 881, 884, 885, 886, 887, 888, 891, 892, 894, 895, 897, 899, 901, 902, 908, 909, 911, 914, 915, 916, 917, 920, 922, 926, 928, 931, 932, 933, 934, 936, 937, 938, 939, 942, 945, 947, 948, 953, 954, 957, 959, 963, 965, 968, 970, 972, 973, 974, 975, 977, 980, 983, 984, 985, 986, 987, 996, 1002, 1003, 1004, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1016, 1017, 1020, 1023, 1024, 1025, 1027, 1028, 1029, 1035, 1039, 1040, 1041, 1042, 1044, 1045, 1046, 1050, 1051, 1052, 1053, 1055, 1058, 1059, 1060, 1063, 1064, 1068, 1069, 1071, 1072, 1073, 1074, 1075, 1076, 1078, 1079, 1080, 1081, 1083, 1085, 1086, 1087, 1089, 1092, 1093 ]
[ 15 , 15 ] [ 797, 799, 808, 813, 826, 841, 855, 858 ]
[ 15 , 17 ] [ 79, 84, 89, 95, 106, 113, 125, 134, 137, 154, 165, 167, 173, 209, 212, 234, 240, 247, 261, 274, 277, 304, 317, 327, 336, 354, 372, 382, 387, 393, 396, 397, 413, 418, 463, 465 ]
[ 15 , 21 ] [ 780, 781, 782, 786, 787, 789, 793, 798, 801, 804, 806, 809, 812, 814, 815, 816, 818, 820, 821, 823, 825, 827, 829, 831, 834, 835, 836, 839, 840, 843, 847, 848, 850, 851, 859, 860, 865, 867, 869, 871, 872, 873 ]
[ 17 , 17 ] [ 72, 80, 86, 91, 101, 107, 111, 114, 117, 120, 124, 130, 140, 163, 168, 170, 180, 181, 185, 188, 192, 194, 207, 208, 213, 220, 222, 223, 225, 233, 235, 242, 269, 270, 284, 289, 297, 299, 303, 309, 346, 365, 367, 380, 391, 415, 423, 426, 427, 430, 447, 460 ]
[ 17 , 21 ] [ 69, 70, 71, 73, 76, 83, 85, 88, 90, 97, 102, 103, 115, 127, 129, 135, 138, 141, 142, 143, 148, 159, 166, 176, 182, 183, 184, 186, 187, 195, 196, 198, 205, 214, 218, 221, 236, 237, 238, 241, 244, 245, 246, 251, 254, 262, 263, 264, 265, 266, 267, 272, 279, 288, 290, 291, 300, 305, 314, 315, 322, 323, 326, 330, 331, 332, 334, 337, 339, 340, 347, 348, 352, 355, 356, 357, 358, 360, 361, 362, 366, 368, 375, 381, 384, 400, 403, 407, 408, 410, 414, 416, 419, 420, 424, 432, 433, 435, 440, 446, 453, 457, 459, 468 ]
[ 21 , 21 ] [ 876, 877, 882, 889, 890, 893, 896, 898, 900, 903, 904, 905, 910, 912, 913, 918, 921, 924, 927, 929, 930, 935, 940, 941, 943, 944, 946, 949, 950, 951, 952, 955, 956, 958, 960, 961, 962, 964, 966, 969, 971, 976, 979, 981, 982, 989, 992, 993, 994, 995, 997, 998, 1001, 1005, 1015, 1019, 1021, 1022, 1026, 1030, 1033, 1036, 1037, 1038, 1043, 1048, 1049, 1056, 1062, 1065, 1082, 1084, 1090, 1091 ]

Number of polytopes of rank 4 : 76

Polytopes References
[ 3 , 3 , 10 ] [ 1229 ]
[ 3 , 4 , 5 ] [ 1252, 1253 ]
[ 3 , 4 , 10 ] [ 1233, 1236 ]
[ 3 , 5 , 4 ] [ 1258 ]
[ 3 , 5 , 6 ] [ 1260 ]
[ 3 , 6 , 4 ] [ 1209, 1211, 1212, 1216 ]
[ 3 , 6 , 5 ] [ 1219, 1254 ]
[ 3 , 6 , 6 ] [ 1238 ]
[ 3 , 6 , 10 ] [ 1235 ]
[ 3 , 10 , 3 ] [ 1259 ]
[ 3 , 10 , 4 ] [ 1244, 1245, 1250, 1255 ]
[ 3 , 15 , 4 ] [ 1256, 1257 ]
[ 4 , 4 , 6 ] [ 1223 ]
[ 4 , 5 , 4 ] [ 1248 ]
[ 4 , 5 , 6 ] [ 1196, 1247 ]
[ 4 , 6 , 4 ] [ 1208, 1213, 1215, 1217, 1261, 1262, 1263 ]
[ 4 , 6 , 5 ] [ 1210 ]
[ 4 , 6 , 6 ] [ 1193, 1194, 1237, 1242 ]
[ 4 , 6 , 10 ] [ 1231, 1232 ]
[ 4 , 7 , 4 ] [ 1251 ]
[ 4 , 10 , 4 ] [ 1191, 1204, 1243, 1246, 1249 ]
[ 4 , 12 , 4 ] [ 1189, 1190, 1205, 1206, 1207, 1214, 1218 ]
[ 4 , 12 , 5 ] [ 1200 ]
[ 4 , 12 , 6 ] [ 1197, 1222, 1239, 1240, 1241 ]
[ 4 , 12 , 10 ] [ 1230, 1234 ]
[ 5 , 3 , 6 ] [ 1192 ]
[ 5 , 4 , 10 ] [ 1226, 1227, 1228 ]
[ 5 , 5 , 6 ] [ 1195 ]
[ 5 , 6 , 5 ] [ 1225 ]
[ 5 , 6 , 6 ] [ 1199 ]
[ 6 , 3 , 6 ] [ 1221 ]
[ 6 , 6 , 6 ] [ 1198, 1201, 1203, 1220, 1224, 1264 ]
[ 6 , 7 , 6 ] [ 1202 ]