Group : Sym(10)

Order : 3628800

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Total number of polytopes : 690

Number of polytopes of rank 3 : 413

Polytopes References
[ 3 , 8 ] [ 5 ]
[ 3 , 10 ] [ 2 ]
[ 3 , 12 ] [ 4 ]
[ 3 , 14 ] [ 3 ]
[ 3 , 20 ] [ 6 ]
[ 3 , 30 ] [ 1 ]
[ 4 , 8 ] [ 8, 21 ]
[ 4 , 9 ] [ 17, 28 ]
[ 4 , 10 ] [ 11, 18, 22, 26, 27, 29, 31 ]
[ 4 , 12 ] [ 20, 24 ]
[ 4 , 14 ] [ 19 ]
[ 4 , 20 ] [ 15, 23 ]
[ 4 , 21 ] [ 7, 10, 13, 16, 25, 30 ]
[ 4 , 30 ] [ 9, 12, 14 ]
[ 5 , 6 ] [ 37, 38, 44, 51, 53 ]
[ 5 , 8 ] [ 35, 47, 48 ]
[ 5 , 10 ] [ 39, 42, 43, 50, 52 ]
[ 5 , 12 ] [ 33, 49, 54 ]
[ 5 , 14 ] [ 34, 46 ]
[ 5 , 20 ] [ 32, 40, 41 ]
[ 5 , 30 ] [ 36, 45 ]
[ 6 , 6 ] [ 59, 92, 106 ]
[ 6 , 7 ] [ 149 ]
[ 6 , 8 ] [ 64, 73, 88, 99, 103, 105, 108, 115, 122, 140 ]
[ 6 , 9 ] [ 57, 65, 71, 82, 85, 90, 139, 147 ]
[ 6 , 10 ] [ 56, 58, 60, 62, 66, 68, 70, 72, 74, 75, 80, 86, 94, 95, 97, 98, 109, 111, 112, 113, 118, 129, 130, 138, 141, 143, 148 ]
[ 6 , 12 ] [ 61, 77, 89, 93, 100, 101, 107, 110, 114, 116, 119, 121, 123, 125, 131, 133, 135, 136, 137, 142, 144 ]
[ 6 , 14 ] [ 63, 83, 102, 117 ]
[ 6 , 15 ] [ 120 ]
[ 6 , 20 ] [ 81, 124, 126, 151 ]
[ 6 , 21 ] [ 55, 67, 69, 78, 79, 84, 87, 91, 128, 132, 145, 150, 152, 154 ]
[ 6 , 30 ] [ 76, 96, 104, 127, 134, 146, 153, 155 ]
[ 7 , 8 ] [ 161, 166 ]
[ 7 , 10 ] [ 157, 158, 160, 162, 164, 165 ]
[ 7 , 12 ] [ 159 ]
[ 7 , 14 ] [ 163 ]
[ 7 , 30 ] [ 156 ]
[ 8 , 8 ] [ 172, 183, 185, 190, 197, 200, 226 ]
[ 8 , 9 ] [ 199, 202, 203, 205, 208, 217 ]
[ 8 , 10 ] [ 167, 181, 184, 187, 191, 196, 201, 206, 207, 213, 215, 219, 221, 224, 225, 227, 229, 230 ]
[ 8 , 12 ] [ 170, 173, 174, 178, 180, 182, 189, 209, 223, 228 ]
[ 8 , 14 ] [ 176, 179, 204, 220 ]
[ 8 , 15 ] [ 177, 195, 222 ]
[ 8 , 20 ] [ 175, 211 ]
[ 8 , 21 ] [ 194, 198, 210, 212, 214, 218 ]
[ 8 , 30 ] [ 168, 169, 171, 186, 188, 192, 193, 216 ]
[ 9 , 10 ] [ 231, 232, 233, 235, 236, 240, 241, 242, 245, 246, 247, 249, 250 ]
[ 9 , 12 ] [ 234, 237, 239, 244, 252, 254 ]
[ 9 , 14 ] [ 256, 257 ]
[ 9 , 20 ] [ 238, 243, 248 ]
[ 9 , 30 ] [ 251, 253, 255, 258 ]
[ 10 , 10 ] [ 259, 260, 262, 263, 265, 267, 276, 282, 284, 294, 309, 322, 325, 326, 328, 329, 330 ]
[ 10 , 12 ] [ 264, 269, 273, 275, 277, 278, 285, 289, 291, 292, 293, 298, 303, 305, 307, 313, 314, 319, 321, 323, 324, 327, 331, 332, 333 ]
[ 10 , 14 ] [ 261, 270, 272, 274, 301 ]
[ 10 , 15 ] [ 297, 300, 302, 311 ]
[ 10 , 20 ] [ 266, 279, 304, 310, 312, 315, 320 ]
[ 10 , 21 ] [ 271, 280, 281, 283, 287, 288, 299, 306, 308, 316, 317, 318 ]
[ 10 , 30 ] [ 268, 286, 290, 295, 296 ]
[ 12 , 12 ] [ 334, 339, 341, 350, 366, 371, 374, 375, 376, 377 ]
[ 12 , 14 ] [ 342, 344, 355, 364, 365, 369, 370, 373, 379 ]
[ 12 , 15 ] [ 340, 360, 362, 368 ]
[ 12 , 20 ] [ 336, 343, 346, 351, 354, 357, 358, 361, 367, 372, 378, 381 ]
[ 12 , 21 ] [ 335, 338, 347, 349, 352, 353 ]
[ 12 , 30 ] [ 337, 345, 348, 356, 359, 363, 380 ]
[ 14 , 14 ] [ 385 ]
[ 14 , 15 ] [ 386 ]
[ 14 , 20 ] [ 384, 389 ]
[ 14 , 21 ] [ 388, 390 ]
[ 14 , 30 ] [ 382, 383, 387 ]
[ 15 , 20 ] [ 391, 393 ]
[ 15 , 30 ] [ 392 ]
[ 20 , 20 ] [ 397, 400, 403, 404 ]
[ 20 , 21 ] [ 394, 395, 396, 399, 401, 402 ]
[ 20 , 30 ] [ 398, 405 ]
[ 21 , 30 ] [ 406, 407, 408, 409 ]
[ 30 , 30 ] [ 410, 411, 412, 413 ]

Number of polytopes of rank 4 : 203

Polytopes References
[ 3 , 4 , 5 ] [ 427 ]
[ 3 , 4 , 6 ] [ 417, 418 ]
[ 3 , 4 , 8 ] [ 415 ]
[ 3 , 4 , 12 ] [ 443 ]
[ 3 , 5 , 4 ] [ 429 ]
[ 3 , 5 , 5 ] [ 428 ]
[ 3 , 5 , 6 ] [ 434 ]
[ 3 , 5 , 12 ] [ 430 ]
[ 3 , 6 , 4 ] [ 420 ]
[ 3 , 6 , 6 ] [ 416, 419 ]
[ 3 , 6 , 8 ] [ 414 ]
[ 3 , 6 , 12 ] [ 442 ]
[ 3 , 8 , 4 ] [ 423, 426, 433 ]
[ 3 , 8 , 6 ] [ 424 ]
[ 3 , 8 , 12 ] [ 425 ]
[ 3 , 10 , 4 ] [ 432 ]
[ 3 , 12 , 4 ] [ 421, 422, 440, 441 ]
[ 4 , 3 , 8 ] [ 431 ]
[ 4 , 3 , 12 ] [ 438 ]
[ 4 , 3 , 15 ] [ 437 ]
[ 4 , 4 , 4 ] [ 478, 486, 526 ]
[ 4 , 4 , 5 ] [ 451, 454, 509, 510, 524, 525, 567 ]
[ 4 , 4 , 6 ] [ 457, 458, 487, 501, 511, 515, 522, 523, 570, 572 ]
[ 4 , 4 , 7 ] [ 531 ]
[ 4 , 4 , 8 ] [ 453, 484, 488, 508, 532, 558 ]
[ 4 , 4 , 10 ] [ 485, 502 ]
[ 4 , 4 , 12 ] [ 449, 450, 507, 519, 520, 569 ]
[ 4 , 4 , 15 ] [ 483 ]
[ 4 , 5 , 4 ] [ 474, 476, 477, 530, 560, 580 ]
[ 4 , 5 , 5 ] [ 562, 564, 571 ]
[ 4 , 5 , 6 ] [ 471, 473, 475, 489, 536, 559, 565, 579 ]
[ 4 , 5 , 8 ] [ 472, 563, 578 ]
[ 4 , 5 , 12 ] [ 561 ]
[ 4 , 6 , 4 ] [ 448, 545 ]
[ 4 , 6 , 5 ] [ 586 ]
[ 4 , 6 , 6 ] [ 446, 447, 455, 498, 512, 533, 535, 543, 554, 573, 575, 577, 584, 587 ]
[ 4 , 6 , 7 ] [ 481, 583 ]
[ 4 , 6 , 8 ] [ 445 ]
[ 4 , 6 , 10 ] [ 527, 538 ]
[ 4 , 6 , 12 ] [ 534, 544, 585, 588 ]
[ 4 , 6 , 15 ] [ 444, 576 ]
[ 4 , 8 , 4 ] [ 456, 459, 490, 528, 529, 556 ]
[ 4 , 8 , 6 ] [ 547, 549, 551, 553, 557 ]
[ 4 , 8 , 7 ] [ 460, 462 ]
[ 4 , 8 , 8 ] [ 461, 482, 491, 492, 546 ]
[ 4 , 8 , 12 ] [ 548, 552 ]
[ 4 , 10 , 4 ] [ 463, 464, 468, 469, 470, 505 ]
[ 4 , 10 , 5 ] [ 497 ]
[ 4 , 10 , 6 ] [ 506, 539, 540 ]
[ 4 , 10 , 8 ] [ 467, 504 ]
[ 4 , 10 , 12 ] [ 503 ]
[ 4 , 12 , 4 ] [ 465, 494, 521 ]
[ 4 , 12 , 6 ] [ 493, 495, 517, 518, 537, 581, 582 ]
[ 4 , 12 , 8 ] [ 479 ]
[ 4 , 12 , 12 ] [ 466, 480, 499 ]
[ 5 , 4 , 5 ] [ 568 ]
[ 5 , 4 , 6 ] [ 566, 589, 591 ]
[ 5 , 4 , 8 ] [ 550 ]
[ 5 , 5 , 5 ] [ 601, 602 ]
[ 5 , 5 , 6 ] [ 595, 596, 600, 605 ]
[ 5 , 6 , 5 ] [ 598 ]
[ 5 , 6 , 6 ] [ 592, 593, 597, 606 ]
[ 5 , 8 , 6 ] [ 604 ]
[ 5 , 8 , 8 ] [ 603 ]
[ 6 , 3 , 6 ] [ 435 ]
[ 6 , 3 , 12 ] [ 436, 439 ]
[ 6 , 4 , 6 ] [ 496, 500, 513, 514, 555, 590 ]
[ 6 , 4 , 8 ] [ 542 ]
[ 6 , 4 , 10 ] [ 541 ]
[ 6 , 4 , 12 ] [ 452, 516, 574 ]
[ 6 , 5 , 6 ] [ 594, 599 ]
[ 6 , 6 , 6 ] [ 609, 610, 612, 614 ]
[ 6 , 6 , 12 ] [ 608 ]
[ 6 , 8 , 6 ] [ 611 ]
[ 6 , 12 , 6 ] [ 607, 613, 615 ]
[ 8 , 8 , 12 ] [ 616 ]

Number of polytopes of rank 5 : 52

Polytopes References
[ 3 , 3 , 6 , 7 ] [ 618 ]
[ 3 , 3 , 10 , 4 ] [ 632 ]
[ 3 , 4 , 4 , 3 ] [ 626 ]
[ 3 , 4 , 4 , 4 ] [ 627, 635 ]
[ 3 , 4 , 4 , 6 ] [ 636, 637 ]
[ 3 , 4 , 6 , 3 ] [ 625 ]
[ 3 , 6 , 3 , 7 ] [ 620 ]
[ 3 , 6 , 4 , 3 ] [ 622 ]
[ 3 , 6 , 4 , 4 ] [ 623, 633 ]
[ 3 , 6 , 4 , 6 ] [ 634, 638 ]
[ 3 , 6 , 4 , 7 ] [ 619 ]
[ 3 , 6 , 6 , 3 ] [ 621, 639 ]
[ 3 , 6 , 6 , 6 ] [ 617 ]
[ 3 , 6 , 6 , 7 ] [ 624 ]
[ 4 , 3 , 6 , 5 ] [ 628 ]
[ 4 , 3 , 6 , 6 ] [ 629 ]
[ 4 , 4 , 4 , 4 ] [ 660 ]
[ 4 , 4 , 4 , 6 ] [ 659 ]
[ 4 , 4 , 6 , 6 ] [ 661 ]
[ 4 , 6 , 3 , 4 ] [ 630, 631 ]
[ 4 , 6 , 4 , 4 ] [ 649, 650, 653 ]
[ 4 , 6 , 4 , 5 ] [ 652 ]
[ 4 , 6 , 4 , 6 ] [ 642, 643, 648, 651, 654 ]
[ 4 , 6 , 6 , 4 ] [ 646 ]
[ 4 , 6 , 6 , 5 ] [ 647 ]
[ 4 , 6 , 6 , 6 ] [ 641, 644, 656 ]
[ 4 , 6 , 10 , 5 ] [ 645 ]
[ 5 , 4 , 4 , 6 ] [ 657 ]
[ 5 , 6 , 4 , 5 ] [ 655 ]
[ 5 , 6 , 4 , 6 ] [ 658, 662, 663 ]
[ 5 , 6 , 6 , 5 ] [ 667, 668 ]
[ 5 , 10 , 4 , 6 ] [ 664 ]
[ 5 , 10 , 6 , 5 ] [ 666 ]
[ 5 , 10 , 10 , 5 ] [ 665 ]
[ 6 , 4 , 3 , 6 ] [ 640 ]

Number of polytopes of rank 6 : 13

Polytopes References
[ 3 , 3 , 3 , 6 , 6 ] [ 671 ]
[ 3 , 4 , 4 , 6 , 3 ] [ 673 ]
[ 3 , 6 , 3 , 3 , 4 ] [ 670 ]
[ 3 , 6 , 4 , 6 , 3 ] [ 672 ]
[ 4 , 3 , 3 , 6 , 4 ] [ 677 ]
[ 4 , 3 , 6 , 4 , 4 ] [ 676 ]
[ 4 , 3 , 6 , 6 , 4 ] [ 674 ]
[ 4 , 6 , 3 , 6 , 5 ] [ 669 ]
[ 4 , 6 , 4 , 4 , 6 ] [ 680 ]
[ 4 , 6 , 6 , 3 , 5 ] [ 675 ]
[ 4 , 6 , 6 , 4 , 5 ] [ 679 ]
[ 4 , 6 , 6 , 4 , 6 ] [ 678 ]
[ 4 , 6 , 6 , 5 , 5 ] [ 681 ]

Number of polytopes of rank 7 : 7

Polytopes References
[ 3 , 3 , 3 , 3 , 6 , 5 ] [ 683 ]
[ 3 , 3 , 3 , 6 , 3 , 4 ] [ 685 ]
[ 3 , 3 , 3 , 6 , 3 , 5 ] [ 684 ]
[ 3 , 3 , 3 , 6 , 4 , 5 ] [ 688 ]
[ 3 , 3 , 3 , 6 , 4 , 6 ] [ 687 ]
[ 3 , 3 , 3 , 6 , 5 , 5 ] [ 682 ]
[ 4 , 6 , 3 , 3 , 6 , 4 ] [ 686 ]

Number of polytopes of rank 8 : 1

Polytopes References
[ 3 , 3 , 3 , 3 , 3 , 6 , 4 ] [ 689 ]

Number of polytopes of rank 9 : 1

Polytopes References
[ 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 ] [ 690 ]