Group : PSL(4,3)

Order : 6065280

Download a file containing the generators referenced below.
Go back to the starting page of the Atlas.

Total number of polytopes : 672

Number of polytopes of rank 3 : 620

Polytopes References
[ 4 , 13 ] [ 21, 28 ]
[ 4 , 20 ] [ 25, 29 ]
[ 5 , 8 ] [ 32, 33 ]
[ 5 , 9 ] [ 34, 35, 51, 55 ]
[ 5 , 12 ] [ 38, 39 ]
[ 5 , 13 ] [ 31, 36, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 56 ]
[ 5 , 20 ] [ 37, 41, 57, 58 ]
[ 6 , 13 ] [ 63, 64, 66, 68, 69, 72, 75, 78, 81, 84, 86, 87, 88, 90 ]
[ 6 , 20 ] [ 73, 74, 97, 98 ]
[ 8 , 5 ] [ 119, 151 ]
[ 8 , 8 ] [ 148, 156 ]
[ 8 , 9 ] [ 103, 105, 114, 123 ]
[ 8 , 10 ] [ 115, 121, 136, 138 ]
[ 8 , 12 ] [ 150, 152, 157, 159 ]
[ 8 , 13 ] [ 100, 102, 104, 106, 108, 109, 112, 113, 117, 118, 124, 126, 127, 129, 131, 132, 133, 134, 137, 139, 140, 143, 145, 146, 147, 149, 153, 162 ]
[ 8 , 20 ] [ 99, 101, 107, 110, 111, 120, 122, 125, 130, 135, 141, 142, 144, 154, 160, 161 ]
[ 9 , 5 ] [ 182, 194, 196, 201 ]
[ 9 , 8 ] [ 164, 169, 170, 171 ]
[ 9 , 9 ] [ 176, 202 ]
[ 9 , 12 ] [ 179, 187, 193, 200 ]
[ 9 , 13 ] [ 163, 166, 167, 168, 172, 173, 174, 175, 177, 178, 181, 183, 184, 186, 188, 190, 192, 197, 198, 199, 203, 204 ]
[ 9 , 20 ] [ 165, 180, 185, 189, 191, 195 ]
[ 10 , 8 ] [ 219, 220, 223, 227 ]
[ 10 , 12 ] [ 222, 228 ]
[ 10 , 13 ] [ 205, 206, 207, 209, 210, 211, 214, 215, 216, 217, 218, 221, 224, 226, 229, 230, 231, 232 ]
[ 10 , 20 ] [ 208, 212, 213, 225 ]
[ 12 , 5 ] [ 294, 310 ]
[ 12 , 8 ] [ 237, 241, 270, 272 ]
[ 12 , 9 ] [ 280, 286, 300, 307 ]
[ 12 , 10 ] [ 233, 242 ]
[ 12 , 12 ] [ 245, 248, 251, 258, 276, 289, 292, 299, 304, 312 ]
[ 12 , 13 ] [ 234, 238, 239, 240, 244, 246, 247, 249, 250, 252, 253, 255, 256, 260, 261, 263, 266, 268, 269, 271, 273, 274, 277, 278, 282, 287, 291, 295, 301, 302, 305, 306, 309, 311, 313, 314 ]
[ 12 , 20 ] [ 235, 236, 243, 254, 257, 259, 262, 264, 265, 267, 275, 279, 281, 283, 284, 285, 288, 290, 293, 296, 297, 298, 303, 308 ]
[ 13 , 4 ] [ 324, 408 ]
[ 13 , 5 ] [ 327, 335, 350, 373, 395, 412, 419, 425, 433, 437, 447, 480, 523, 529, 544, 547 ]
[ 13 , 6 ] [ 328, 355, 363, 364, 401, 409, 451, 463, 474, 478, 492, 509, 515, 528 ]
[ 13 , 8 ] [ 315, 317, 319, 344, 346, 365, 375, 381, 397, 405, 407, 411, 421, 439, 445, 446, 454, 458, 459, 486, 489, 499, 505, 510, 521, 537, 539, 556 ]
[ 13 , 9 ] [ 316, 333, 349, 378, 384, 388, 404, 415, 424, 432, 436, 438, 469, 476, 488, 490, 497, 519, 527, 530, 550, 559 ]
[ 13 , 10 ] [ 329, 330, 331, 339, 353, 357, 386, 398, 406, 423, 448, 481, 484, 506, 516, 535, 536, 560 ]
[ 13 , 12 ] [ 334, 338, 341, 342, 356, 358, 361, 370, 374, 377, 380, 416, 417, 422, 427, 435, 449, 450, 452, 461, 462, 464, 466, 471, 485, 487, 494, 522, 525, 534, 538, 540, 552, 554, 555, 566 ]
[ 13 , 13 ] [ 318, 322, 323, 325, 326, 332, 336, 337, 340, 345, 347, 351, 352, 354, 359, 360, 362, 367, 368, 369, 372, 379, 382, 383, 385, 390, 391, 392, 393, 394, 399, 400, 403, 410, 413, 414, 420, 426, 429, 431, 434, 440, 441, 442, 443, 453, 455, 457, 465, 467, 468, 470, 472, 473, 475, 482, 483, 491, 493, 495, 498, 500, 501, 503, 504, 507, 511, 514, 517, 518, 520, 531, 532, 533, 541, 542, 543, 548, 549, 551, 553, 561, 564, 565 ]
[ 13 , 20 ] [ 320, 321, 343, 348, 366, 371, 376, 387, 389, 396, 402, 418, 428, 430, 444, 456, 460, 477, 479, 496, 502, 508, 512, 513, 524, 526, 545, 546, 557, 558, 562, 563 ]
[ 20 , 4 ] [ 609, 658 ]
[ 20 , 5 ] [ 587, 610, 611, 615 ]
[ 20 , 6 ] [ 627, 628, 638, 660 ]
[ 20 , 8 ] [ 575, 577, 581, 586, 590, 597, 601, 629, 632, 637, 645, 647, 654, 664, 667, 670 ]
[ 20 , 9 ] [ 600, 605, 621, 625, 636, 653 ]
[ 20 , 10 ] [ 594, 618, 656, 672 ]
[ 20 , 12 ] [ 567, 580, 583, 584, 585, 591, 592, 596, 603, 607, 608, 612, 613, 620, 630, 635, 642, 643, 650, 652, 661, 665, 666, 669 ]
[ 20 , 13 ] [ 568, 569, 571, 573, 576, 578, 579, 582, 589, 595, 598, 602, 606, 614, 616, 619, 622, 623, 626, 633, 634, 640, 644, 649, 651, 655, 657, 659, 662, 663, 668, 671 ]
[ 20 , 20 ] [ 570, 572, 574, 588, 593, 599, 604, 617, 624, 631, 639, 641, 646, 648 ]

Number of polytopes of rank 4 : 52

Polytopes References
[ 3 , 8 , 6 ] [ 9, 10 ]
[ 3 , 9 , 6 ] [ 3, 4, 5, 6, 7, 8 ]
[ 3 , 12 , 4 ] [ 11, 12 ]
[ 3 , 12 , 6 ] [ 1, 2 ]
[ 4 , 5 , 6 ] [ 15, 16 ]
[ 4 , 8 , 6 ] [ 13, 14 ]
[ 4 , 9 , 4 ] [ 19, 20, 22, 26 ]
[ 4 , 9 , 6 ] [ 17, 18 ]
[ 4 , 12 , 3 ] [ 27, 30 ]
[ 4 , 12 , 6 ] [ 23, 24 ]
[ 6 , 5 , 4 ] [ 67, 79 ]
[ 6 , 8 , 3 ] [ 92, 95 ]
[ 6 , 8 , 4 ] [ 83, 91 ]
[ 6 , 8 , 6 ] [ 61, 62, 85, 93 ]
[ 6 , 9 , 3 ] [ 65, 76, 82, 89, 94, 96 ]
[ 6 , 9 , 4 ] [ 70, 71 ]
[ 6 , 12 , 3 ] [ 77, 80 ]
[ 6 , 12 , 4 ] [ 59, 60 ]
[ 8 , 8 , 8 ] [ 116, 128, 155, 158 ]