| Acronym | srek |
| Name |
small rhombated diacosipentacontahexazetton, cantellated octacross |
| Circumradius | sqrt(3) = 1.732051 |
| Coordinates | (sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0, 0, 0, 0) & all permutations, all changes of sign |
| Face vector | 1344, 14784, 47488, 81760, 82432, 44800, 10464, 384 |
| Confer |
|
Incidence matrix according to Dynkin symbol
x3o3x3o3o3o3o4o . . . . . . . . | 1344 | 2 20 | 1 20 10 80 | 12 80 40 160 | 40 160 80 160 | 80 160 80 64 | 80 64 32 2 | 32 2 1 ----------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+----------- x . . . . . . . | 2 | 1344 * | 1 10 0 0 | 10 40 0 0 | 40 80 0 0 | 80 80 0 0 | 80 32 0 0 | 32 1 0 . . x . . . . . | 2 | * 13440 | 0 1 1 8 | 1 8 8 24 | 8 24 24 32 | 24 32 32 16 | 32 16 16 1 | 16 1 1 ----------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+----------- x3o . . . . . . | 3 | 3 0 | 448 * * * ♦ 10 0 0 0 | 40 0 0 0 | 80 0 0 0 | 80 0 0 0 | 32 0 0 x . x . . . . . | 4 | 2 2 | * 6720 * * | 1 8 0 0 | 8 24 0 0 | 24 32 0 0 | 32 16 0 0 | 16 1 0 . o3x . . . . . | 3 | 0 3 | * * 4480 * | 1 0 8 0 | 8 0 24 0 | 24 0 32 0 | 32 0 16 0 | 16 0 1 . . x3o . . . . | 3 | 0 3 | * * * 35840 | 0 1 1 6 | 1 6 6 12 | 6 12 12 8 | 12 8 8 1 | 8 1 1 ----------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+----------- x3o3x . . . . . ♦ 12 | 12 12 | 4 6 4 0 | 1120 * * * ♦ 8 0 0 0 | 24 0 0 0 | 32 0 0 0 | 16 0 0 x . x3o . . . . ♦ 6 | 3 6 | 0 3 0 2 | * 17920 * * | 1 6 0 0 | 6 12 0 0 | 12 8 0 0 | 8 1 0 . o3x3o . . . . ♦ 6 | 0 12 | 0 0 4 4 | * * 8960 * | 1 0 6 0 | 6 0 12 0 | 12 0 8 0 | 8 0 1 . . x3o3o . . . ♦ 4 | 0 6 | 0 0 0 4 | * * * 53760 | 0 1 1 4 | 1 4 4 4 | 4 4 4 1 | 4 1 1 ----------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+----------- x3o3x3o . . . . ♦ 30 | 30 60 | 10 30 20 20 | 5 10 5 0 | 1792 * * * ♦ 6 0 0 0 | 12 0 0 0 | 8 0 0 x . x3o3o . . . ♦ 8 | 4 12 | 0 6 0 8 | 0 4 0 2 | * 26880 * * | 1 4 0 0 | 4 4 0 0 | 4 1 0 . o3x3o3o . . . ♦ 10 | 0 30 | 0 0 10 20 | 0 0 5 5 | * * 10752 * | 1 0 4 0 | 4 0 4 0 | 4 0 1 . . x3o3o3o . . ♦ 5 | 0 10 | 0 0 0 10 | 0 0 0 5 | * * * 43008 | 0 1 1 2 | 1 2 2 1 | 2 1 1 ----------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+----------- x3o3x3o3o . . . ♦ 60 | 60 180 | 20 90 60 120 | 15 60 30 30 | 6 15 6 0 | 1792 * * * | 4 0 0 0 | 4 0 0 x . x3o3o3o . . ♦ 10 | 5 20 | 0 10 0 20 | 0 10 0 10 | 0 5 0 2 | * 21504 * * | 1 2 0 0 | 2 1 0 . o3x3o3o3o . . ♦ 15 | 0 60 | 0 0 20 60 | 0 0 15 30 | 0 0 6 6 | * * 7168 * | 1 0 2 0 | 2 0 1 . . x3o3o3o3o . ♦ 6 | 0 15 | 0 0 0 20 | 0 0 0 15 | 0 0 0 6 | * * * 14336 | 0 1 1 1 | 1 1 1 ----------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+----------- x3o3x3o3o3o . . ♦ 105 | 105 420 | 35 210 140 420 | 35 210 105 210 | 21 105 42 42 | 7 21 7 0 | 1024 * * * | 2 0 0 x . x3o3o3o3o . ♦ 12 | 6 30 | 0 15 0 40 | 0 20 0 30 | 0 15 0 12 | 0 6 0 2 | * 7168 * * | 1 1 0 . o3x3o3o3o3o . ♦ 21 | 0 105 | 0 0 35 140 | 0 0 35 105 | 0 0 21 42 | 0 0 7 7 | * * 2048 * | 1 0 1 . . x3o3o3o3o4o ♦ 12 | 0 60 | 0 0 0 160 | 0 0 0 240 | 0 0 0 192 | 0 0 0 64 | * * * 224 | 0 1 1 ----------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+----------- x3o3x3o3o3o3o . ♦ 168 | 168 840 | 56 420 280 1120 | 70 560 280 840 | 56 420 168 336 | 28 168 56 56 | 8 28 8 0 | 256 * * x . x3o3o3o3o4o ♦ 24 | 12 120 | 0 60 0 320 | 0 160 0 480 | 0 240 0 384 | 0 192 0 128 | 0 64 0 2 | * 112 * . o3x3o3o3o3o4o ♦ 84 | 0 840 | 0 0 280 2240 | 0 0 560 3360 | 0 0 672 2688 | 0 0 448 896 | 0 0 128 14 | * * 16
x3o3x3o3o3o3o4/3o . . . . . . . . | 1344 | 2 20 | 1 20 10 80 | 12 80 40 160 | 40 160 80 160 | 80 160 80 64 | 80 64 32 2 | 32 2 1 ------------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+----------- x . . . . . . . | 2 | 1344 * | 1 10 0 0 | 10 40 0 0 | 40 80 0 0 | 80 80 0 0 | 80 32 0 0 | 32 1 0 . . x . . . . . | 2 | * 13440 | 0 1 1 8 | 1 8 8 24 | 8 24 24 32 | 24 32 32 16 | 32 16 16 1 | 16 1 1 ------------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+----------- x3o . . . . . . | 3 | 3 0 | 448 * * * ♦ 10 0 0 0 | 40 0 0 0 | 80 0 0 0 | 80 0 0 0 | 32 0 0 x . x . . . . . | 4 | 2 2 | * 6720 * * | 1 8 0 0 | 8 24 0 0 | 24 32 0 0 | 32 16 0 0 | 16 1 0 . o3x . . . . . | 3 | 0 3 | * * 4480 * | 1 0 8 0 | 8 0 24 0 | 24 0 32 0 | 32 0 16 0 | 16 0 1 . . x3o . . . . | 3 | 0 3 | * * * 35840 | 0 1 1 6 | 1 6 6 12 | 6 12 12 8 | 12 8 8 1 | 8 1 1 ------------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+----------- x3o3x . . . . . ♦ 12 | 12 12 | 4 6 4 0 | 1120 * * * ♦ 8 0 0 0 | 24 0 0 0 | 32 0 0 0 | 16 0 0 x . x3o . . . . ♦ 6 | 3 6 | 0 3 0 2 | * 17920 * * | 1 6 0 0 | 6 12 0 0 | 12 8 0 0 | 8 1 0 . o3x3o . . . . ♦ 6 | 0 12 | 0 0 4 4 | * * 8960 * | 1 0 6 0 | 6 0 12 0 | 12 0 8 0 | 8 0 1 . . x3o3o . . . ♦ 4 | 0 6 | 0 0 0 4 | * * * 53760 | 0 1 1 4 | 1 4 4 4 | 4 4 4 1 | 4 1 1 ------------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+----------- x3o3x3o . . . . ♦ 30 | 30 60 | 10 30 20 20 | 5 10 5 0 | 1792 * * * ♦ 6 0 0 0 | 12 0 0 0 | 8 0 0 x . x3o3o . . . ♦ 8 | 4 12 | 0 6 0 8 | 0 4 0 2 | * 26880 * * | 1 4 0 0 | 4 4 0 0 | 4 1 0 . o3x3o3o . . . ♦ 10 | 0 30 | 0 0 10 20 | 0 0 5 5 | * * 10752 * | 1 0 4 0 | 4 0 4 0 | 4 0 1 . . x3o3o3o . . ♦ 5 | 0 10 | 0 0 0 10 | 0 0 0 5 | * * * 43008 | 0 1 1 2 | 1 2 2 1 | 2 1 1 ------------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+----------- x3o3x3o3o . . . ♦ 60 | 60 180 | 20 90 60 120 | 15 60 30 30 | 6 15 6 0 | 1792 * * * | 4 0 0 0 | 4 0 0 x . x3o3o3o . . ♦ 10 | 5 20 | 0 10 0 20 | 0 10 0 10 | 0 5 0 2 | * 21504 * * | 1 2 0 0 | 2 1 0 . o3x3o3o3o . . ♦ 15 | 0 60 | 0 0 20 60 | 0 0 15 30 | 0 0 6 6 | * * 7168 * | 1 0 2 0 | 2 0 1 . . x3o3o3o3o . ♦ 6 | 0 15 | 0 0 0 20 | 0 0 0 15 | 0 0 0 6 | * * * 14336 | 0 1 1 1 | 1 1 1 ------------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+----------- x3o3x3o3o3o . . ♦ 105 | 105 420 | 35 210 140 420 | 35 210 105 210 | 21 105 42 42 | 7 21 7 0 | 1024 * * * | 2 0 0 x . x3o3o3o3o . ♦ 12 | 6 30 | 0 15 0 40 | 0 20 0 30 | 0 15 0 12 | 0 6 0 2 | * 7168 * * | 1 1 0 . o3x3o3o3o3o . ♦ 21 | 0 105 | 0 0 35 140 | 0 0 35 105 | 0 0 21 42 | 0 0 7 7 | * * 2048 * | 1 0 1 . . x3o3o3o3o4/3o ♦ 12 | 0 60 | 0 0 0 160 | 0 0 0 240 | 0 0 0 192 | 0 0 0 64 | * * * 224 | 0 1 1 ------------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+----------- x3o3x3o3o3o3o . ♦ 168 | 168 840 | 56 420 280 1120 | 70 560 280 840 | 56 420 168 336 | 28 168 56 56 | 8 28 8 0 | 256 * * x . x3o3o3o3o4/3o ♦ 24 | 12 120 | 0 60 0 320 | 0 160 0 480 | 0 240 0 384 | 0 192 0 128 | 0 64 0 2 | * 112 * . o3x3o3o3o3o4/3o ♦ 84 | 0 840 | 0 0 280 2240 | 0 0 560 3360 | 0 0 672 2688 | 0 0 448 896 | 0 0 128 14 | * * 16
o3o3o *b3o3o3x3o3x . . . . . . . . | 1344 | 20 2 | 80 10 20 1 | 160 40 80 12 | 160 80 160 40 | 32 32 80 160 80 | 2 16 32 16 32 80 | 1 2 16 16 -------------------+------+------------+---------------------+-----------------------+------------------------+---------------------------+------------------------------+--------------- . . . . . x . . | 2 | 13440 * | 8 1 1 0 | 24 8 8 1 | 32 24 24 8 | 8 8 32 32 24 | 1 8 8 8 8 32 | 1 1 8 8 . . . . . . . x | 2 | * 1344 | 0 0 10 1 | 0 0 40 10 | 0 0 80 40 | 0 0 0 80 80 | 0 0 16 0 16 80 | 0 1 16 16 -------------------+------+------------+---------------------+-----------------------+------------------------+---------------------------+------------------------------+--------------- . . . . o3x . . | 3 | 3 0 | 35840 * * * | 6 1 1 0 | 12 6 6 1 | 4 4 12 12 6 | 1 4 4 4 4 12 | 1 1 4 4 . . . . . x3o . | 3 | 3 0 | * 4480 * * | 0 8 0 1 | 0 24 0 8 | 0 0 32 0 24 | 0 8 0 8 0 32 | 1 0 8 8 . . . . . x . x | 4 | 2 2 | * * 6720 * | 0 0 8 1 | 0 0 24 8 | 0 0 0 32 24 | 0 0 8 0 8 32 | 0 1 8 8 . . . . . . o3x | 3 | 0 3 | * * * 448 ♦ 0 0 0 10 | 0 0 0 40 | 0 0 0 0 80 | 0 0 0 0 0 80 | 0 0 16 16 -------------------+------+------------+---------------------+-----------------------+------------------------+---------------------------+------------------------------+--------------- . . . o3o3x . . ♦ 4 | 6 0 | 4 0 0 0 | 53760 * * * | 4 1 1 0 | 2 2 4 4 1 | 1 2 2 2 2 4 | 1 1 2 2 . . . . o3x3o . ♦ 6 | 12 0 | 4 4 0 0 | * 8960 * * | 0 6 0 1 | 0 0 12 0 6 | 0 4 0 4 0 12 | 1 0 4 4 . . . . o3x . x ♦ 6 | 6 3 | 2 0 3 0 | * * 17920 * | 0 0 6 1 | 0 0 0 12 6 | 0 0 4 0 4 12 | 0 1 4 4 . . . . . x3o3x ♦ 12 | 12 12 | 0 4 6 4 | * * * 1120 ♦ 0 0 0 8 | 0 0 0 0 24 | 0 0 0 0 0 32 | 0 0 8 8 -------------------+------+------------+---------------------+-----------------------+------------------------+---------------------------+------------------------------+--------------- . o . *b3o3o3x . . ♦ 5 | 10 0 | 10 0 0 0 | 5 0 0 0 | 43008 * * * | 1 1 1 1 0 | 1 1 1 1 1 1 | 1 1 1 1 . . . o3o3x3o . ♦ 10 | 30 0 | 20 10 0 0 | 5 5 0 0 | * 10752 * * | 0 0 4 0 1 | 0 2 0 2 0 4 | 1 0 2 2 . . . o3o3x . x ♦ 8 | 12 4 | 8 0 6 0 | 2 0 4 0 | * * 26880 * | 0 0 0 4 1 | 0 0 2 0 2 4 | 0 1 2 2 . . . . o3x3o3x ♦ 30 | 60 30 | 20 20 30 10 | 0 5 10 5 | * * * 1792 ♦ 0 0 0 0 6 | 0 0 0 0 0 12 | 0 0 4 4 -------------------+------+------------+---------------------+-----------------------+------------------------+---------------------------+------------------------------+--------------- o3o . *b3o3o3x . . ♦ 6 | 15 0 | 20 0 0 0 | 15 0 0 0 | 6 0 0 0 | 7168 * * * * | 1 1 1 0 0 0 | 1 1 1 0 . o3o *b3o3o3x . . ♦ 6 | 15 0 | 20 0 0 0 | 15 0 0 0 | 6 0 0 0 | * 7168 * * * | 1 0 0 1 1 0 | 1 1 0 1 . o . *b3o3o3x3o . ♦ 15 | 60 0 | 60 20 0 0 | 30 15 0 0 | 6 6 0 0 | * * 7168 * * | 0 1 0 1 0 1 | 1 0 1 1 . o . *b3o3o3x . x ♦ 10 | 20 5 | 20 0 10 0 | 10 0 10 0 | 2 0 5 0 | * * * 21504 * | 0 0 1 0 1 1 | 0 1 1 1 . . . o3o3x3o3x ♦ 60 | 180 60 | 120 60 90 20 | 30 30 60 15 | 0 6 15 6 | * * * * 1792 | 0 0 0 0 0 4 | 0 0 2 2 -------------------+------+------------+---------------------+-----------------------+------------------------+---------------------------+------------------------------+--------------- o3o3o *b3o3o3x . . ♦ 12 | 60 0 | 160 0 0 0 | 240 0 0 0 | 192 0 0 0 | 32 32 0 0 0 | 224 * * * * * | 1 1 0 0 o3o . *b3o3o3x3o . ♦ 21 | 105 0 | 140 35 0 0 | 105 35 0 0 | 42 21 0 0 | 7 0 7 0 0 | * 1024 * * * * | 1 0 1 0 o3o . *b3o3o3x . x ♦ 12 | 30 6 | 40 0 15 0 | 30 0 20 0 | 12 0 15 0 | 2 0 0 6 0 | * * 3584 * * * | 0 1 1 0 . o3o *b3o3o3x3o . ♦ 21 | 105 0 | 140 35 0 0 | 105 35 0 0 | 42 21 0 0 | 0 7 7 0 0 | * * * 1024 * * | 1 0 0 1 . o3o *b3o3o3x . x ♦ 12 | 30 6 | 40 0 15 0 | 30 0 20 0 | 12 0 15 0 | 0 2 0 6 0 | * * * * 3584 * | 0 1 0 1 . o . *b3o3o3x3o3x ♦ 105 | 420 105 | 420 140 210 35 | 210 105 210 35 | 42 42 105 21 | 0 0 7 21 7 | * * * * * 1024 | 0 0 1 1 -------------------+------+------------+---------------------+-----------------------+------------------------+---------------------------+------------------------------+--------------- o3o3o *b3o3o3x3o . ♦ 84 | 840 0 | 2240 280 0 0 | 3360 560 0 0 | 2688 672 0 0 | 448 448 448 0 0 | 14 64 0 64 0 0 | 16 * * * o3o3o *b3o3o3x . x ♦ 24 | 120 12 | 320 0 60 0 | 480 0 160 0 | 384 0 240 0 | 64 64 0 192 0 | 2 0 32 0 32 0 | * 112 * * o3o . *b3o3o3x3o3x ♦ 168 | 840 168 | 1120 280 420 56 | 840 280 560 70 | 336 168 420 56 | 56 0 56 168 28 | 0 8 28 0 0 8 | * * 128 * . o3o *b3o3o3x3o3x ♦ 168 | 840 168 | 1120 280 420 56 | 840 280 560 70 | 336 168 420 56 | 0 56 56 168 28 | 0 0 0 8 28 8 | * * * 128
© 2004-2024 | top of page |