| Acronym | berlin (old: shabrilq) |
| Name |
birectified pentacontihexahecatonicosihexaexon (small demibirhombated pentacontihexapentacosiheptacontihexaexon) |
| Circumradius | sqrt(51)/2 = 3.570714 |
| Face vector | 40320, 302400, 544320, 403200, 142632, 22428, 758 |
| Confer |
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Incidence matrix according to Dynkin symbol
o3x3o3o *c3x3o3o . . . . . . . | 40320 | 6 9 | 3 6 18 9 9 | 3 9 2 18 18 3 9 3 | 1 9 9 6 18 6 3 3 | 3 9 3 6 6 4 | 3 3 2 -----------------+-------+---------------+----------------------------------+--------------------------------------------------+-----------------------------------------------+-------------------------------+----------- . x . . . . . | 2 | 120960 * | 1 2 3 0 0 | 2 3 1 6 3 0 0 0 | 1 6 3 3 6 1 0 0 | 3 6 1 3 2 0 | 3 2 1 . . . . x . . | 2 | * 181440 | 0 0 2 2 2 | 0 1 0 4 4 1 4 1 | 0 2 2 2 8 2 2 2 | 1 4 1 4 4 1 | 2 2 2 -----------------+-------+---------------+----------------------------------+--------------------------------------------------+-----------------------------------------------+-------------------------------+----------- o3x . . . . . | 3 | 3 0 | 40320 * * * * | 2 3 0 0 0 0 0 0 | 1 6 3 0 0 0 0 0 | 3 6 1 0 0 0 | 3 2 0 . x3o . . . . | 3 | 3 0 | * 80640 * * * | 1 0 1 3 0 0 0 0 | 1 3 0 3 3 0 0 0 | 3 3 0 3 1 0 | 3 1 1 . x . . x . . | 4 | 2 2 | * * 181440 * * | 0 1 0 2 2 0 0 0 | 0 2 2 1 4 1 0 0 | 1 4 1 2 2 0 | 2 2 1 . . o . *c3x . . | 3 | 0 3 | * * * 120960 * | 0 0 0 2 0 1 2 0 | 0 1 0 2 4 0 2 1 | 1 2 0 4 2 1 | 2 1 2 . . . . x3o . | 3 | 0 3 | * * * * 120960 | 0 0 0 0 2 0 2 1 | 0 0 1 0 4 2 1 2 | 0 2 1 2 4 1 | 1 2 2 -----------------+-------+---------------+----------------------------------+--------------------------------------------------+-----------------------------------------------+-------------------------------+----------- o3x3o . . . . ♦ 6 | 12 0 | 4 4 0 0 0 | 20160 * * * * * * * | 1 3 0 0 0 0 0 0 | 3 3 0 0 0 0 | 3 1 0 o3x . . x . . ♦ 6 | 6 3 | 2 0 3 0 0 | * 60480 * * * * * * | 0 2 2 0 0 0 0 0 | 1 4 1 0 0 0 | 2 2 0 . x3o3o . . . ♦ 4 | 6 0 | 0 4 0 0 0 | * * 20160 * * * * * | 1 0 0 3 0 0 0 0 | 3 0 0 3 0 0 | 3 0 1 . x3o . *c3x . . ♦ 12 | 12 12 | 0 4 6 4 0 | * * * 60480 * * * * | 0 1 0 1 2 0 0 0 | 1 2 0 2 1 0 | 2 1 1 . x . . x3o . ♦ 6 | 3 6 | 0 0 3 0 2 | * * * * 120960 * * * | 0 0 1 0 2 1 0 0 | 0 2 1 1 2 0 | 1 2 1 . . o3o *c3x . . ♦ 4 | 0 6 | 0 0 0 4 0 | * * * * * 30240 * * | 0 0 0 2 0 0 2 0 | 1 0 0 4 0 1 | 2 0 2 . . o . *c3x3o . ♦ 6 | 0 12 | 0 0 0 4 4 | * * * * * * 60480 * | 0 0 0 0 2 0 1 1 | 0 1 0 2 2 1 | 1 1 2 . . . . x3o3o ♦ 4 | 0 6 | 0 0 0 0 4 | * * * * * * * 30240 | 0 0 0 0 0 2 0 2 | 0 0 1 0 4 1 | 0 2 2 -----------------+-------+---------------+----------------------------------+--------------------------------------------------+-----------------------------------------------+-------------------------------+----------- o3x3o3o . . . ♦ 10 | 30 0 | 10 20 0 0 0 | 5 0 5 0 0 0 0 0 | 4032 * * * * * * * | 3 0 0 0 0 0 | 3 0 0 o3x3o . *c3x . . ♦ 30 | 60 30 | 20 20 30 10 0 | 5 10 0 5 0 0 0 0 | * 12096 * * * * * * | 1 2 0 0 0 0 | 2 1 0 o3x . . x3o . ♦ 9 | 9 9 | 3 0 9 0 3 | 0 3 0 0 3 0 0 0 | * * 40320 * * * * * | 0 2 1 0 0 0 | 1 2 0 . x3o3o *c3x . . ♦ 32 | 48 48 | 0 32 24 32 0 | 0 0 8 8 0 8 0 0 | * * * 7560 * * * * | 1 0 0 2 0 0 | 2 0 1 . x3o . *c3x3o . ♦ 30 | 30 60 | 0 10 30 20 20 | 0 0 0 5 10 0 5 0 | * * * * 24192 * * * | 0 1 0 1 1 0 | 1 1 1 . x . . x3o3o ♦ 8 | 4 12 | 0 0 6 0 8 | 0 0 0 0 4 0 0 2 | * * * * * 30240 * * | 0 0 1 0 2 0 | 0 2 1 . . o3o *c3x3o . ♦ 10 | 0 30 | 0 0 0 20 10 | 0 0 0 0 0 5 5 0 | * * * * * * 12096 * | 0 0 0 2 0 1 | 1 0 2 . . o . *c3x3o3o ♦ 10 | 0 30 | 0 0 0 10 20 | 0 0 0 0 0 0 5 5 | * * * * * * * 12096 | 0 0 0 0 2 1 | 0 1 2 -----------------+-------+---------------+----------------------------------+--------------------------------------------------+-----------------------------------------------+-------------------------------+----------- o3x3o3o *c3x . . ♦ 160 | 480 240 | 160 320 240 160 0 | 80 80 80 80 0 40 0 0 | 16 16 0 10 0 0 0 0 | 756 * * * * * | 2 0 0 o3x3o . *c3x3o . ♦ 90 | 180 180 | 60 60 180 60 60 | 15 60 0 30 60 0 15 0 | 0 6 20 0 6 0 0 0 | * 4032 * * * * | 1 1 0 o3x . . x3o3o ♦ 12 | 12 18 | 4 0 18 0 12 | 0 6 0 0 12 0 0 3 | 0 0 4 0 0 3 0 0 | * * 10080 * * * | 0 2 0 . x3o3o *c3x3o . ♦ 160 | 240 480 | 0 160 240 320 160 | 0 0 40 80 80 80 80 0 | 0 0 0 10 16 0 16 0 | * * * 1512 * * | 1 0 1 . x3o . *c3x3o3o ♦ 60 | 60 180 | 0 20 90 60 120 | 0 0 0 15 60 0 30 30 | 0 0 0 0 6 15 0 6 | * * * * 4032 * | 0 1 1 . . o3o *c3x3o3o ♦ 20 | 0 90 | 0 0 0 60 60 | 0 0 0 0 0 15 30 15 | 0 0 0 0 0 0 6 6 | * * * * * 2016 | 0 0 2 -----------------+-------+---------------+----------------------------------+--------------------------------------------------+-----------------------------------------------+-------------------------------+----------- o3x3o3o *c3x3o . ♦ 2160 | 6480 6480 | 2160 4320 6480 4320 2160 | 1080 2160 1080 2160 2160 1080 1080 0 | 216 432 720 270 432 0 216 0 | 27 72 0 27 0 0 | 56 * * o3x3o . *c3x3o3o ♦ 210 | 420 630 | 140 140 630 210 420 | 35 210 0 105 420 0 105 105 | 0 21 140 0 42 105 0 21 | 0 7 35 0 7 0 | * 576 * . x3o3o *c3x3o3o ♦ 640 | 960 2880 | 0 640 1440 1920 1920 | 0 0 160 480 960 480 960 480 | 0 0 0 60 192 240 192 192 | 0 0 0 12 32 32 | * * 126
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