(small centrorhombated pentacontitetrapeton)
- general polytopal classes:
- Wythoffian polypeta lace simplices
links
| Acronym | barm (old: scram, bram, remak, kram) |
| Name |
birectified pentacontitetrapeton, (small centrorhombated pentacontitetrapeton) |
| Circumradius | sqrt(6) = 2.449490 |
| Face vector | 2160, 12960, 19440, 10800, 2286, 126 |
| Confer |
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External links |
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As abstract polytope barm is isomorphic to its (Grünbaumian) isomorph, thereby replacing some prograde by retrograde triangles, co by 2thah, resp. rit by 2tho+24{4} and srip by pinnip+5 2thah, resp. sirhin by its isomorph and sibrid by its isomorph.
Incidence matrix according to Dynkin symbol
o3x3o3x3o *c3o . . . . . . | 2160 | 6 6 | 3 6 12 6 3 | 3 6 12 2 6 3 2 | 6 1 3 6 4 1 | 3 2 2 ---------------+------+-----------+--------------------------+------------------------------------+-------------------------+--------- . x . . . . | 2 | 6480 * | 1 2 2 0 0 | 2 2 4 1 1 0 0 | 4 1 1 2 2 0 | 2 2 1 . . . x . . | 2 | * 6480 | 0 0 2 2 1 | 0 1 4 0 2 2 1 | 2 0 1 4 2 1 | 2 1 2 ---------------+------+-----------+--------------------------+------------------------------------+-------------------------+--------- o3x . . . . | 3 | 3 0 | 2160 * * * * | 2 2 0 0 0 0 0 | 4 1 1 0 0 0 | 2 2 0 . x3o . . . | 3 | 3 0 | * 4320 * * * | 1 0 2 1 0 0 0 | 2 1 0 1 2 0 | 1 2 1 . x . x . . | 4 | 2 2 | * * 6480 * * | 0 1 2 0 1 0 0 | 2 0 1 2 1 0 | 2 1 1 . . o3x . . | 3 | 0 3 | * * * 4320 * | 0 0 2 0 0 1 1 | 1 0 0 2 2 1 | 1 1 2 . . . x3o . | 3 | 0 3 | * * * * 2160 | 0 0 0 0 2 2 0 | 0 0 1 4 0 1 | 2 0 2 ---------------+------+-----------+--------------------------+------------------------------------+-------------------------+--------- o3x3o . . . ♦ 6 | 12 0 | 4 4 0 0 0 | 1080 * * * * * * | 2 1 0 0 0 0 | 1 2 0 o3x . x . . ♦ 6 | 6 3 | 2 0 3 0 0 | * 2160 * * * * * | 2 0 1 0 0 0 | 2 1 0 . x3o3x . . ♦ 12 | 12 12 | 0 4 6 4 0 | * * 2160 * * * * | 1 0 0 1 1 0 | 1 1 1 . x3o . . *c3o ♦ 4 | 6 0 | 0 4 0 0 0 | * * * 1080 * * * | 0 1 0 0 2 0 | 0 2 1 . x . x3o . ♦ 6 | 3 6 | 0 0 3 0 2 | * * * * 2160 * * | 0 0 1 2 0 0 | 2 0 1 . . o3x3o . ♦ 6 | 0 12 | 0 0 0 4 4 | * * * * * 1080 * | 0 0 0 2 0 1 | 1 0 2 . . o3x . *c3o ♦ 4 | 0 6 | 0 0 0 4 0 | * * * * * * 1080 | 0 0 0 0 2 1 | 0 1 2 ---------------+------+-----------+--------------------------+------------------------------------+-------------------------+--------- o3x3o3x . . ♦ 30 | 60 30 | 20 20 30 10 0 | 5 10 5 0 0 0 0 | 432 * * * * * | 1 1 0 o3x3o . . *c3o ♦ 10 | 30 0 | 10 20 0 0 0 | 5 0 0 5 0 0 0 | * 216 * * * * | 0 2 0 o3x . x3o . ♦ 9 | 9 9 | 3 0 9 0 3 | 0 3 0 0 3 0 0 | * * 720 * * * | 2 0 0 . x3o3x3o . ♦ 30 | 30 60 | 0 10 30 20 20 | 0 0 5 0 10 5 0 | * * * 432 * * | 1 0 1 . x3o3x . *c3o ♦ 32 | 48 48 | 0 32 24 32 0 | 0 0 8 8 0 0 8 | * * * * 270 * | 0 1 1 . . o3x3o *c3o ♦ 10 | 0 30 | 0 0 0 20 10 | 0 0 0 0 0 5 5 | * * * * * 216 | 0 0 2 ---------------+------+-----------+--------------------------+------------------------------------+-------------------------+--------- o3x3o3x3o . ♦ 90 | 180 180 | 60 60 180 60 60 | 15 60 30 0 60 15 0 | 6 0 20 6 0 0 | 72 * * o3x3o3x . *c3o ♦ 160 | 480 240 | 160 320 240 160 0 | 80 80 80 80 0 0 40 | 16 16 0 0 10 0 | * 27 * . x3o3x3o *c3o ♦ 160 | 240 480 | 0 160 240 320 160 | 0 0 80 40 80 80 80 | 0 0 0 16 10 16 | * * 27
or . . . . . . | 2160 | 12 | 6 12 12 | 6 12 12 4 | 12 2 3 4 | 3 4 ------------------+------+-------+----------------+---------------------+-----------------+------ . x . . . . & | 2 | 12960 | 1 2 2 | 2 3 4 1 | 6 1 1 2 | 2 3 ------------------+------+-------+----------------+---------------------+-----------------+------ o3x . . . . & | 3 | 3 | 4320 * * | 2 2 0 0 | 4 1 1 0 | 2 2 . x3o . . . & | 3 | 3 | * 8640 * | 1 0 2 1 | 3 1 0 2 | 1 3 . x . x . . | 4 | 4 | * * 6480 | 0 2 2 0 | 4 0 1 1 | 2 2 ------------------+------+-------+----------------+---------------------+-----------------+------ o3x3o . . . & ♦ 6 | 12 | 4 4 0 | 2160 * * * | 2 1 0 0 | 1 2 o3x . x . . & ♦ 6 | 9 | 2 0 3 | * 4320 * * | 2 0 1 0 | 2 1 . x3o3x . . ♦ 12 | 24 | 0 8 6 | * * 2160 * | 2 0 0 1 | 1 2 . x3o . . *c3o & ♦ 4 | 6 | 0 4 0 | * * * 2160 | 0 1 0 2 | 0 3 ------------------+------+-------+----------------+---------------------+-----------------+------ o3x3o3x . . & ♦ 30 | 90 | 20 30 30 | 5 10 5 0 | 864 * * * | 1 1 o3x3o . . *c3o & ♦ 10 | 30 | 10 20 0 | 5 0 0 5 | * 432 * * | 0 2 o3x . x3o . ♦ 9 | 18 | 6 0 9 | 0 6 0 0 | * * 720 * | 2 0 . x3o3x . *c3o ♦ 32 | 96 | 0 64 24 | 0 0 8 16 | * * * 270 | 0 2 ------------------+------+-------+----------------+---------------------+-----------------+------ o3x3o3x3o . ♦ 90 | 360 | 120 120 180 | 30 120 30 0 | 12 0 20 0 | 72 * o3x3o3x . *c3o & ♦ 160 | 720 | 160 480 240 | 80 80 80 120 | 16 16 0 10 | * 54
o3/2x3o3x3o *c3o . . . . . . | 2160 | 6 6 | 3 6 12 6 3 | 3 6 12 2 6 3 2 | 6 1 3 6 4 1 | 3 2 2 -----------------+------+-----------+--------------------------+------------------------------------+-------------------------+--------- . x . . . . | 2 | 6480 * | 1 2 2 0 0 | 2 2 4 1 1 0 0 | 4 1 1 2 2 0 | 2 2 1 . . . x . . | 2 | * 6480 | 0 0 2 2 1 | 0 1 4 0 2 2 1 | 2 0 1 4 2 1 | 2 1 2 -----------------+------+-----------+--------------------------+------------------------------------+-------------------------+--------- o3/2x . . . . | 3 | 3 0 | 2160 * * * * | 2 2 0 0 0 0 0 | 4 1 1 0 0 0 | 2 2 0 . x3o . . . | 3 | 3 0 | * 4320 * * * | 1 0 2 1 0 0 0 | 2 1 0 1 2 0 | 1 2 1 . x . x . . | 4 | 2 2 | * * 6480 * * | 0 1 2 0 1 0 0 | 2 0 1 2 1 0 | 2 1 1 . . o3x . . | 3 | 0 3 | * * * 4320 * | 0 0 2 0 0 1 1 | 1 0 0 2 2 1 | 1 1 2 . . . x3o . | 3 | 0 3 | * * * * 2160 | 0 0 0 0 2 2 0 | 0 0 1 4 0 1 | 2 0 2 -----------------+------+-----------+--------------------------+------------------------------------+-------------------------+--------- o3/2x3o . . . ♦ 6 | 12 0 | 4 4 0 0 0 | 1080 * * * * * * | 2 1 0 0 0 0 | 1 2 0 o3/2x . x . . ♦ 6 | 6 3 | 2 0 3 0 0 | * 2160 * * * * * | 2 0 1 0 0 0 | 2 1 0 . x3o3x . . ♦ 12 | 12 12 | 0 4 6 4 0 | * * 2160 * * * * | 1 0 0 1 1 0 | 1 1 1 . x3o . . *c3o ♦ 4 | 6 0 | 0 4 0 0 0 | * * * 1080 * * * | 0 1 0 0 2 0 | 0 2 1 . x . x3o . ♦ 6 | 3 6 | 0 0 3 0 2 | * * * * 2160 * * | 0 0 1 2 0 0 | 2 0 1 . . o3x3o . ♦ 6 | 0 12 | 0 0 0 4 4 | * * * * * 1080 * | 0 0 0 2 0 1 | 1 0 2 . . o3x . *c3o ♦ 4 | 0 6 | 0 0 0 4 0 | * * * * * * 1080 | 0 0 0 0 2 1 | 0 1 2 -----------------+------+-----------+--------------------------+------------------------------------+-------------------------+--------- o3/2x3o3x . . ♦ 30 | 60 30 | 20 20 30 10 0 | 5 10 5 0 0 0 0 | 432 * * * * * | 1 1 0 o3/2x3o . . *c3o ♦ 10 | 30 0 | 10 20 0 0 0 | 5 0 0 5 0 0 0 | * 216 * * * * | 0 2 0 o3/2x . x3o . ♦ 9 | 9 9 | 3 0 9 0 3 | 0 3 0 0 3 0 0 | * * 720 * * * | 2 0 0 . x3o3x3o . ♦ 30 | 30 60 | 0 10 30 20 20 | 0 0 5 0 10 5 0 | * * * 432 * * | 1 0 1 . x3o3x . *c3o ♦ 32 | 48 48 | 0 32 24 32 0 | 0 0 8 8 0 0 8 | * * * * 270 * | 0 1 1 . . o3x3o *c3o ♦ 10 | 0 30 | 0 0 0 20 10 | 0 0 0 0 0 5 5 | * * * * * 216 | 0 0 2 -----------------+------+-----------+--------------------------+------------------------------------+-------------------------+--------- o3/2x3o3x3o . ♦ 90 | 180 180 | 60 60 180 60 60 | 15 60 30 0 60 15 0 | 6 0 20 6 0 0 | 72 * * o3/2x3o3x . *c3o ♦ 160 | 480 240 | 160 320 240 160 0 | 80 80 80 80 0 0 40 | 16 16 0 0 10 0 | * 27 * . x3o3x3o *c3o ♦ 160 | 240 480 | 0 160 240 320 160 | 0 0 80 40 80 80 80 | 0 0 0 16 10 16 | * * 27
o3x3o3x3o *c3/2o . . . . . . | 2160 | 6 6 | 3 6 12 6 3 | 3 6 12 2 6 3 2 | 6 1 3 6 4 1 | 3 2 2 -----------------+------+-----------+--------------------------+------------------------------------+-------------------------+--------- . x . . . . | 2 | 6480 * | 1 2 2 0 0 | 2 2 4 1 1 0 0 | 4 1 1 2 2 0 | 2 2 1 . . . x . . | 2 | * 6480 | 0 0 2 2 1 | 0 1 4 0 2 2 1 | 2 0 1 4 2 1 | 2 1 2 -----------------+------+-----------+--------------------------+------------------------------------+-------------------------+--------- o3x . . . . | 3 | 3 0 | 2160 * * * * | 2 2 0 0 0 0 0 | 4 1 1 0 0 0 | 2 2 0 . x3o . . . | 3 | 3 0 | * 4320 * * * | 1 0 2 1 0 0 0 | 2 1 0 1 2 0 | 1 2 1 . x . x . . | 4 | 2 2 | * * 6480 * * | 0 1 2 0 1 0 0 | 2 0 1 2 1 0 | 2 1 1 . . o3x . . | 3 | 0 3 | * * * 4320 * | 0 0 2 0 0 1 1 | 1 0 0 2 2 1 | 1 1 2 . . . x3o . | 3 | 0 3 | * * * * 2160 | 0 0 0 0 2 2 0 | 0 0 1 4 0 1 | 2 0 2 -----------------+------+-----------+--------------------------+------------------------------------+-------------------------+--------- o3x3o . . . ♦ 6 | 12 0 | 4 4 0 0 0 | 1080 * * * * * * | 2 1 0 0 0 0 | 1 2 0 o3x . x . . ♦ 6 | 6 3 | 2 0 3 0 0 | * 2160 * * * * * | 2 0 1 0 0 0 | 2 1 0 . x3o3x . . ♦ 12 | 12 12 | 0 4 6 4 0 | * * 2160 * * * * | 1 0 0 1 1 0 | 1 1 1 . x3o . . *c3/2o ♦ 4 | 6 0 | 0 4 0 0 0 | * * * 1080 * * * | 0 1 0 0 2 0 | 0 2 1 . x . x3o . ♦ 6 | 3 6 | 0 0 3 0 2 | * * * * 2160 * * | 0 0 1 2 0 0 | 2 0 1 . . o3x3o . ♦ 6 | 0 12 | 0 0 0 4 4 | * * * * * 1080 * | 0 0 0 2 0 1 | 1 0 2 . . o3x . *c3/2o ♦ 4 | 0 6 | 0 0 0 4 0 | * * * * * * 1080 | 0 0 0 0 2 1 | 0 1 2 -----------------+------+-----------+--------------------------+------------------------------------+-------------------------+--------- o3x3o3x . . ♦ 30 | 60 30 | 20 20 30 10 0 | 5 10 5 0 0 0 0 | 432 * * * * * | 1 1 0 o3x3o . . *c3/2o ♦ 10 | 30 0 | 10 20 0 0 0 | 5 0 0 5 0 0 0 | * 216 * * * * | 0 2 0 o3x . x3o . ♦ 9 | 9 9 | 3 0 9 0 3 | 0 3 0 0 3 0 0 | * * 720 * * * | 2 0 0 . x3o3x3o . ♦ 30 | 30 60 | 0 10 30 20 20 | 0 0 5 0 10 5 0 | * * * 432 * * | 1 0 1 . x3o3x . *c3/2o ♦ 32 | 48 48 | 0 32 24 32 0 | 0 0 8 8 0 0 8 | * * * * 270 * | 0 1 1 . . o3x3o *c3/2o ♦ 10 | 0 30 | 0 0 0 20 10 | 0 0 0 0 0 5 5 | * * * * * 216 | 0 0 2 -----------------+------+-----------+--------------------------+------------------------------------+-------------------------+--------- o3x3o3x3o . ♦ 90 | 180 180 | 60 60 180 60 60 | 15 60 30 0 60 15 0 | 6 0 20 6 0 0 | 72 * * o3x3o3x . *c3/2o ♦ 160 | 480 240 | 160 320 240 160 0 | 80 80 80 80 0 0 40 | 16 16 0 0 10 0 | * 27 * . x3o3x3o *c3/2o ♦ 160 | 240 480 | 0 160 240 320 160 | 0 0 80 40 80 80 80 | 0 0 0 16 10 16 | * * 27
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