- general polytopal classes:
- Wythoffian polytera
links
| Acronym | setitdin |
| Name | small tesseractitriacontidiadispenteract |
| Circumradius | sqrt[15+6 sqrt(2)]/2 = 2.423081 |
| Coordinates | (1+2 sqrt(2), 1+sqrt(2), 1, 1, 1)/2 & all permutations, all changes of sign |
| Colonel of regiment | cappin |
| Face vector | 640, 2240, 2160, 760, 92 |
| Confer |
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External links |
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As abstract polytope setitdin is isomorphic to getitdin, thereby replacing octagons by octagrams, resp. girco by quitco and socco by gocco, resp. steth by gittith and sichado by gichado. – As such setitdin is a lieutenant.
Incidence matrix according to Dynkin symbol
3 3 3
x---x---o---o
4 \ / 4/3
x
x3x3o3o *b4x4/3*c . . . . . | 640 | 1 3 3 | 3 3 3 3 3 | 3 3 3 1 3 1 | 1 3 1 1 ------------------+-----+-------------+---------------------+----------------------+------------ x . . . . | 2 | 320 * * | 3 3 0 0 0 | 3 3 3 0 0 0 | 1 3 1 0 . x . . . | 2 | * 960 * | 1 0 2 1 0 | 2 1 0 1 2 0 | 1 2 0 1 . . . . x | 2 | * * 960 | 0 1 0 1 2 | 0 1 2 0 2 1 | 0 2 1 1 ------------------+-----+-------------+---------------------+----------------------+------------ x3x . . . | 6 | 3 3 0 | 320 * * * * | 2 1 0 0 0 0 | 1 2 0 0 x . . . x | 4 | 2 0 2 | * 480 * * * | 0 1 2 0 0 0 | 0 2 1 0 . x3o . . | 3 | 0 3 0 | * * 640 * * | 1 0 0 1 1 0 | 1 1 0 1 . x . . *b4x | 8 | 0 4 4 | * * * 240 * | 0 1 0 0 2 0 | 0 2 0 1 . . o . x4/3*c | 4 | 0 0 4 | * * * * 480 | 0 0 1 0 1 1 | 0 1 1 1 ------------------+-----+-------------+---------------------+----------------------+------------ x3x3o . . ♦ 12 | 6 12 0 | 4 0 4 0 0 | 160 * * * * * | 1 1 0 0 x3x . . *b4x ♦ 48 | 24 24 24 | 8 12 0 6 0 | * 40 * * * * | 0 2 0 0 x . o . x4/3*c ♦ 8 | 4 0 8 | 0 4 0 0 2 | * * 240 * * * | 0 1 1 0 . x3o3o . ♦ 4 | 0 6 0 | 0 0 4 0 0 | * * * 160 * * | 1 0 0 1 . x3o . *b4x4/3*c ♦ 24 | 0 24 24 | 0 0 8 6 6 | * * * * 80 * | 0 1 0 1 . . o3o x4/3*c ♦ 8 | 0 0 12 | 0 0 0 0 6 | * * * * * 80 | 0 0 1 1 ------------------+-----+-------------+---------------------+----------------------+------------ x3x3o3o . ♦ 20 | 10 30 0 | 10 0 20 0 0 | 5 0 0 5 0 0 | 32 * * * x3x3o . *b4x4/3*c ♦ 192 | 96 192 192 | 64 96 64 48 48 | 16 8 24 0 8 0 | * 10 * * x . o3o x4/3*c ♦ 16 | 8 0 24 | 0 12 0 0 12 | 0 0 6 0 0 2 | * * 40 * . x3o3o *b4x4/3*c ♦ 64 | 0 96 96 | 0 0 64 24 48 | 0 0 0 16 8 8 | * * * 10
3 3 3/2
x---x---o---o
4 \ / 4/3
x
x3x3o3/2o *b4x4/3*c . . . . . | 640 | 1 3 3 | 3 3 3 3 3 | 3 3 3 1 3 1 | 1 3 1 1 --------------------+-----+-------------+---------------------+----------------------+------------ x . . . . | 2 | 320 * * | 3 3 0 0 0 | 3 3 3 0 0 0 | 1 3 1 0 . x . . . | 2 | * 960 * | 1 0 2 1 0 | 2 1 0 1 2 0 | 1 2 0 1 . . . . x | 2 | * * 960 | 0 1 0 1 2 | 0 1 2 0 2 1 | 0 2 1 1 --------------------+-----+-------------+---------------------+----------------------+------------ x3x . . . | 6 | 3 3 0 | 320 * * * * | 2 1 0 0 0 0 | 1 2 0 0 x . . . x | 4 | 2 0 2 | * 480 * * * | 0 1 2 0 0 0 | 0 2 1 0 . x3o . . | 3 | 0 3 0 | * * 640 * * | 1 0 0 1 1 0 | 1 1 0 1 . x . . *b4x | 8 | 0 4 4 | * * * 240 * | 0 1 0 0 2 0 | 0 2 0 1 . . o . x4/3*c | 4 | 0 0 4 | * * * * 480 | 0 0 1 0 1 1 | 0 1 1 1 --------------------+-----+-------------+---------------------+----------------------+------------ x3x3o . . ♦ 12 | 6 12 0 | 4 0 4 0 0 | 160 * * * * * | 1 1 0 0 x3x . . *b4x ♦ 48 | 24 24 24 | 8 12 0 6 0 | * 40 * * * * | 0 2 0 0 x . o . x4/3*c ♦ 8 | 4 0 8 | 0 4 0 0 2 | * * 240 * * * | 0 1 1 0 . x3o3/2o . ♦ 4 | 0 6 0 | 0 0 4 0 0 | * * * 160 * * | 1 0 0 1 . x3o . *b4x4/3*c ♦ 24 | 0 24 24 | 0 0 8 6 6 | * * * * 80 * | 0 1 0 1 . . o3/2o x4/3*c ♦ 8 | 0 0 12 | 0 0 0 0 6 | * * * * * 80 | 0 0 1 1 --------------------+-----+-------------+---------------------+----------------------+------------ x3x3o3/2o . ♦ 20 | 10 30 0 | 10 0 20 0 0 | 5 0 0 5 0 0 | 32 * * * x3x3o . *b4x4/3*c ♦ 192 | 96 192 192 | 64 96 64 48 48 | 16 8 24 0 8 0 | * 10 * * x . o3/2o x4/3*c ♦ 16 | 8 0 24 | 0 12 0 0 12 | 0 0 6 0 0 2 | * * 40 * . x3o3/2o *b4x4/3*c ♦ 64 | 0 96 96 | 0 0 64 24 48 | 0 0 0 16 8 8 | * * * 10
3 3/2 3
x---x---o---o
4 \ / 4
x
x3x3/2o3o *b4x4*c . . . . . | 640 | 1 3 3 | 3 3 3 3 3 | 3 3 3 1 3 1 | 1 3 1 1 ------------------+-----+-------------+---------------------+----------------------+------------ x . . . . | 2 | 320 * * | 3 3 0 0 0 | 3 3 3 0 0 0 | 1 3 1 0 . x . . . | 2 | * 960 * | 1 0 2 1 0 | 2 1 0 1 2 0 | 1 2 0 1 . . . . x | 2 | * * 960 | 0 1 0 1 2 | 0 1 2 0 2 1 | 0 2 1 1 ------------------+-----+-------------+---------------------+----------------------+------------ x3x . . . | 6 | 3 3 0 | 320 * * * * | 2 1 0 0 0 0 | 1 2 0 0 x . . . x | 4 | 2 0 2 | * 480 * * * | 0 1 2 0 0 0 | 0 2 1 0 . x3/2o . . | 3 | 0 3 0 | * * 640 * * | 1 0 0 1 1 0 | 1 1 0 1 . x . . *b4x | 8 | 0 4 4 | * * * 240 * | 0 1 0 0 2 0 | 0 2 0 1 . . o . x4*c | 4 | 0 0 4 | * * * * 480 | 0 0 1 0 1 1 | 0 1 1 1 ------------------+-----+-------------+---------------------+----------------------+------------ x3x3/2o . . ♦ 12 | 6 12 0 | 4 0 4 0 0 | 160 * * * * * | 1 1 0 0 x3x . . *b4x ♦ 48 | 24 24 24 | 8 12 0 6 0 | * 40 * * * * | 0 2 0 0 x . o . x4*c ♦ 8 | 4 0 8 | 0 4 0 0 2 | * * 240 * * * | 0 1 1 0 . x3/2o3o . ♦ 4 | 0 6 0 | 0 0 4 0 0 | * * * 160 * * | 1 0 0 1 . x3/2o . *b4x4*c ♦ 24 | 0 24 24 | 0 0 8 6 6 | * * * * 80 * | 0 1 0 1 . . o3o x4*c ♦ 8 | 0 0 12 | 0 0 0 0 6 | * * * * * 80 | 0 0 1 1 ------------------+-----+-------------+---------------------+----------------------+------------ x3x3/2o3o . ♦ 20 | 10 30 0 | 10 0 20 0 0 | 5 0 0 5 0 0 | 32 * * * x3x3/2o . *b4x4*c ♦ 192 | 96 192 192 | 64 96 64 48 48 | 16 8 24 0 8 0 | * 10 * * x . o3o x4*c ♦ 16 | 8 0 24 | 0 12 0 0 12 | 0 0 6 0 0 2 | * * 40 * . x3/2o3o *b4x4*c ♦ 64 | 0 96 96 | 0 0 64 24 48 | 0 0 0 16 8 8 | * * * 10
3 3/2 3/2
x---x---o---o
4 \ / 4
x
x3x3/2o3/2o *b4x4*c . . . . . | 640 | 1 3 3 | 3 3 3 3 3 | 3 3 3 1 3 1 | 1 3 1 1 --------------------+-----+-------------+---------------------+----------------------+------------ x . . . . | 2 | 320 * * | 3 3 0 0 0 | 3 3 3 0 0 0 | 1 3 1 0 . x . . . | 2 | * 960 * | 1 0 2 1 0 | 2 1 0 1 2 0 | 1 2 0 1 . . . . x | 2 | * * 960 | 0 1 0 1 2 | 0 1 2 0 2 1 | 0 2 1 1 --------------------+-----+-------------+---------------------+----------------------+------------ x3x . . . | 6 | 3 3 0 | 320 * * * * | 2 1 0 0 0 0 | 1 2 0 0 x . . . x | 4 | 2 0 2 | * 480 * * * | 0 1 2 0 0 0 | 0 2 1 0 . x3/2o . . | 3 | 0 3 0 | * * 640 * * | 1 0 0 1 1 0 | 1 1 0 1 . x . . *b4x | 8 | 0 4 4 | * * * 240 * | 0 1 0 0 2 0 | 0 2 0 1 . . o . x4*c | 4 | 0 0 4 | * * * * 480 | 0 0 1 0 1 1 | 0 1 1 1 --------------------+-----+-------------+---------------------+----------------------+------------ x3x3/2o . . ♦ 12 | 6 12 0 | 4 0 4 0 0 | 160 * * * * * | 1 1 0 0 x3x . . *b4x ♦ 48 | 24 24 24 | 8 12 0 6 0 | * 40 * * * * | 0 2 0 0 x . o . x4*c ♦ 8 | 4 0 8 | 0 4 0 0 2 | * * 240 * * * | 0 1 1 0 . x3/2o3/2o . ♦ 4 | 0 6 0 | 0 0 4 0 0 | * * * 160 * * | 1 0 0 1 . x3/2o . *b4x4*c ♦ 24 | 0 24 24 | 0 0 8 6 6 | * * * * 80 * | 0 1 0 1 . . o3/2o x4*c ♦ 8 | 0 0 12 | 0 0 0 0 6 | * * * * * 80 | 0 0 1 1 --------------------+-----+-------------+---------------------+----------------------+------------ x3x3/2o3/2o . ♦ 20 | 10 30 0 | 10 0 20 0 0 | 5 0 0 5 0 0 | 32 * * * x3x3/2o . *b4x4*c ♦ 192 | 96 192 192 | 64 96 64 48 48 | 16 8 24 0 8 0 | * 10 * * x . o3/2o x4*c ♦ 16 | 8 0 24 | 0 12 0 0 12 | 0 0 6 0 0 2 | * * 40 * . x3/2o3/2o *b4x4*c ♦ 64 | 0 96 96 | 0 0 64 24 48 | 0 0 0 16 8 8 | * * * 10
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