- general polytopal classes:
- Wythoffian polytera
links
| Acronym | rawcbinant |
| Name | retrosphenary cellibiprismatopenteractipenteractitriacontaditeron |
| Circumradius | sqrt[17+8 sqrt(2)]/2 = 2.660531 |
| Coordinates | (1+2 sqrt(2), 1+sqrt(2), 1+sqrt(2), 1, 1)/2 & all permutations, all changes of sign |
| General of army | carnit |
| Colonel of regiment | carnit |
| Face vector | 960, 3840, 4240, 1600, 172 |
| Confer |
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External links |
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As abstract polytope rawcbinant is isomorphic to wacbinant, thereby replacing octagons by octagrams, resp. socco by gocco, op by stop, and tic by quith, resp. proh by quiproh, soccope by goccope, and rawvatoth by wavitoth. As such rawcbinant is a lieutenant.
Incidence matrix according to Dynkin symbol
3 3 3
x---o---x---o
4 \ / 4/3
x
x3o3x3o4/3x4*c . . . . . | 960 | 2 4 2 | 1 4 4 2 2 4 1 | 2 2 2 4 2 1 2 2 | 1 2 1 2 1 ---------------+-----+--------------+-----------------------------+-------------------------------+--------------- x . . . . | 2 | 960 * * | 1 2 2 0 0 0 0 | 2 2 1 2 1 0 0 0 | 1 2 1 1 0 . . x . . | 2 | * 1920 * | 0 1 0 1 1 1 0 | 1 0 1 1 0 1 1 1 | 1 1 0 1 1 . . . . x | 2 | * * 960 | 0 0 2 0 0 2 1 | 0 1 0 2 2 0 1 2 | 0 1 1 2 1 ---------------+-----+--------------+-----------------------------+-------------------------------+--------------- x3o . . . | 3 | 3 0 0 | 320 * * * * * * | 2 2 0 0 0 0 0 0 | 1 2 1 0 0 x . x . . | 4 | 2 2 0 | * 960 * * * * * | 1 0 1 1 0 0 0 0 | 1 1 0 1 0 x . . . x | 4 | 2 0 2 | * * 960 * * * * | 0 1 0 1 1 0 0 0 | 0 1 1 1 0 . o3x . . | 3 | 0 3 0 | * * * 640 * * * | 1 0 0 0 0 1 1 0 | 1 1 0 0 1 . . x3o . | 3 | 0 3 0 | * * * * 640 * * | 0 0 1 0 0 1 0 1 | 1 0 0 1 1 . . x . x4*c | 8 | 0 4 4 | * * * * * 480 * | 0 0 0 1 0 0 1 1 | 0 1 0 1 1 . . . o4/3x | 4 | 0 0 4 | * * * * * * 240 | 0 0 0 0 2 0 0 2 | 0 0 1 2 1 ---------------+-----+--------------+-----------------------------+-------------------------------+--------------- x3o3x . . ♦ 12 | 12 12 0 | 4 6 0 4 0 0 0 | 160 * * * * * * * | 1 1 0 0 0 x3o . . x ♦ 6 | 6 0 3 | 2 0 3 0 0 0 0 | * 320 * * * * * * | 0 1 1 0 0 x . x3o . ♦ 6 | 3 6 0 | 0 3 0 0 2 0 0 | * * 320 * * * * * | 1 0 0 1 0 x . x . x4*c ♦ 16 | 8 8 8 | 0 4 4 0 0 2 0 | * * * 240 * * * * | 0 1 0 1 0 x . . o4/3x ♦ 8 | 4 0 8 | 0 0 4 0 0 0 2 | * * * * 240 * * * | 0 0 1 1 0 . o3x3o . ♦ 6 | 0 12 0 | 0 0 0 4 4 0 0 | * * * * * 160 * * | 1 0 0 0 1 . o3x . x4*c ♦ 24 | 0 24 12 | 0 0 0 8 0 6 0 | * * * * * * 80 * | 0 1 0 0 1 . . x3o4/3x4*c ♦ 24 | 0 24 24 | 0 0 0 0 8 6 6 | * * * * * * * 80 | 0 0 0 1 1 ---------------+-----+--------------+-----------------------------+-------------------------------+--------------- x3o3x3o . ♦ 30 | 30 60 0 | 10 30 0 20 20 0 0 | 5 0 10 0 0 5 0 0 | 32 * * * * x3o3x . x4*c ♦ 192 | 192 192 96 | 64 96 96 64 0 48 0 | 16 32 0 24 0 0 8 0 | * 10 * * * x3o . o4/3x ♦ 12 | 12 0 12 | 4 0 12 0 0 0 3 | 0 4 0 0 3 0 0 0 | * * 80 * * x . x3o4/3x4*c ♦ 48 | 24 48 48 | 0 24 24 0 16 12 12 | 0 0 8 6 6 0 0 2 | * * * 40 * . o3x3o4/3x4*c ♦ 96 | 0 192 96 | 0 0 0 64 64 48 24 | 0 0 0 0 0 16 8 8 | * * * * 10
3 3 3/2
x---o---x---o
4 \ / 4
x
x3o3x3/2o4x4*c . . . . . | 960 | 2 4 2 | 1 4 4 2 2 4 1 | 2 2 2 4 2 1 2 2 | 1 2 1 2 1 ---------------+-----+--------------+-----------------------------+-------------------------------+--------------- x . . . . | 2 | 960 * * | 1 2 2 0 0 0 0 | 2 2 1 2 1 0 0 0 | 1 2 1 1 0 . . x . . | 2 | * 1920 * | 0 1 0 1 1 1 0 | 1 0 1 1 0 1 1 1 | 1 1 0 1 1 . . . . x | 2 | * * 960 | 0 0 2 0 0 2 1 | 0 1 0 2 2 0 1 2 | 0 1 1 2 1 ---------------+-----+--------------+-----------------------------+-------------------------------+--------------- x3o . . . | 3 | 3 0 0 | 320 * * * * * * | 2 2 0 0 0 0 0 0 | 1 2 1 0 0 x . x . . | 4 | 2 2 0 | * 960 * * * * * | 1 0 1 1 0 0 0 0 | 1 1 0 1 0 x . . . x | 4 | 2 0 2 | * * 960 * * * * | 0 1 0 1 1 0 0 0 | 0 1 1 1 0 . o3x . . | 3 | 0 3 0 | * * * 640 * * * | 1 0 0 0 0 1 1 0 | 1 1 0 0 1 . . x3/2o . | 3 | 0 3 0 | * * * * 640 * * | 0 0 1 0 0 1 0 1 | 1 0 0 1 1 . . x . x4*c | 8 | 0 4 4 | * * * * * 480 * | 0 0 0 1 0 0 1 1 | 0 1 0 1 1 . . . o4x | 4 | 0 0 4 | * * * * * * 240 | 0 0 0 0 2 0 0 2 | 0 0 1 2 1 ---------------+-----+--------------+-----------------------------+-------------------------------+--------------- x3o3x . . ♦ 12 | 12 12 0 | 4 6 0 4 0 0 0 | 160 * * * * * * * | 1 1 0 0 0 x3o . . x ♦ 6 | 6 0 3 | 2 0 3 0 0 0 0 | * 320 * * * * * * | 0 1 1 0 0 x . x3/2o . ♦ 6 | 3 6 0 | 0 3 0 0 2 0 0 | * * 320 * * * * * | 1 0 0 1 0 x . x . x4*c ♦ 16 | 8 8 8 | 0 4 4 0 0 2 0 | * * * 240 * * * * | 0 1 0 1 0 x . . o4x ♦ 8 | 4 0 8 | 0 0 4 0 0 0 2 | * * * * 240 * * * | 0 0 1 1 0 . o3x3/2o . ♦ 6 | 0 12 0 | 0 0 0 4 4 0 0 | * * * * * 160 * * | 1 0 0 0 1 . o3x . x4*c ♦ 24 | 0 24 12 | 0 0 0 8 0 6 0 | * * * * * * 80 * | 0 1 0 0 1 . . x3/2o4x4*c ♦ 24 | 0 24 24 | 0 0 0 0 8 6 6 | * * * * * * * 80 | 0 0 0 1 1 ---------------+-----+--------------+-----------------------------+-------------------------------+--------------- x3o3x3/2o . ♦ 30 | 30 60 0 | 10 30 0 20 20 0 0 | 5 0 10 0 0 5 0 0 | 32 * * * * x3o3x . x4*c ♦ 192 | 192 192 96 | 64 96 96 64 0 48 0 | 16 32 0 24 0 0 8 0 | * 10 * * * x3o . o4x ♦ 12 | 12 0 12 | 4 0 12 0 0 0 3 | 0 4 0 0 3 0 0 0 | * * 80 * * x . x3/2o4x4*c ♦ 48 | 24 48 48 | 0 24 24 0 16 12 12 | 0 0 8 6 6 0 0 2 | * * * 40 * . o3x3/2o4x4*c ♦ 96 | 0 192 96 | 0 0 0 64 64 48 24 | 0 0 0 0 0 16 8 8 | * * * * 10
3/2 3/2 3
x---o---x---o
4 \ / 4/3
x
x3o3/2x3o4/3x4*c . . . . . | 960 | 2 4 2 | 1 4 4 2 2 4 1 | 2 2 2 4 2 1 2 2 | 1 2 1 2 1 -------------------+-----+--------------+-----------------------------+-------------------------------+--------------- x . . . . | 2 | 960 * * | 1 2 2 0 0 0 0 | 2 2 1 2 1 0 0 0 | 1 2 1 1 0 . . x . . | 2 | * 1920 * | 0 1 0 1 1 1 0 | 1 0 1 1 0 1 1 1 | 1 1 0 1 1 . . . . x | 2 | * * 960 | 0 0 2 0 0 2 1 | 0 1 0 2 2 0 1 2 | 0 1 1 2 1 -------------------+-----+--------------+-----------------------------+-------------------------------+--------------- x3/2o . . . | 3 | 3 0 0 | 320 * * * * * * | 2 2 0 0 0 0 0 0 | 1 2 1 0 0 x . x . . | 4 | 2 2 0 | * 960 * * * * * | 1 0 1 1 0 0 0 0 | 1 1 0 1 0 x . . . x | 4 | 2 0 2 | * * 960 * * * * | 0 1 0 1 1 0 0 0 | 0 1 1 1 0 . o3/2x . . | 3 | 0 3 0 | * * * 640 * * * | 1 0 0 0 0 1 1 0 | 1 1 0 0 1 . . x3o . | 3 | 0 3 0 | * * * * 640 * * | 0 0 1 0 0 1 0 1 | 1 0 0 1 1 . . x . x4*c | 8 | 0 4 4 | * * * * * 480 * | 0 0 0 1 0 0 1 1 | 0 1 0 1 1 . . . o4/3x | 4 | 0 0 4 | * * * * * * 240 | 0 0 0 0 2 0 0 2 | 0 0 1 2 1 -------------------+-----+--------------+-----------------------------+-------------------------------+--------------- x3/2o3/2x . . ♦ 12 | 12 12 0 | 4 6 0 4 0 0 0 | 160 * * * * * * * | 1 1 0 0 0 x3/2o . . x ♦ 6 | 6 0 3 | 2 0 3 0 0 0 0 | * 320 * * * * * * | 0 1 1 0 0 x . x3o . ♦ 6 | 3 6 0 | 0 3 0 0 2 0 0 | * * 320 * * * * * | 1 0 0 1 0 x . x . x4*c ♦ 16 | 8 8 8 | 0 4 4 0 0 2 0 | * * * 240 * * * * | 0 1 0 1 0 x . . o4/3x ♦ 8 | 4 0 8 | 0 0 4 0 0 0 2 | * * * * 240 * * * | 0 0 1 1 0 . o3/2x3o . ♦ 6 | 0 12 0 | 0 0 0 4 4 0 0 | * * * * * 160 * * | 1 0 0 0 1 . o3/2x . x4*c ♦ 24 | 0 24 12 | 0 0 0 8 0 6 0 | * * * * * * 80 * | 0 1 0 0 1 . . x3o4/3x4*c ♦ 24 | 0 24 24 | 0 0 0 0 8 6 6 | * * * * * * * 80 | 0 0 0 1 1 -------------------+-----+--------------+-----------------------------+-------------------------------+--------------- x3/2o3/2x3o . ♦ 30 | 30 60 0 | 10 30 0 20 20 0 0 | 5 0 10 0 0 5 0 0 | 32 * * * * x3/2o3/2x . x4*c ♦ 192 | 192 192 96 | 64 96 96 64 0 48 0 | 16 32 0 24 0 0 8 0 | * 10 * * * x3/2o . o4/3x ♦ 12 | 12 0 12 | 4 0 12 0 0 0 3 | 0 4 0 0 3 0 0 0 | * * 80 * * x . x3o4/3x4*c ♦ 48 | 24 48 48 | 0 24 24 0 16 12 12 | 0 0 8 6 6 0 0 2 | * * * 40 * . o3/2x3o4/3x4*c ♦ 96 | 0 192 96 | 0 0 0 64 64 48 24 | 0 0 0 0 0 16 8 8 | * * * * 10
3/2 3/2 3/2
x---o---x---o
4 \ / 4
x
x3/2o3/2x3/2o4x4*c . . . . . | 960 | 2 4 2 | 1 4 4 2 2 4 1 | 2 2 2 4 2 1 2 2 | 1 2 1 2 1 -------------------+-----+--------------+-----------------------------+-------------------------------+--------------- x . . . . | 2 | 960 * * | 1 2 2 0 0 0 0 | 2 2 1 2 1 0 0 0 | 1 2 1 1 0 . . x . . | 2 | * 1920 * | 0 1 0 1 1 1 0 | 1 0 1 1 0 1 1 1 | 1 1 0 1 1 . . . . x | 2 | * * 960 | 0 0 2 0 0 2 1 | 0 1 0 2 2 0 1 2 | 0 1 1 2 1 -------------------+-----+--------------+-----------------------------+-------------------------------+--------------- x3/2o . . . | 3 | 3 0 0 | 320 * * * * * * | 2 2 0 0 0 0 0 0 | 1 2 1 0 0 x . x . . | 4 | 2 2 0 | * 960 * * * * * | 1 0 1 1 0 0 0 0 | 1 1 0 1 0 x . . . x | 4 | 2 0 2 | * * 960 * * * * | 0 1 0 1 1 0 0 0 | 0 1 1 1 0 . o3/2x . . | 3 | 0 3 0 | * * * 640 * * * | 1 0 0 0 0 1 1 0 | 1 1 0 0 1 . . x3/2o . | 3 | 0 3 0 | * * * * 640 * * | 0 0 1 0 0 1 0 1 | 1 0 0 1 1 . . x . x4*c | 8 | 0 4 4 | * * * * * 480 * | 0 0 0 1 0 0 1 1 | 0 1 0 1 1 . . . o4x | 4 | 0 0 4 | * * * * * * 240 | 0 0 0 0 2 0 0 2 | 0 0 1 2 1 -------------------+-----+--------------+-----------------------------+-------------------------------+--------------- x3/2o3/2x . . ♦ 12 | 12 12 0 | 4 6 0 4 0 0 0 | 160 * * * * * * * | 1 1 0 0 0 x3/2o . . x ♦ 6 | 6 0 3 | 2 0 3 0 0 0 0 | * 320 * * * * * * | 0 1 1 0 0 x . x3/2o . ♦ 6 | 3 6 0 | 0 3 0 0 2 0 0 | * * 320 * * * * * | 1 0 0 1 0 x . x . x4*c ♦ 16 | 8 8 8 | 0 4 4 0 0 2 0 | * * * 240 * * * * | 0 1 0 1 0 x . . o4x ♦ 8 | 4 0 8 | 0 0 4 0 0 0 2 | * * * * 240 * * * | 0 0 1 1 0 . o3/2x3/2o . ♦ 6 | 0 12 0 | 0 0 0 4 4 0 0 | * * * * * 160 * * | 1 0 0 0 1 . o3/2x . x4*c ♦ 24 | 0 24 12 | 0 0 0 8 0 6 0 | * * * * * * 80 * | 0 1 0 0 1 . . x3/2o4x4*c ♦ 24 | 0 24 24 | 0 0 0 0 8 6 6 | * * * * * * * 80 | 0 0 0 1 1 -------------------+-----+--------------+-----------------------------+-------------------------------+--------------- x3/2o3/2x3/2o . ♦ 30 | 30 60 0 | 10 30 0 20 20 0 0 | 5 0 10 0 0 5 0 0 | 32 * * * * x3/2o3/2x . x4*c ♦ 192 | 192 192 96 | 64 96 96 64 0 48 0 | 16 32 0 24 0 0 8 0 | * 10 * * * x3/2o . o4x ♦ 12 | 12 0 12 | 4 0 12 0 0 0 3 | 0 4 0 0 3 0 0 0 | * * 80 * * x . x3/2o4x4*c ♦ 48 | 24 48 48 | 0 24 24 0 16 12 12 | 0 0 8 6 6 0 0 2 | * * * 40 * . o3/2x3/2o4x4*c ♦ 96 | 0 192 96 | 0 0 0 64 64 48 24 | 0 0 0 0 0 16 8 8 | * * * * 10
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