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- general polytopal classes:
- Wythoffian polytera
links
| Acronym | gircaptint (old: grecaptint) |
| Name | great retrocelliprismatotruncated penteractitriacontaditeron |
| Field of sections |
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| Circumradius | sqrt[35-14 sqrt(2)]/2 = 1.949424 |
| Vertex figure |
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| Coordinates | (3 sqrt(2)-1, 2 sqrt(2)-1, sqrt(2)-1, sqrt(2)-1, 1)/2 & all permutations, all changes of sign |
| Colonel of regiment | quicpatint |
| Face vector | 1920, 5760, 5440, 1840, 172 |
| Confer |
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External links |
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As abstract polytope gircaptint is isomorphic to sircaptint, thereby replacing octagrams by octagons, resp. stop by op, quitco by girco, and quith by tic, resp. gaquidpoth by gidpith, quithip by ticcup, and giphado by siphado.
Incidence matrix according to Dynkin symbol
4/3 3 3
x---x---x---x
3 \ / 3/2
o
x4/3x3x3x *b3o3/2*c . . . . . | 1920 | 1 2 2 1 | 2 2 1 2 2 1 2 1 | 2 2 1 2 1 2 1 1 1 | 2 1 1 1 1 --------------------+------+-------------------+---------------------------------+-----------------------------------+--------------- x . . . . | 2 | 960 * * * | 2 2 1 0 0 0 0 0 | 2 2 1 2 1 0 0 0 0 | 2 1 1 1 0 . x . . . | 2 | * 1920 * * | 1 0 0 1 1 1 0 0 | 1 1 1 0 0 1 1 1 0 | 1 1 1 0 1 . . x . . | 2 | * * 1920 * | 0 1 0 1 0 0 1 1 | 1 0 0 1 1 1 1 0 1 | 1 1 0 1 1 . . . x . | 2 | * * * 960 | 0 0 1 0 2 0 2 0 | 0 2 0 2 0 2 0 1 1 | 2 0 1 1 1 --------------------+------+-------------------+---------------------------------+-----------------------------------+--------------- x4/3x . . . | 8 | 4 4 0 0 | 480 * * * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 x . x . . | 4 | 2 0 2 0 | * 960 * * * * * * | 1 0 0 1 1 0 0 0 0 | 1 1 0 1 0 x . . x . | 4 | 2 0 0 2 | * * 480 * * * * * | 0 2 0 2 0 0 0 0 0 | 2 0 1 1 0 . x3x . . | 6 | 0 3 3 0 | * * * 640 * * * * | 1 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . x . x . | 4 | 0 2 0 2 | * * * * 960 * * * | 0 1 0 0 0 1 0 1 0 | 1 0 1 0 1 . x . . *b3o | 3 | 0 3 0 0 | * * * * * 640 * * | 0 0 1 0 0 0 1 1 0 | 0 1 1 0 1 . . x3x . | 6 | 0 0 3 3 | * * * * * * 640 * | 0 0 0 1 0 1 0 0 1 | 1 0 0 1 1 . . x . o3/2*c | 3 | 0 0 3 0 | * * * * * * * 640 | 0 0 0 0 1 0 1 0 1 | 0 1 0 1 1 --------------------+------+-------------------+---------------------------------+-----------------------------------+--------------- x4/3x3x . . ♦ 48 | 24 24 24 0 | 6 12 0 8 0 0 0 0 | 80 * * * * * * * * | 1 1 0 0 0 x4/3x . x . ♦ 16 | 8 8 0 8 | 2 0 4 0 4 0 0 0 | * 240 * * * * * * * | 1 0 1 0 0 x4/3x . . *b3o ♦ 24 | 12 24 0 0 | 6 0 0 0 0 8 0 0 | * * 80 * * * * * * | 0 1 1 0 0 x . x3x . ♦ 12 | 6 0 6 6 | 0 3 3 0 0 0 2 0 | * * * 320 * * * * * | 1 0 0 1 0 x . x . o3/2*c ♦ 6 | 3 0 6 0 | 0 3 0 0 0 0 0 2 | * * * * 320 * * * * | 0 1 0 1 0 . x3x3x . ♦ 24 | 0 12 12 12 | 0 0 0 4 6 0 4 0 | * * * * * 160 * * * | 1 0 0 0 1 . x3x . *b3o3/2*c ♦ 12 | 0 12 12 0 | 0 0 0 4 0 4 0 4 | * * * * * * 160 * * | 0 1 0 0 1 . x . x *b3o ♦ 6 | 0 6 0 3 | 0 0 0 0 3 2 0 0 | * * * * * * * 320 * | 0 0 1 0 1 . . x3x o3/2*c ♦ 12 | 0 0 12 6 | 0 0 0 0 0 0 4 4 | * * * * * * * * 160 | 0 0 0 1 1 --------------------+------+-------------------+---------------------------------+-----------------------------------+--------------- x4/3x3x3x . ♦ 384 | 192 192 192 192 | 48 96 96 64 96 0 64 0 | 8 24 0 32 0 16 0 0 0 | 10 * * * * x4/3x3x . *b3o3/2*c ♦ 192 | 96 192 192 0 | 48 96 0 64 0 64 0 64 | 8 0 8 0 32 0 16 0 0 | * 10 * * * x4/3x . x *b3o ♦ 48 | 24 48 0 24 | 12 0 12 0 24 16 0 0 | 0 6 2 0 0 0 0 8 0 | * * 40 * * x . x3x o3/2*c ♦ 24 | 12 0 24 12 | 0 12 6 0 0 0 8 8 | 0 0 0 4 4 0 0 0 2 | * * * 80 * . x3x3x *b3o3/2*c ♦ 60 | 0 60 60 30 | 0 0 0 20 30 20 20 20 | 0 0 0 0 0 5 5 10 5 | * * * * 32
4/3 3 3
x---x---x---x
3/2 \ / 3
o
x4/3x3x3x *b3/2o3*c . . . . . | 1920 | 1 2 2 1 | 2 2 1 2 2 1 2 1 | 2 2 1 2 1 2 1 1 1 | 2 1 1 1 1 --------------------+------+-------------------+---------------------------------+-----------------------------------+--------------- x . . . . | 2 | 960 * * * | 2 2 1 0 0 0 0 0 | 2 2 1 2 1 0 0 0 0 | 2 1 1 1 0 . x . . . | 2 | * 1920 * * | 1 0 0 1 1 1 0 0 | 1 1 1 0 0 1 1 1 0 | 1 1 1 0 1 . . x . . | 2 | * * 1920 * | 0 1 0 1 0 0 1 1 | 1 0 0 1 1 1 1 0 1 | 1 1 0 1 1 . . . x . | 2 | * * * 960 | 0 0 1 0 2 0 2 0 | 0 2 0 2 0 2 0 1 1 | 2 0 1 1 1 --------------------+------+-------------------+---------------------------------+-----------------------------------+--------------- x4/3x . . . | 8 | 4 4 0 0 | 480 * * * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 x . x . . | 4 | 2 0 2 0 | * 960 * * * * * * | 1 0 0 1 1 0 0 0 0 | 1 1 0 1 0 x . . x . | 4 | 2 0 0 2 | * * 480 * * * * * | 0 2 0 2 0 0 0 0 0 | 2 0 1 1 0 . x3x . . | 6 | 0 3 3 0 | * * * 640 * * * * | 1 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . x . x . | 4 | 0 2 0 2 | * * * * 960 * * * | 0 1 0 0 0 1 0 1 0 | 1 0 1 0 1 . x . . *b3/2o | 3 | 0 3 0 0 | * * * * * 640 * * | 0 0 1 0 0 0 1 1 0 | 0 1 1 0 1 . . x3x . | 6 | 0 0 3 3 | * * * * * * 640 * | 0 0 0 1 0 1 0 0 1 | 1 0 0 1 1 . . x . o3*c | 3 | 0 0 3 0 | * * * * * * * 640 | 0 0 0 0 1 0 1 0 1 | 0 1 0 1 1 --------------------+------+-------------------+---------------------------------+-----------------------------------+--------------- x4/3x3x . . ♦ 48 | 24 24 24 0 | 6 12 0 8 0 0 0 0 | 80 * * * * * * * * | 1 1 0 0 0 x4/3x . x . ♦ 16 | 8 8 0 8 | 2 0 4 0 4 0 0 0 | * 240 * * * * * * * | 1 0 1 0 0 x4/3x . . *b3/2o ♦ 24 | 12 24 0 0 | 6 0 0 0 0 8 0 0 | * * 80 * * * * * * | 0 1 1 0 0 x . x3x . ♦ 12 | 6 0 6 6 | 0 3 3 0 0 0 2 0 | * * * 320 * * * * * | 1 0 0 1 0 x . x . o3*c ♦ 6 | 3 0 6 0 | 0 3 0 0 0 0 0 2 | * * * * 320 * * * * | 0 1 0 1 0 . x3x3x . ♦ 24 | 0 12 12 12 | 0 0 0 4 6 0 4 0 | * * * * * 160 * * * | 1 0 0 0 1 . x3x . *b3/2o3*c ♦ 12 | 0 12 12 0 | 0 0 0 4 0 4 0 4 | * * * * * * 160 * * | 0 1 0 0 1 . x . x *b3/2o ♦ 6 | 0 6 0 3 | 0 0 0 0 3 2 0 0 | * * * * * * * 320 * | 0 0 1 0 1 . . x3x o3*c ♦ 12 | 0 0 12 6 | 0 0 0 0 0 0 4 4 | * * * * * * * * 160 | 0 0 0 1 1 --------------------+------+-------------------+---------------------------------+-----------------------------------+--------------- x4/3x3x3x . ♦ 384 | 192 192 192 192 | 48 96 96 64 96 0 64 0 | 8 24 0 32 0 16 0 0 0 | 10 * * * * x4/3x3x . *b3/2o3*c ♦ 192 | 96 192 192 0 | 48 96 0 64 0 64 0 64 | 8 0 8 0 32 0 16 0 0 | * 10 * * * x4/3x . x *b3/2o ♦ 48 | 24 48 0 24 | 12 0 12 0 24 16 0 0 | 0 6 2 0 0 0 0 8 0 | * * 40 * * x . x3x o3*c ♦ 24 | 12 0 24 12 | 0 12 6 0 0 0 8 8 | 0 0 0 4 4 0 0 0 2 | * * * 80 * . x3x3x *b3/2o3*c ♦ 60 | 0 60 60 30 | 0 0 0 20 30 20 20 20 | 0 0 0 0 0 5 5 10 5 | * * * * 32
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