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| by facets: | cope | gaqrit | gaquidpoth | ohope | pittip | prip | quitcope | tistodip |
| quacgarn | 80 | 10 | 0 | 0 | 0 | 32 | 40 | 80 |
| gorcgrin | 0 | 10 | 10 | 80 | 32 | 0 | 0 | 80 |
- general polytopal classes:
- Wythoffian polytera
links
| Acronym | quacgarn | |||||||||||||||||||||||||||
| Name | quasicelligreatorhombated penteract | |||||||||||||||||||||||||||
| Field of sections |
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| Circumradius | sqrt[41-16 sqrt(2)]/2 = 2.143163 | |||||||||||||||||||||||||||
| Vertex figure |
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| Coordinates | (3 sqrt(2)-1, 2 sqrt(2)-1, 2 sqrt(2)-1, sqrt(2)-1, 1)/2 & all permutations, all changes of sign | |||||||||||||||||||||||||||
| Colonel of regiment |
(is itself locally convex
– uniform polyteral members:
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| Face vector | 1920, 5760, 6000, 2400, 242 | |||||||||||||||||||||||||||
| Confer |
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External links |
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As abstract polytope quacgarn is isomorphic to cogrin, thereby replacing octagrams by octagons, resp. stop by op and quitco by girco, resp. tistodip by todip, quitcope by gircope, and gaqrit by grit.
Incidence matrix according to Dynkin symbol
x3o3x3x4/3x . . . . . | 1920 | 2 2 1 1 | 1 2 2 2 1 2 2 1 | 1 1 1 2 2 2 1 1 2 | 1 1 1 2 1 ------------+------+-------------------+---------------------------------+------------------------------------+--------------- x . . . . | 2 | 1920 * * * | 1 1 1 1 0 0 0 0 | 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0 . . x . . | 2 | * 1920 * * | 0 1 0 0 1 1 1 0 | 1 0 0 1 1 0 1 1 1 | 1 1 0 1 1 . . . x . | 2 | * * 960 * | 0 0 2 0 0 2 0 1 | 0 1 0 2 0 2 1 0 2 | 1 0 1 2 1 . . . . x | 2 | * * * 960 | 0 0 0 2 0 0 2 1 | 0 0 1 0 2 2 0 1 2 | 0 1 1 2 1 ------------+------+-------------------+---------------------------------+------------------------------------+--------------- x3o . . . | 3 | 3 0 0 0 | 640 * * * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 x . x . . | 4 | 2 2 0 0 | * 960 * * * * * * | 1 0 0 1 1 0 0 0 0 | 1 1 0 1 0 x . . x . | 4 | 2 0 2 0 | * * 960 * * * * * | 0 1 0 1 0 1 0 0 0 | 1 0 1 1 0 x . . . x | 4 | 2 0 0 2 | * * * 960 * * * * | 0 0 1 0 1 1 0 0 0 | 0 1 1 1 0 . o3x . . | 3 | 0 3 0 0 | * * * * 640 * * * | 1 0 0 0 0 0 1 1 0 | 1 1 0 0 1 . . x3x . | 6 | 0 3 3 0 | * * * * * 640 * * | 0 0 0 1 0 0 1 0 1 | 1 0 0 1 1 . . x . x | 4 | 0 2 0 2 | * * * * * * 960 * | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1 . . . x4/3x | 8 | 0 0 4 4 | * * * * * * * 240 | 0 0 0 0 0 2 0 0 2 | 0 0 1 2 1 ------------+------+-------------------+---------------------------------+------------------------------------+--------------- x3o3x . . ♦ 12 | 12 12 0 0 | 4 6 0 0 4 0 0 0 | 160 * * * * * * * * | 1 1 0 0 0 x3o . x . ♦ 6 | 6 0 3 0 | 2 0 3 0 0 0 0 0 | * 320 * * * * * * * | 1 0 1 0 0 x3o . . x ♦ 6 | 6 0 0 3 | 2 0 0 3 0 0 0 0 | * * 320 * * * * * * | 0 1 1 0 0 x . x3x . ♦ 12 | 6 6 6 0 | 0 3 3 0 0 2 0 0 | * * * 320 * * * * * | 1 0 0 1 0 x . x . x ♦ 8 | 4 4 0 4 | 0 2 0 2 0 0 2 0 | * * * * 480 * * * * | 0 1 0 1 0 x . . x4/3x ♦ 16 | 8 0 8 8 | 0 0 4 4 0 0 0 2 | * * * * * 240 * * * | 0 0 1 1 0 . o3x3x . ♦ 12 | 0 12 6 0 | 0 0 0 0 4 4 0 0 | * * * * * * 160 * * | 1 0 0 0 1 . o3x . x ♦ 6 | 0 6 0 3 | 0 0 0 0 2 0 3 0 | * * * * * * * 320 * | 0 1 0 0 1 . . x3x4/3x ♦ 48 | 0 24 24 24 | 0 0 0 0 0 8 12 6 | * * * * * * * * 80 | 0 0 0 1 1 ------------+------+-------------------+---------------------------------+------------------------------------+--------------- x3o3x3x . ♦ 60 | 60 60 30 0 | 20 30 30 0 20 20 0 0 | 5 10 0 10 0 0 5 0 0 | 32 * * * * x3o3x . x ♦ 24 | 24 24 0 12 | 8 12 0 12 8 0 12 0 | 2 0 4 0 6 0 0 4 0 | * 80 * * * x3o . x4/3x ♦ 24 | 24 0 12 12 | 8 0 12 12 0 0 0 3 | 0 4 4 0 0 3 0 0 0 | * * 80 * * x . x3x4/3x ♦ 96 | 48 48 48 48 | 0 24 24 24 0 16 24 12 | 0 0 0 8 12 6 0 0 2 | * * * 40 * . o3x3x4/3x ♦ 192 | 0 192 96 96 | 0 0 0 0 64 64 96 24 | 0 0 0 0 0 0 16 32 8 | * * * * 10
x3/2o3/2x3x4/3x . . . . . | 1920 | 2 2 1 1 | 1 2 2 2 1 2 2 1 | 1 1 1 2 2 2 1 1 2 | 1 1 1 2 1 ----------------+------+-------------------+---------------------------------+------------------------------------+--------------- x . . . . | 2 | 1920 * * * | 1 1 1 1 0 0 0 0 | 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0 . . x . . | 2 | * 1920 * * | 0 1 0 0 1 1 1 0 | 1 0 0 1 1 0 1 1 1 | 1 1 0 1 1 . . . x . | 2 | * * 960 * | 0 0 2 0 0 2 0 1 | 0 1 0 2 0 2 1 0 2 | 1 0 1 2 1 . . . . x | 2 | * * * 960 | 0 0 0 2 0 0 2 1 | 0 0 1 0 2 2 0 1 2 | 0 1 1 2 1 ----------------+------+-------------------+---------------------------------+------------------------------------+--------------- x3/2o . . . | 3 | 3 0 0 0 | 640 * * * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 x . x . . | 4 | 2 2 0 0 | * 960 * * * * * * | 1 0 0 1 1 0 0 0 0 | 1 1 0 1 0 x . . x . | 4 | 2 0 2 0 | * * 960 * * * * * | 0 1 0 1 0 1 0 0 0 | 1 0 1 1 0 x . . . x | 4 | 2 0 0 2 | * * * 960 * * * * | 0 0 1 0 1 1 0 0 0 | 0 1 1 1 0 . o3/2x . . | 3 | 0 3 0 0 | * * * * 640 * * * | 1 0 0 0 0 0 1 1 0 | 1 1 0 0 1 . . x3x . | 6 | 0 3 3 0 | * * * * * 640 * * | 0 0 0 1 0 0 1 0 1 | 1 0 0 1 1 . . x . x | 4 | 0 2 0 2 | * * * * * * 960 * | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1 . . . x4/3x | 8 | 0 0 4 4 | * * * * * * * 240 | 0 0 0 0 0 2 0 0 2 | 0 0 1 2 1 ----------------+------+-------------------+---------------------------------+------------------------------------+--------------- x3/2o3/2x . . ♦ 12 | 12 12 0 0 | 4 6 0 0 4 0 0 0 | 160 * * * * * * * * | 1 1 0 0 0 x3/2o . x . ♦ 6 | 6 0 3 0 | 2 0 3 0 0 0 0 0 | * 320 * * * * * * * | 1 0 1 0 0 x3/2o . . x ♦ 6 | 6 0 0 3 | 2 0 0 3 0 0 0 0 | * * 320 * * * * * * | 0 1 1 0 0 x . x3x . ♦ 12 | 6 6 6 0 | 0 3 3 0 0 2 0 0 | * * * 320 * * * * * | 1 0 0 1 0 x . x . x ♦ 8 | 4 4 0 4 | 0 2 0 2 0 0 2 0 | * * * * 480 * * * * | 0 1 0 1 0 x . . x4/3x ♦ 16 | 8 0 8 8 | 0 0 4 4 0 0 0 2 | * * * * * 240 * * * | 0 0 1 1 0 . o3/2x3x . ♦ 12 | 0 12 6 0 | 0 0 0 0 4 4 0 0 | * * * * * * 160 * * | 1 0 0 0 1 . o3/2x . x ♦ 6 | 0 6 0 3 | 0 0 0 0 2 0 3 0 | * * * * * * * 320 * | 0 1 0 0 1 . . x3x4/3x ♦ 48 | 0 24 24 24 | 0 0 0 0 0 8 12 6 | * * * * * * * * 80 | 0 0 0 1 1 ----------------+------+-------------------+---------------------------------+------------------------------------+--------------- x3/2o3/2x3x . ♦ 60 | 60 60 30 0 | 20 30 30 0 20 20 0 0 | 5 10 0 10 0 0 5 0 0 | 32 * * * * x3/2o3/2x . x ♦ 24 | 24 24 0 12 | 8 12 0 12 8 0 12 0 | 2 0 4 0 6 0 0 4 0 | * 80 * * * x3/2o . x4/3x ♦ 24 | 24 0 12 12 | 8 0 12 12 0 0 0 3 | 0 4 4 0 0 3 0 0 0 | * * 80 * * x . x3x4/3x ♦ 96 | 48 48 48 48 | 0 24 24 24 0 16 24 12 | 0 0 0 8 12 6 0 0 2 | * * * 40 * . o3/2x3x4/3x ♦ 192 | 0 192 96 96 | 0 0 0 0 64 64 96 24 | 0 0 0 0 0 0 16 32 8 | * * * * 10
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