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| by facets: | gaquidpoth | giphado | histodip | pittip | prip | proh | quithip | tuttip |
| gircaptint | 10 | 10 | 0 | 32 | 0 | 0 | 40 | 80 |
| quicpatint | 0 | 0 | 80 | 0 | 32 | 10 | 40 | 80 |
- general polytopal classes:
- Wythoffian polytera
links
| Acronym | quicpatint | |||||||||||||||||||||||||||
| Name | quasicelliprismatotruncated penteractitriacontiditeron | |||||||||||||||||||||||||||
| 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 |
(is itself locally convex
– uniform polyteral members:
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| Face vector | 1920, 5760, 5760, 2160, 242 | |||||||||||||||||||||||||||
| Confer |
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As abstract polytope quicpatint is isomorphic to captint, thereby replacing octagrams by octagons, resp. stop by op and quith by tic, resp. histodip by hodip, quithip by ticcup, and quiproh by proh.
Incidence matrix according to Dynkin symbol
x3x3o3x4/3x . . . . . | 1920 | 1 2 2 1 | 2 2 1 1 2 2 1 2 | 1 2 2 1 2 1 1 2 1 | 1 1 2 1 1 ------------+------+-------------------+---------------------------------+------------------------------------+--------------- x . . . . | 2 | 960 * * * | 2 2 1 0 0 0 0 0 | 1 2 2 1 2 0 0 0 0 | 1 1 2 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 0 1 0 1 1 | 0 1 0 1 1 1 0 1 1 | 1 0 1 1 1 . . . . x | 2 | * * * 960 | 0 0 1 0 0 2 0 2 | 0 0 2 0 2 0 1 2 1 | 0 1 2 1 1 ------------+------+-------------------+---------------------------------+------------------------------------+--------------- x3x . . . | 6 | 3 3 0 0 | 640 * * * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 x . . x . | 4 | 2 0 2 0 | * 960 * * * * * * | 0 1 0 1 1 0 0 0 0 | 1 0 1 1 0 x . . . x | 4 | 2 0 0 2 | * * 480 * * * * * | 0 0 2 0 2 0 0 0 0 | 0 1 2 1 0 . x3o . . | 3 | 0 3 0 0 | * * * 640 * * * * | 1 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . x . x . | 4 | 0 2 2 0 | * * * * 960 * * * | 0 1 0 0 0 1 0 1 0 | 1 0 1 0 1 . x . . x | 4 | 0 2 0 2 | * * * * * 960 * * | 0 0 1 0 0 0 1 1 0 | 0 1 1 0 1 . . o3x . | 3 | 0 0 3 0 | * * * * * * 640 * | 0 0 0 1 0 1 0 0 1 | 1 0 0 1 1 . . . x4/3x | 8 | 0 0 4 4 | * * * * * * * 480 | 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 ------------+------+-------------------+---------------------------------+------------------------------------+--------------- x3x3o . . ♦ 12 | 6 12 0 0 | 4 0 0 4 0 0 0 0 | 160 * * * * * * * * | 1 1 0 0 0 x3x . x . ♦ 12 | 6 6 6 0 | 2 3 0 0 3 0 0 0 | * 320 * * * * * * * | 1 0 1 0 0 x3x . . x ♦ 12 | 6 6 0 6 | 2 0 3 0 0 3 0 0 | * * 320 * * * * * * | 0 1 1 0 0 x . o3x . ♦ 6 | 3 0 6 0 | 0 3 0 0 0 0 2 0 | * * * 320 * * * * * | 1 0 0 1 0 x . . x4/3x ♦ 16 | 8 0 8 8 | 0 4 4 0 0 0 0 2 | * * * * 240 * * * * | 0 0 1 1 0 . x3o3x . ♦ 12 | 0 12 12 0 | 0 0 0 4 6 0 4 0 | * * * * * 160 * * * | 1 0 0 0 1 . x3o . x ♦ 6 | 0 6 0 3 | 0 0 0 2 0 3 0 0 | * * * * * * 320 * * | 0 1 0 0 1 . x . x4/3x ♦ 16 | 0 8 8 8 | 0 0 0 0 4 4 0 2 | * * * * * * * 240 * | 0 0 1 0 1 . . o3x4/3x ♦ 24 | 0 0 24 12 | 0 0 0 0 0 0 8 6 | * * * * * * * * 80 | 0 0 0 1 1 ------------+------+-------------------+---------------------------------+------------------------------------+--------------- x3x3o3x . ♦ 60 | 30 60 60 0 | 20 30 0 20 30 0 20 0 | 5 10 0 10 0 5 0 0 0 | 32 * * * * x3x3o . x ♦ 24 | 12 24 0 12 | 8 0 6 8 0 12 0 0 | 2 0 4 0 0 0 4 0 0 | * 80 * * * x3x . x4/3x ♦ 48 | 24 24 24 24 | 8 12 12 0 12 12 0 6 | 0 4 4 0 3 0 0 3 0 | * * 80 * * x . o3x4/3x ♦ 48 | 24 0 48 24 | 0 24 12 0 0 0 16 13 | 0 0 0 8 6 0 0 0 2 | * * * 40 * . x3o3x4/3x ♦ 192 | 0 192 192 96 | 0 0 0 64 96 96 64 48 | 0 0 0 0 0 16 32 24 8 | * * * * 10
x3x3/2o3/2x4/3x . . . . . | 1920 | 1 2 2 1 | 2 2 1 1 2 2 1 2 | 1 2 2 1 2 1 1 2 1 | 1 1 2 1 1 ----------------+------+-------------------+---------------------------------+------------------------------------+--------------- x . . . . | 2 | 960 * * * | 2 2 1 0 0 0 0 0 | 1 2 2 1 2 0 0 0 0 | 1 1 2 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 0 1 0 1 1 | 0 1 0 1 1 1 0 1 1 | 1 0 1 1 1 . . . . x | 2 | * * * 960 | 0 0 1 0 0 2 0 2 | 0 0 2 0 2 0 1 2 1 | 0 1 2 1 1 ----------------+------+-------------------+---------------------------------+------------------------------------+--------------- x3x . . . | 6 | 3 3 0 0 | 640 * * * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 x . . x . | 4 | 2 0 2 0 | * 960 * * * * * * | 0 1 0 1 1 0 0 0 0 | 1 0 1 1 0 x . . . x | 4 | 2 0 0 2 | * * 480 * * * * * | 0 0 2 0 2 0 0 0 0 | 0 1 2 1 0 . x3/2o . . | 3 | 0 3 0 0 | * * * 640 * * * * | 1 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . x . x . | 4 | 0 2 2 0 | * * * * 960 * * * | 0 1 0 0 0 1 0 1 0 | 1 0 1 0 1 . x . . x | 4 | 0 2 0 2 | * * * * * 960 * * | 0 0 1 0 0 0 1 1 0 | 0 1 1 0 1 . . o3/2x . | 3 | 0 0 3 0 | * * * * * * 640 * | 0 0 0 1 0 1 0 0 1 | 1 0 0 1 1 . . . x4/3x | 8 | 0 0 4 4 | * * * * * * * 480 | 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 ----------------+------+-------------------+---------------------------------+------------------------------------+--------------- x3x3/2o . . ♦ 12 | 6 12 0 0 | 4 0 0 4 0 0 0 0 | 160 * * * * * * * * | 1 1 0 0 0 x3x . x . ♦ 12 | 6 6 6 0 | 2 3 0 0 3 0 0 0 | * 320 * * * * * * * | 1 0 1 0 0 x3x . . x ♦ 12 | 6 6 0 6 | 2 0 3 0 0 3 0 0 | * * 320 * * * * * * | 0 1 1 0 0 x . o3/2x . ♦ 6 | 3 0 6 0 | 0 3 0 0 0 0 2 0 | * * * 320 * * * * * | 1 0 0 1 0 x . . x4/3x ♦ 16 | 8 0 8 8 | 0 4 4 0 0 0 0 2 | * * * * 240 * * * * | 0 0 1 1 0 . x3/2o3/2x . ♦ 12 | 0 12 12 0 | 0 0 0 4 6 0 4 0 | * * * * * 160 * * * | 1 0 0 0 1 . x3/2o . x ♦ 6 | 0 6 0 3 | 0 0 0 2 0 3 0 0 | * * * * * * 320 * * | 0 1 0 0 1 . x . x4/3x ♦ 16 | 0 8 8 8 | 0 0 0 0 4 4 0 2 | * * * * * * * 240 * | 0 0 1 0 1 . . o3/2x4/3x ♦ 24 | 0 0 24 12 | 0 0 0 0 0 0 8 6 | * * * * * * * * 80 | 0 0 0 1 1 ----------------+------+-------------------+---------------------------------+------------------------------------+--------------- x3x3/2o3/2x . ♦ 60 | 30 60 60 0 | 20 30 0 20 30 0 20 0 | 5 10 0 10 0 5 0 0 0 | 32 * * * * x3x3/2o . x ♦ 24 | 12 24 0 12 | 8 0 6 8 0 12 0 0 | 2 0 4 0 0 0 4 0 0 | * 80 * * * x3x . x4/3x ♦ 48 | 24 24 24 24 | 8 12 12 0 12 12 0 6 | 0 4 4 0 3 0 0 3 0 | * * 80 * * x . o3/2x4/3x ♦ 48 | 24 0 48 24 | 0 24 12 0 0 0 16 13 | 0 0 0 8 6 0 0 0 2 | * * * 40 * . x3/2o3/2x4/3x ♦ 192 | 0 192 192 96 | 0 0 0 64 96 96 64 48 | 0 0 0 0 0 16 32 24 8 | * * * * 10
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