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©
- general polytopal classes:
- Wythoffian polytera
links
| Acronym | gaqrin |
| Name | great quasirhombated penteract |
| Field of sections |
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| Circumradius | sqrt[31-14 sqrt(2)]/2 = 1.673396 |
| Vertex figure |
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| Coordinates | (2 sqrt(2)-1, 2 sqrt(2)-1, 2 sqrt(2)-1, sqrt(2)-1, 1)/2 & all permutations, all changes of sign |
| Face vector | 640, 1600, 1520, 680, 122 |
| Confer |
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External links |
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As abstract polyteron gaqrin is isomorph to girn, thereby replacing octagrams by octagons, resp. quitco by girco, resp. gaqrit by grit.
Incidence matrix according to Dynkin symbol
o3o3x3x4/3x . . . . . | 640 | 3 1 1 | 3 3 3 1 | 1 3 3 3 | 1 1 3 ------------+-----+-------------+----------------+----------------+--------- . . x . . | 2 | 960 * * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . x . | 2 | * 320 * | 0 3 0 1 | 0 3 0 3 | 1 0 3 . . . . x | 2 | * * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 ------------+-----+-------------+----------------+----------------+--------- . o3x . . | 3 | 3 0 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3x . | 6 | 3 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x | 4 | 2 0 2 | * * 480 * | 0 0 2 1 | 0 1 2 . . . x4/3x | 8 | 0 4 4 | * * * 80 | 0 0 0 3 | 0 0 3 ------------+-----+-------------+----------------+----------------+--------- o3o3x . . ♦ 4 | 6 0 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3x3x . ♦ 12 | 12 6 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3x . x ♦ 6 | 6 0 3 | 2 0 3 0 | * * 320 * | 0 1 1 . . x3x4/3x ♦ 48 | 24 24 24 | 0 8 12 6 | * * * 40 | 0 0 2 ------------+-----+-------------+----------------+----------------+--------- o3o3x3x . ♦ 20 | 30 10 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3o3x . x ♦ 8 | 6 0 4 | 8 0 6 0 | 2 0 4 0 | * 80 * . o3x3x4/3x ♦ 192 | 192 96 96 | 64 64 96 24 | 0 16 32 8 | * * 10
o3o3/2x3x4/3x . . . . . | 640 | 3 1 1 | 3 3 3 1 | 1 3 3 3 | 1 1 3 --------------+-----+-------------+----------------+----------------+--------- . . x . . | 2 | 960 * * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . x . | 2 | * 320 * | 0 3 0 1 | 0 3 0 3 | 1 0 3 . . . . x | 2 | * * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 --------------+-----+-------------+----------------+----------------+--------- . o3/2x . . | 3 | 3 0 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3x . | 6 | 3 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x | 4 | 2 0 2 | * * 480 * | 0 0 2 1 | 0 1 2 . . . x4/3x | 8 | 0 4 4 | * * * 80 | 0 0 0 3 | 0 0 3 --------------+-----+-------------+----------------+----------------+--------- o3o3/2x . . ♦ 4 | 6 0 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3/2x3x . ♦ 12 | 12 6 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3/2x . x ♦ 6 | 6 0 3 | 2 0 3 0 | * * 320 * | 0 1 1 . . x3x4/3x ♦ 48 | 24 24 24 | 0 8 12 6 | * * * 40 | 0 0 2 --------------+-----+-------------+----------------+----------------+--------- o3o3/2x3x . ♦ 20 | 30 10 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3o3/2x . x ♦ 8 | 6 0 4 | 8 0 6 0 | 2 0 4 0 | * 80 * . o3/2x3x4/3x ♦ 192 | 192 96 96 | 64 64 96 24 | 0 16 32 8 | * * 10
o3/2o3x3x4/3x . . . . . | 640 | 3 1 1 | 3 3 3 1 | 1 3 3 3 | 1 1 3 --------------+-----+-------------+----------------+----------------+--------- . . x . . | 2 | 960 * * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . x . | 2 | * 320 * | 0 3 0 1 | 0 3 0 3 | 1 0 3 . . . . x | 2 | * * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 --------------+-----+-------------+----------------+----------------+--------- . o3x . . | 3 | 3 0 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3x . | 6 | 3 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x | 4 | 2 0 2 | * * 480 * | 0 0 2 1 | 0 1 2 . . . x4/3x | 8 | 0 4 4 | * * * 80 | 0 0 0 3 | 0 0 3 --------------+-----+-------------+----------------+----------------+--------- o3/2o3x . . ♦ 4 | 6 0 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3x3x . ♦ 12 | 12 6 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3x . x ♦ 6 | 6 0 3 | 2 0 3 0 | * * 320 * | 0 1 1 . . x3x4/3x ♦ 48 | 24 24 24 | 0 8 12 6 | * * * 40 | 0 0 2 --------------+-----+-------------+----------------+----------------+--------- o3/2o3x3x . ♦ 20 | 30 10 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3/2o3x . x ♦ 8 | 6 0 4 | 8 0 6 0 | 2 0 4 0 | * 80 * . o3x3x4/3x ♦ 192 | 192 96 96 | 64 64 96 24 | 0 16 32 8 | * * 10
o3/2o3/2x3x4/3x . . . . . | 640 | 3 1 1 | 3 3 3 1 | 1 3 3 3 | 1 1 3 ----------------+-----+-------------+----------------+----------------+--------- . . x . . | 2 | 960 * * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . x . | 2 | * 320 * | 0 3 0 1 | 0 3 0 3 | 1 0 3 . . . . x | 2 | * * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 ----------------+-----+-------------+----------------+----------------+--------- . o3/2x . . | 3 | 3 0 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3x . | 6 | 3 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x | 4 | 2 0 2 | * * 480 * | 0 0 2 1 | 0 1 2 . . . x4/3x | 8 | 0 4 4 | * * * 80 | 0 0 0 3 | 0 0 3 ----------------+-----+-------------+----------------+----------------+--------- o3/2o3/2x . . ♦ 4 | 6 0 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3/2x3x . ♦ 12 | 12 6 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3/2x . x ♦ 6 | 6 0 3 | 2 0 3 0 | * * 320 * | 0 1 1 . . x3x4/3x ♦ 48 | 24 24 24 | 0 8 12 6 | * * * 40 | 0 0 2 ----------------+-----+-------------+----------------+----------------+--------- o3/2o3/2x3x . ♦ 20 | 30 10 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3/2o3/2x . x ♦ 8 | 6 0 4 | 8 0 6 0 | 2 0 4 0 | * 80 * . o3/2x3x4/3x ♦ 192 | 192 96 96 | 64 64 96 24 | 0 16 32 8 | * * 10
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