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wrt. quitit
wrt. pen
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- analogs:
- quasitruncated hypercube qtCn
links
| Acronym | quittin |
| Name | quasitruncated penteract |
| Field of sections |
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| Circumradius | sqrt[13-8 sqrt(2)]/2 = 0.649286 |
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Inradius wrt. quitit | [sqrt(2)-1]/2 = 0.207107 |
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Inradius wrt. pen | (5-4 sqrt(2))/sqrt(20) = -0.146877 |
| Vertex figure |
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| Coordinates | (sqrt(2)-1, sqrt(2)-1, sqrt(2)-1, sqrt(2)-1, 1)/2 & all permutations, all changes of sign |
| Volume | (1230-869 sqrt(2))/30 = 0.034947 |
| Face vector | 160, 400, 400, 200, 42 |
| Confer |
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External links |
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As abstract polytope quittin is isomorphic to tan, thereby replacing octagrams by octagons, resp. quith by tic, resp. quitit by tat.
Note that the tets and pens become retrograde here.
Incidence matrix according to Dynkin symbol
o3o3o3x4/3x . . . . . | 160 | 4 1 | 6 4 | 4 6 | 1 4 ------------+-----+--------+--------+--------+------ . . . x . | 2 | 320 * | 3 1 | 3 3 | 1 3 . . . . x | 2 | * 80 ♦ 0 4 | 0 6 | 0 4 ------------+-----+--------+--------+--------+------ . . o3x . | 3 | 3 0 | 320 * | 2 1 | 1 2 . . . x4/3x | 8 | 4 4 | * 80 | 0 3 | 0 3 ------------+-----+--------+--------+--------+------ . o3o3x . ♦ 4 | 6 0 | 4 0 | 160 * | 1 1 . . o3x4/3x ♦ 24 | 24 12 | 8 6 | * 40 | 0 2 ------------+-----+--------+--------+--------+------ o3o3o3x . ♦ 5 | 10 0 | 10 0 | 5 0 | 32 * . o3o3x4/3x ♦ 64 | 96 32 | 64 24 | 16 8 | * 10
o3o3o3/2x4/3x . . . . . | 160 | 4 1 | 6 4 | 4 6 | 1 4 --------------+-----+--------+--------+--------+------ . . . x . | 2 | 320 * | 3 1 | 3 3 | 1 3 . . . . x | 2 | * 80 ♦ 0 4 | 0 6 | 0 4 --------------+-----+--------+--------+--------+------ . . o3/2x . | 3 | 3 0 | 320 * | 2 1 | 1 2 . . . x4/3x | 8 | 4 4 | * 80 | 0 3 | 0 3 --------------+-----+--------+--------+--------+------ . o3o3/2x . ♦ 4 | 6 0 | 4 0 | 160 * | 1 1 . . o3/2x4/3x ♦ 24 | 24 12 | 8 6 | * 40 | 0 2 --------------+-----+--------+--------+--------+------ o3o3o3/2x . ♦ 5 | 10 0 | 10 0 | 5 0 | 32 * . o3o3/2x4/3x ♦ 64 | 96 32 | 64 24 | 16 8 | * 10
o3o3/2o3x4/3x . . . . . | 160 | 4 1 | 6 4 | 4 6 | 1 4 --------------+-----+--------+--------+--------+------ . . . x . | 2 | 320 * | 3 1 | 3 3 | 1 3 . . . . x | 2 | * 80 ♦ 0 4 | 0 6 | 0 4 --------------+-----+--------+--------+--------+------ . . o3x . | 3 | 3 0 | 320 * | 2 1 | 1 2 . . . x4/3x | 8 | 4 4 | * 80 | 0 3 | 0 3 --------------+-----+--------+--------+--------+------ . o3/2o3x . ♦ 4 | 6 0 | 4 0 | 160 * | 1 1 . . o3x4/3x ♦ 24 | 24 12 | 8 6 | * 40 | 0 2 --------------+-----+--------+--------+--------+------ o3o3/2o3x . ♦ 5 | 10 0 | 10 0 | 5 0 | 32 * . o3/2o3x4/3x ♦ 64 | 96 32 | 64 24 | 16 8 | * 10
o3o3/2o3/2x4/3x . . . . . | 160 | 4 1 | 6 4 | 4 6 | 1 4 ----------------+-----+--------+--------+--------+------ . . . x . | 2 | 320 * | 3 1 | 3 3 | 1 3 . . . . x | 2 | * 80 ♦ 0 4 | 0 6 | 0 4 ----------------+-----+--------+--------+--------+------ . . o3/2x . | 3 | 3 0 | 320 * | 2 1 | 1 2 . . . x4/3x | 8 | 4 4 | * 80 | 0 3 | 0 3 ----------------+-----+--------+--------+--------+------ . o3/2o3/2x . ♦ 4 | 6 0 | 4 0 | 160 * | 1 1 . . o3/2x4/3x ♦ 24 | 24 12 | 8 6 | * 40 | 0 2 ----------------+-----+--------+--------+--------+------ o3o3/2o3/2x . ♦ 5 | 10 0 | 10 0 | 5 0 | 32 * . o3/2o3/2x4/3x ♦ 64 | 96 32 | 64 24 | 16 8 | * 10
o3/2o3o3x4/3x . . . . . | 160 | 4 1 | 6 4 | 4 6 | 1 4 --------------+-----+--------+--------+--------+------ . . . x . | 2 | 320 * | 3 1 | 3 3 | 1 3 . . . . x | 2 | * 80 ♦ 0 4 | 0 6 | 0 4 --------------+-----+--------+--------+--------+------ . . o3x . | 3 | 3 0 | 320 * | 2 1 | 1 2 . . . x4/3x | 8 | 4 4 | * 80 | 0 3 | 0 3 --------------+-----+--------+--------+--------+------ . o3o3x . ♦ 4 | 6 0 | 4 0 | 160 * | 1 1 . . o3x4/3x ♦ 24 | 24 12 | 8 6 | * 40 | 0 2 --------------+-----+--------+--------+--------+------ o3/2o3o3x . ♦ 5 | 10 0 | 10 0 | 5 0 | 32 * . o3o3x4/3x ♦ 64 | 96 32 | 64 24 | 16 8 | * 10
o3/2o3o3/2x4/3x . . . . . | 160 | 4 1 | 6 4 | 4 6 | 1 4 ----------------+-----+--------+--------+--------+------ . . . x . | 2 | 320 * | 3 1 | 3 3 | 1 3 . . . . x | 2 | * 80 ♦ 0 4 | 0 6 | 0 4 ----------------+-----+--------+--------+--------+------ . . o3/2x . | 3 | 3 0 | 320 * | 2 1 | 1 2 . . . x4/3x | 8 | 4 4 | * 80 | 0 3 | 0 3 ----------------+-----+--------+--------+--------+------ . o3o3/2x . ♦ 4 | 6 0 | 4 0 | 160 * | 1 1 . . o3/2x4/3x ♦ 24 | 24 12 | 8 6 | * 40 | 0 2 ----------------+-----+--------+--------+--------+------ o3/2o3o3/2x . ♦ 5 | 10 0 | 10 0 | 5 0 | 32 * . o3o3/2x4/3x ♦ 64 | 96 32 | 64 24 | 16 8 | * 10
o3/2o3/2o3x4/3x . . . . . | 160 | 4 1 | 6 4 | 4 6 | 1 4 ----------------+-----+--------+--------+--------+------ . . . x . | 2 | 320 * | 3 1 | 3 3 | 1 3 . . . . x | 2 | * 80 ♦ 0 4 | 0 6 | 0 4 ----------------+-----+--------+--------+--------+------ . . o3x . | 3 | 3 0 | 320 * | 2 1 | 1 2 . . . x4/3x | 8 | 4 4 | * 80 | 0 3 | 0 3 ----------------+-----+--------+--------+--------+------ . o3/2o3x . ♦ 4 | 6 0 | 4 0 | 160 * | 1 1 . . o3x4/3x ♦ 24 | 24 12 | 8 6 | * 40 | 0 2 ----------------+-----+--------+--------+--------+------ o3/2o3/2o3x . ♦ 5 | 10 0 | 10 0 | 5 0 | 32 * . o3/2o3x4/3x ♦ 64 | 96 32 | 64 24 | 16 8 | * 10
o3/2o3/2o3/2x4/3x . . . . . | 160 | 4 1 | 6 4 | 4 6 | 1 4 ------------------+-----+--------+--------+--------+------ . . . x . | 2 | 320 * | 3 1 | 3 3 | 1 3 . . . . x | 2 | * 80 ♦ 0 4 | 0 6 | 0 4 ------------------+-----+--------+--------+--------+------ . . o3/2x . | 3 | 3 0 | 320 * | 2 1 | 1 2 . . . x4/3x | 8 | 4 4 | * 80 | 0 3 | 0 3 ------------------+-----+--------+--------+--------+------ . o3/2o3/2x . ♦ 4 | 6 0 | 4 0 | 160 * | 1 1 . . o3/2x4/3x ♦ 24 | 24 12 | 8 6 | * 40 | 0 2 ------------------+-----+--------+--------+--------+------ o3/2o3/2o3/2x . ♦ 5 | 10 0 | 10 0 | 5 0 | 32 * . o3/2o3/2x4/3x ♦ 64 | 96 32 | 64 24 | 16 8 | * 10
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