Acronym | ... |
Name | 2titho (?) |
Circumradius | sqrt(5/2) = 1.581139 |
Coordinates | (sqrt(2), 1/sqrt(2), 0, 0) & all permutations, all changes of sign |
General of army | thex |
Colonel of regiment | thex |
Confer |
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This Grünbaumian polychoron indeed has all elements in coincident pairs, only the Grünbaumian double-covers of thah interconnect the 2 layers. Esp. the toes come in 4 coincident pairs, while the 2 types of tuts coincide one by one of either type each. Each individual vertex figure is the same as the vertex figure of titho: a tall pyramid based on a crossed square.
Incidence matrix according to Dynkin symbol
x3x3x3o3/2*a . . . . | 96 | 2 1 2 | 2 2 1 2 1 | 2 1 1 1 -------------+----+----------+----------------+-------- x . . . | 2 | 96 * * | 1 1 1 0 0 | 1 1 1 0 . x . . | 2 | * 48 * | 2 0 0 2 0 | 2 1 0 1 . . x . | 2 | * * 96 | 0 1 0 1 1 | 1 0 1 1 -------------+----+----------+----------------+-------- x3x . . | 6 | 3 3 0 | 32 * * * * | 1 1 0 0 x . x . | 4 | 2 0 2 | * 48 * * * | 1 0 1 0 x . . o3/2*a | 3 | 3 0 0 | * * 32 * * | 0 1 1 0 . x3x . | 6 | 0 3 3 | * * * 32 * | 1 0 0 1 . . x3o | 3 | 0 0 3 | * * * * 32 | 0 0 1 1 -------------+----+----------+----------------+-------- x3x3x . ♦ 24 | 12 12 12 | 4 6 0 4 0 | 8 * * * x3x . o3/2*a ♦ 12 | 12 6 0 | 4 0 4 0 0 | * 8 * * x . x3o3/2*a ♦ 12 | 12 0 12 | 0 6 4 0 4 | * * 8 * . x3x3o ♦ 12 | 0 6 12 | 0 0 0 4 4 | * * * 8
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