Acronym | ... |
Name | hyperbolic x3x4x3x8o tesselation |
Circumradius | sqrt[-(4+7 sqrt(2))]/2 = 1.864101 i |
Confer |
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This hypercompact hyperbolic tesselation uses the truncated order 8 triangle tiling (totrat) in the sense of an infinite bollohedron as one of its cell types. Further it uses x x3x8o and x4x3x8o in the sense of infinite bollochora alike.
As the latter of these very bollochora are hemi-teral (have same curvature resp. intersect the hypersphere of infinity orthogonally) those could be replaced by mirror images of the remainder each. This transforms the hypercompact tetracomb back into a compact one, into lamina-trunc( x3x4x3x8o )).
Incidence matrix according to Dynkin symbol
x3x4x3x8o (N,M,K → ∞) . . . . . | 576NMK | 1 1 1 2 | 1 1 2 1 2 2 1 | 1 2 2 1 2 1 1 | 2 1 1 1 ----------+--------+-----------------------------+-----------------------------------------------+------------------------------------------+-------------------- x . . . . | 2 | 288NMK * * * | 1 1 2 0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0 . x . . . | 2 | * 288NMK * * | 1 0 0 1 2 0 0 | 1 2 0 0 2 1 0 | 2 1 0 1 . . x . . | 2 | * * 288NMK * | 0 1 0 1 0 2 0 | 1 0 2 0 2 0 1 | 2 0 1 1 . . . x . | 2 | * * * 576NMK | 0 0 1 0 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1 ----------+--------+-----------------------------+-----------------------------------------------+------------------------------------------+-------------------- x3x . . . | 6 | 3 3 0 0 | 96NMK * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0 x . x . . | 4 | 2 0 2 0 | * 144NMK * * * * * | 1 0 2 0 0 0 0 | 2 0 1 0 x . . x . | 4 | 2 0 0 2 | * * 288NMK * * * * | 0 1 1 1 0 0 0 | 1 1 1 0 . x4x . . | 8 | 0 4 4 0 | * * * 72NMK * * * | 1 0 0 0 2 0 0 | 2 0 0 1 . x . x . | 4 | 0 2 0 2 | * * * * 288NMK * * | 0 1 0 0 1 1 0 | 1 1 0 1 . . x3x . | 6 | 0 0 3 3 | * * * * * 192NMK * | 0 0 1 0 1 0 1 | 1 0 1 1 . . . x8o | 8 | 0 0 0 8 | * * * * * * 72NMK | 0 0 0 1 0 1 1 | 0 1 1 1 ----------+--------+-----------------------------+-----------------------------------------------+------------------------------------------+-------------------- x3x4x . . ♦ 48 | 24 24 24 0 | 8 12 0 6 0 0 0 | 12NMK * * * * * * | 2 0 0 0 x3x . x . ♦ 12 | 6 6 0 6 | 2 0 3 0 3 0 0 | * 96NMK * * * * * | 1 1 0 0 x . x3x . ♦ 12 | 6 0 6 6 | 0 3 3 0 0 2 0 | * * 96NMK * * * * | 1 0 1 0 x . . x8o ♦ 16 | 8 0 0 16 | 0 0 8 0 0 0 2 | * * * 36NMK * * * | 0 1 1 0 . x4x3x . ♦ 48 | 0 24 24 24 | 0 0 0 6 12 8 0 | * * * * 24NMK * * | 1 0 0 1 . x . x8o ♦ 16 | 0 8 0 16 | 0 0 0 0 8 0 2 | * * * * * 36NMK * | 0 1 0 1 . . x3x8o ♦ 24M | 0 0 12M 24M | 0 0 0 0 0 8M 3M | * * * * * * 24NK | 0 0 1 1 ----------+--------+-----------------------------+-----------------------------------------------+------------------------------------------+-------------------- x3x4x3x . ♦ 1152 | 576 576 576 576 | 192 288 288 144 288 192 0 | 24 96 96 0 24 0 0 | NMK * * * x3x . x8o ♦ 48 | 24 24 0 48 | 8 0 24 0 24 0 6 | 0 8 0 3 0 3 0 | * 12NMK * * x . x3x8o ♦ 48M | 24M 0 24M 48M | 0 12M 24M 0 0 16M 6M | 0 0 8M 3M 0 0 2 | * * 12NK * . x4x3x8o ♦ 48MK | 0 24MK 24MK 48MK | 0 0 0 6MK 24MK 16MK 6MK | 0 0 0 0 2MK 3MK 2K | * * * 12NM
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