Acronym | ... |
Name | hyperbolic o8o4x *b3x tesselation |
Circumradius | sqrt[1-sqrt(2)]/2 = 0.321797 i |
Vertex figure | xq8oo&#q |
Confer |
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This hypercompact hyperbolic tesselation uses the order 8 triangle tiling and the order 8 square tiling in the sense of infinite bollohedra as some of its cell types.
As the order 8 square tiling (osquat) here are hemi-choral (have same curvature resp. intersect the sphere of infinity orthogonally) those could be replaced by mirror images of the remainder each. Further the order 8 triangle tiling (otrat) allows for an attaching layer of trips. The magic then would be, that the bollo-surface through their center points again happens to be hemi-choral, thus there too a second type of mirror can be placed. Accordingly we thus would produce the lamina-trunc( o8o4x *b3x ), built from sircoes and trips only.
Incidence matrix according to Dynkin symbol
o8o4x *b3x (N,M,K → ∞) . . . . | 3NMK | 8 8 | 8 8 8 | 1 1 8 -----------+------+-------------+----------------+----------- . . x . | 2 | 12NMK * | 2 1 0 | 1 0 2 . . . x | 2 | * 12NMK | 0 1 2 | 0 1 2 -----------+------+-------------+----------------+----------- . o4x . | 4 | 4 0 | 6NMK * * | 1 0 1 . . x x | 4 | 2 2 | * 6NMK * | 0 0 2 . o . *b3x | 3 | 0 3 | * * 8NMK | 0 1 1 -----------+------+-------------+----------------+----------- o8o4x . ♦ M | 4M 0 | 2M 0 0 | 3NK * * o8o . *b3x ♦ 3K | 0 12K | 0 0 8K | * NM * . o4x *b3x ♦ 24 | 24 24 | 6 12 8 | * * NMK
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