Acronym  ... 
Name  hyperbolic x4x3o8o tesselation 
Circumradius  sqrt[sqrt(2)]/2 = 0.594604 i 
Confer 

This hypercompact hyperbolic tesselation uses the order 8 triangle tiling in the sense of an infinite bollohedron as one of its cell types.
As these very cells are hemichoral (have same curvature resp. intersect the sphere of infinity orthogonally) those could be replaced by mirror images of the remainder each. This transforms the hypercompact honeycomb back into a compact one, into laminatrunc( x4x3o8o ).
Incidence matrix according to Dynkin symbol
x4x3o8o (N,M → ∞) . . . .  6NM  1 8  8 8  8 1 ++++ x . . .  2  3NM *  8 0  8 0 . x . .  2  * 24NM  1 2  2 1 ++++ x4x . .  8  4 4  6NM *  2 0 . x3o .  3  0 3  * 16NM  1 1 ++++ x4x3o . ♦ 24  12 24  6 8  2NM * . x3o8o ♦ 3M  0 12M  0 8M  * 2N
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