Acronym  ... 
Name  hyperbolic o8o4x *b3x tesselation 
Circumradius  sqrt[1sqrt(2)]/2 = 0.321797 i 
Confer 

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 here are hemichoral (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 allow for an attaching layer of trips. The magic then would be, that the bollosurface through their center points again happens to be hemichoral, thus there too a second type of mirror can be placed. Accordingly we thus would produce the laminatrunc( 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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