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

As the order 8 square tiling within o8o4x *b3x were 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 there allow for an attaching layer of trips. The magic then is, 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 obtain this still uniform laminatruncate, built from sircoes and trips only.
laminatruncate( o8o4x *b3x ) (N → ∞) 3N ♦ 2 16 8  16 16 16 8  16 16 +++ 2  3N * *  8 0 0 0  8 0 2  * 24N *  1 2 1 0  2 2 2  * * 12N  0 0 2 2  0 4 +++ 4  2 2 0  12N * * *  2 0 3  0 3 0  * 16N * *  1 1 4  0 2 2  * * 12N *  0 2 4  0 0 4  * * * 6N  0 2 +++ 6  3 6 0  3 2 0 0  8N * trip 24  0 24 24  0 8 12 6  * 2N sirco
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