Acronym  ... 
Name  hyperbolic o4x4x4o tesselation 
Circumradius  sqrt[1sqrt(2)] = 1.553774 i 
Confer 

This noble, noncompact hyperbolic tesselation uses the euclidean tiling tosquat in the sense of an infinite horohedron as its single cell type.
As can be read from the matrices below, at every edge there are 2 octagons. Thus we get as pseudo cells something with octagons only. From the vertex incidence we further read off that this pseudo tiling happens to use 4 octagons per vertex. From the here truely being used cells (tosquat) it is deduced, that any straight edge sequence of that seeming x8o4o needs to be modwrapped to square holes. Therefore those pseudo cells rather are the skew polyhedron x8o4o4 instead.
Incidence matrix according to Dynkin symbol
o4x4x4o (N,M,K → ∞) . . . .  4NMK  2 2  1 4 1  2 2 ++++ . x . .  2  4NMK *  1 2 0  2 1 . . x .  2  * 4NMK  0 2 1  1 2 ++++ o4x . .  4  4 0  NMK * *  2 0 . x4x .  8  4 4  * 2NMK *  1 1 . . x4o  4  0 4  * * NMK  0 2 ++++ o4x4x . ♦ 4M  4M 2M  M M 0  2NK * . x4x4o ♦ 4K  2K 4K  0 K K  * 2NM
or . . . .  2NM  4  2 4  4 ++++ . x . . &  2  4NM  1 2  3 ++++ o4x . . &  4  4  NM *  2 . x4x .  8  8  * NM  2 ++++ o4x4x . & ♦ 4M  6M  M M  2N
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