Order-4 square tiling honeycomb

The order-4 square tiling honeycomb is a paracompact regular tiling of 3D hyperbolic space. 4 ideal square tilings meet at each edge. All vertices are ideal points at infinity, with infinitely many square tilings meeting at each vertex in a square tiling arrangement.

Representations
The order-4 square tiling has the following Coxeter diagrams:


 * x4o4o4o (full symmetry)
 * x4o4o *b4o (cells of two types)
 * x4o4o4o4*a (cells of three types, x4o4x verf)
 * s4o4o4o
 * s4o4o *b4o
 * s4o4o4o4*a