Square tiling honeycomb

The order-3 square tiling honeycomb, or just square tiling honeycomb, is a paracompact regular tiling of 3D hyperbolic space. Each cell is a square tiling whose vertices lie on a horosphere, a surface in hyperbolic space that approaches a single ideal point at infinity. 3 square tilings meet at each edge, and 6 meet at each vertex.

It can be formed by rectifying the order-4 square tiling honeycomb.

Representations
The square tiling honeycomb has the following Coxeter diagrams:


 * x4o4o3o (full symmetry)
 * o4x4o4o (as rectified order-4 square tiling honeycomb)
 * o4x4o *b4o (cuboid verf)
 * x4o4x *b4o (square frustum verf)
 * x4o4x4o4*a (rectangle trapezoprism verf)