Cubic-square tiling honeycomb

In the geometry of hyperbolic 3-space, the cubic-square tiling honeycomb is a paracompact uniform honeycomb, constructed from cube and square tiling cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram,, and is named by its two regular cells.
It represents a semiregular honeycomb as defined by all regular cells, although from the Wythoff construction, rectified square tiling r, becomes the regular square tiling.

Symmetry

A lower symmetry form, index 6, of this honeycomb can be constructed with symmetry, represented by a trigonal trapezohedron fundamental domain, and Coxeter diagram. Another lower symmetry constructions exists with symmetry, index 48 and an ideal regular octahedral fundamental domain.