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.
A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells, so that there are no gaps.
It is an example of the more general mathematical tiling or tessellation in any number of dimensions.
They may also be constructed in non-Euclidean spaces, such as hyperbolic uniform honeycombs.
It represents a semiregular honeycomb as defined by all regular cells, although from the Wythoff construction, rectified square tiling r{4,4}, becomes the regular square tiling {4,4}.