In the geometry of hyperbolic 3-space, the tetrahedron-octahedron honeycomb is a compact uniform honeycomb, constructed from octahedron and tetrahedron 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 tetrahedral r{3,3}, becomes the regular octahedron {3,4}.