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.
The cyclotruncated dodecahedral-icosahedral honeycomb is a compact uniform honeycomb, constructed from truncated dodecahedron and icosahedron cells, in a pentagonal antiprism vertex figure.
The cyclotruncated icosahedral-dodecahedral honeycomb is a compact uniform honeycomb, constructed from dodecahedron and truncated icosahedron cells, in a triangular antiprism vertex figure.