A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells, so that there are no gaps.
The cyclotruncated cubic-octahedral honeycomb is a compact uniform honeycomb, constructed from truncated cube and octahedron cells, in a square antiprism vertex figure.
It can be seen as somewhat analogous to the trioctagonal tiling, which has truncated square and triangle facets: The cyclotruncated octahedral-cubic honeycomb is a compact uniform honeycomb, constructed from cube and truncated octahedron cells, in a triangular antiprism vertex figure.
It contains an H2 subgroup tetrahexagonal tiling alternating square and hexagonal faces, with Coxeter diagram or half symmetry : A radial subgroup symmetry, index 6, of this honeycomb can be constructed with [(4,3,4,3*)], , represented by a trigonal trapezohedron fundamental domain, and Coxeter diagram .
It has a Coxeter diagram with [2,2]+ (order 4) extended symmetry in its rhombic disphenoid vertex figure.