Cubic-octahedral honeycomb honeycomb is a compact uniform honeycomb, constructed from cube, truncated octahedron cells, in a triangular antiprism vertex figure. It has a Coxeter diagram . 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 . This lower symmetry can be extended by restoring one mirror as . The truncated cubic-octahedral honeycomb is a compact uniform honeycomb, constructed from truncated octahedron, truncated cube, rhombicuboctahedron, truncated cuboctahedron cells,
Quarter cubic honeycomb Quarter cubic honeycomb The quarter cubic honeycomb, quarter cubic cellulation or bitruncated alternated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of tetrahedra and truncated tetrahedra in a ratio of 1:1. It is called "quarter-cubic" because its symmetry unit – the minimal block from which the pattern is developed by reflections – consists of four such units of the cubic honeycomb. It is vertex-transitive with 6 truncated tetrahedra and 2 tetrahedra around each vertex. It is one of the 28 convex uniform honeycombs. The faces of this honeycomb's cells form four families of parallel