Octahedral-hexagonal tiling honeycomb has a Coxeter diagram . A radial subgroup symmetry, index 6, of this honeycomb can be constructed with [(4,3,6,3)], represented by a trigonal trapezohedron fundamental domain, and Coxeter diagram . Octahedral-hexagonal tiling honeycomb In the geometry of hyperbolic 3-space, the octahedron-hexagonal tiling honeycomb is a paracompact uniform honeycomb, constructed from octahedron, hexagonal tiling, and trihexagonal tiling cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram, , and is named by its two regular cells. A lower symmetry form, index 6, of this honeycomb can be constructed with [(6,3,4,3)] symmetry, represented by a trigonal trapezohedron fundamental domain, and
Tetragonal disphenoid honeycomb edge. It can be seen as a cubic honeycomb with each cube subdivided by a center point into 6 square pyramid cells. The original cubic honeycomb walls are removed, joining pairs of square pyramids into square bipyramids (octahedra). Its vertex and edge framework is identical to the hexakis cubic honeycomb. There is one type of plane with faces: a flattended triangular tiling with half of the triangles as "holes". These cut face-diagonally through the original cubes. There are also square tiling plane that exist as nonface "holes" passing through the centers of the octahedral cells. It is dual to the