Octahedral-hexagonal tiling honeycomb 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 a Coxeter diagram . The cyclotruncated octahedral-hexagonal tiling honeycomb is a compact uniform honeycomb, constructed from hexagonal tiling, cube, and truncated octahedron cells, in a triangular antiprism vertex figure. It
Cubic honeycomb projected into the euclidean plane with various symmetry arrangements. There is a second uniform coloring by reflectional symmetry of the Coxeter groups, the second seen with alternately colored truncated cubic cells. <HR> The alternated bitruncated cubic honeycomb or bisnub cubic honeycomb can be creating regular icosahedron from the truncated octahedra with irregular tetrahedral cells created in the gaps. There are three constructions from three related Coxeter diagrams: , , and . These have symmetry [4,3,4], [4,(3)] and [3] respectively. The first and last symmetry can be doubled as <nowiki></nowiki>4,3,4 and [[3]]. This honeycomb is represented in the boron atoms of