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
2 22 honeycomb types of cells: octahedron, 0, and tetrahedron, 0. The 2 honeycomb, is fourth in a dimensional series of uniform polytopes, expressed by Coxeter as k series. The final is a paracompact hyperbolic honeycomb, 3. Each progressive uniform polytope is constructed from the previous as its vertex figure. The 2 honeycomb is third in another dimensional series 2. 2 22 honeycomb In geometry, the 2 honeycomb is a uniform tessellation of the six-dimensional Euclidean space. It can be represented by the Schläfli symbol {3,3,3}. It is constructed from 2 facets and has a 1 vertex figure, with 54 2 polytopes around