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
24-cell honeycomb 24-cell honeycomb In four-dimensional Euclidean geometry, the 24-cell honeycomb, or icositetrachoric honeycomb is a regular space-filling tessellation (or honeycomb) of 4-dimensional Euclidean space by regular 24-cells. It can be represented by Schläfli symbol {3,4,3,3}. The dual tessellation by regular 16-cell honeycomb has Schläfli symbol {3,3,4,3}. Together with the tesseractic honeycomb (or 4-cubic honeycomb) these are the only regular tessellations of Euclidean 4-space. If a 3-sphere is inscribed in each hypercell of this tessellation, the resulting arrangement is the densest possible regular sphere packing in four dimensions, with the kissing number 24. The packing density of this arrangement is The 24-cell