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
Rectified tesseractic honeycomb Rectified tesseractic honeycomb In four-dimensional Euclidean geometry, the rectified tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a rectification of a tesseractic honeycomb which creates new vertices on the middle of all the original edges, rectifying the cells into rectified tesseracts, and adding new 16-cell facets at the original vertices. Its vertex figure is an octahedral prism, {3,4}×{}. It is also called a quarter tesseractic honeycomb since it has half the vertices of the 4-demicubic honeycomb, and a quarter of the vertices of a tesseractic honeycomb. Regular and uniform honeycombs in 4-space: