Cubic-octahedral honeycomb honeycomb is a compact uniform honeycomb, constructed from cube, truncated octahedron cells, in a triangular antiprism vertex figure. It has a Coxeter diagram . It contains an H2 subgroup tetrahexagonal tiling alternating square and hexagonal faces, with Coxeter diagram or half symmetry : A radial subgroup symmetry, index 6, of this honeycomb can be constructed with [(4,3,4,3)], , represented by a trigonal trapezohedron fundamental domain, and Coxeter diagram . This lower symmetry can be extended by restoring one mirror as . The truncated cubic-octahedral honeycomb is a compact uniform honeycomb, constructed from truncated octahedron, truncated cube, rhombicuboctahedron, truncated cuboctahedron cells,
Cyclotruncated 5-simplex honeycomb on each hyperplane. Regular and uniform honeycombs in 5-space: Cyclotruncated 5-simplex honeycomb In five-dimensional Euclidean geometry, the cyclotruncated 5-simplex honeycomb or cyclotruncated hexateric honeycomb is a space-filling tessellation (or honeycomb). It is composed of 5-simplex, truncated 5-simplex, and bitruncated 5-simplex facets in a ratio of 1:1:1. Its vertex figure is an elongated 5-cell antiprism, two parallel 5-cells in dual configurations, connected by 10 tetrahedral pyramids (elongated 5-cells) from the cell of one side to a point on the other. The vertex figure has 8 vertices and 12 5-cells. It can be constructed as six sets of parallel hyperplanes that divide