Order-6 dodecahedral honeycomb are on the ideal surface. It is one of 15 regular hyperbolic honeycombs in 3-space, 11 of which like this one are paracompact, with infinite cells or vertex figures. There are 15 uniform honeycombs in the [5,3,6] Coxeter group family, including this regular form and its regular dual, order-5 hexagonal tiling honeycomb, {6,3,5}. This honeycomb is a part of a sequence of polychora and honeycombs with triangular tiling vertex figures: This honeycomb is a part of a sequence of regular polytopes and honeycombs with dodecahedral cells: The rectified order-6 dodecahedral honeycomb, t{5,3,6} has icosidodecahedron and triangular tiling cells connected in
Cubic-octahedral honeycomb in a rectangular pyramid vertex figure. It has a Coxeter diagram . The omnitruncated cubic-octahedral honeycomb is a compact uniform honeycomb, constructed from truncated cuboctahedron cells, in a rhombic disphenoid vertex figure. It has a Coxeter diagram with [2,2] (order 4) extended symmetry in its rhombic disphenoid vertex figure. Cubic-octahedral honeycomb In the geometry of hyperbolic 3-space, the cube-octahedron honeycomb is a compact uniform honeycomb, constructed from cube, octahedron, and cuboctahedron cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram, , and is named by its two regular cells. Wide-angle perspective views: It contains a subgroup H2