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-square tiling honeycomb constructions exists with symmetry [(4,4,(4,3)*)], index 48 and an ideal regular octahedral fundamental domain. Cubic-square tiling honeycomb In the geometry of hyperbolic 3-space, the cubic-square tiling honeycomb is a paracompact uniform honeycomb, constructed from cube and square tiling cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram, , and is named by its two regular cells. It represents a semiregular honeycomb as defined by all regular cells, although from the Wythoff construction, rectified square tiling r{4,4}, becomes the regular square tiling {4,4}. A lower symmetry form, index 6, of this honeycomb can be constructed with [(4,4,4,3*] symmetry,