Triangular tiling honeycomb The omnitruncated triangular tiling honeycomb, , has truncated trihexagonal tiling and hexagonal prism cells, with a tetrahedron vertex figure. The runcisnub triangular tiling honeycomb, , has trihexagonal tiling, triangular tiling, triangular prism, and triangular cupola cells. It is vertex-transitive, but not uniform, since it contains Johnson solid triangular cupola cells. Triangular tiling honeycomb The triangular tiling honeycomb is one of 11 paracompact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. It is called "paracompact" because it has infinite cells and vertex figures, with all vertices as ideal points at infinity. It has Schläfli symbol {3,6,3}, being composed of triangular tiling
Icosahedral honeycomb part of a sequence of regular polychora and honeycombs {3,"p",3}: It a part of a sequence of regular polychora and honeycombs {"p",5,"p"}: There are nine uniform honeycombs in the [3,5,3] Coxeter group family, including this regular form as well as the bitruncated form, t{3,5,3}, , also called "truncated dodecahedral honeycomb", each of whose cells are truncated dodecahedra. The rectified icosahedral honeycomb, t{3,5,3}, , has alternating dodecahedron and icosidodecahedron cells, with a triangular prism vertex figure: There are four rectified compact regular honeycombs: The truncated icosahedral honeycomb, t{3,5,3}, , has alternating dodecahedron and truncated icosahedron cells, with a triangular pyramid vertex