Triangular tiling honeycomb infinite cells or vertex figures. There are nine uniform honeycombs in the [3,6,3] Coxeter group family, including this regular form as well as the bitruncated form, t{3,6,3}, with all truncated hexagonal tiling facets. The rectified triangular tiling honeycomb, , has alternating trihexagonal tiling and hexagonal tiling cells, with a triangular prism vertex figure. A lower symmetry of this honeycomb can be constructed as a "cantic order-6 hexagonal tiling honeycomb", ↔ . A second lower construction, index is ↔ . The truncated triangular tiling honeycomb, is the same as the hexagonal tiling honeycomb, . The bitruncated triangular tiling honeycomb, , has
Order-5 cubic honeycomb and pentagonal prism cells, with an octahedron vertex figure. It is analogous to the 2D hyperbolic rhombitetrapentagonal tiling, rr{4,5}, with square and pentagonal faces: It is similar to the Euclidean (order-4) runcinated cubic honeycomb, t{4,3,4}: The runcitruncated order-5 cubic honeycomb or runcicantellated order-4 dodecahedral honeycomb , has cube, dodecahedron, and pentagonal prism cells, with a quad-pyramid vertex figure. It is similar to the Euclidean (order-4) runcitruncated cubic honeycomb, t{4,3,4}: The omnitruncated order-5 cubic honeycomb or omnitruncated order-4 dodecahedral honeycomb has Coxeter diagram . It is similar to the Euclidean (order-4) omnitruncated cubic honeycomb, t{4,3,4}: In 3-dimensional hyperbolic geometry, the alternated