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 form: It is in a sequence of polychora and honeycomb with icosahedron vertex figures: It in a sequence of regular polychora and honeycombs with cubic cells. The first polytope in the sequence is the tesseract, and the second is the Euclidean cubic honeycomb. The rectified order-5 cubic honeycomb, , has alternating icosahedron and cuboctahedron cells, with a pentagonal prism vertex figure. There are four rectified compact regular honeycombs: The truncated order-5 cubic honeycomb, , has truncated cube and icosahedron cells, with a pentagonal pyramid vertex figure. It can be seen as analogous to the 2D hyperbolic truncated order-5 square tiling,