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 dodecahedral honeycomb pentagonal prism vertex figure. There are four rectified compact regular honeycombs: The truncated order-5 dodecahedral honeycomb, , has icosahedron and truncated dodecahedron cells, with a pentagonal pyramid vertex figure. The bitruncated order-5 dodecahedral honeycomb, , has truncated icosahedron cells, with a disphenoid vertex figure. The cantellated order-5 dodecahedral honeycomb, , has alternating rhombicosidodecahedron and icosidodecahedron cells, with a triangular prism vertex figure. The cantitruncated order-5 dodecahedral honeycomb, , has truncated icosidodecahedron, icosidodecahedron, and pentagonal prism cells, with a mirrored sphenoid vertex figure. The runcinated order-5 dodecahedral honeycomb, , has dodecahedron and pentagonal prism cells, with a triangular antiprism vertex figure.