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
Rectified tesseractic honeycomb Rectified tesseractic honeycomb In four-dimensional Euclidean geometry, the rectified tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a rectification of a tesseractic honeycomb which creates new vertices on the middle of all the original edges, rectifying the cells into rectified tesseracts, and adding new 16-cell facets at the original vertices. Its vertex figure is an octahedral prism, {3,4}×{}. It is also called a quarter tesseractic honeycomb since it has half the vertices of the 4-demicubic honeycomb, and a quarter of the vertices of a tesseractic honeycomb. Regular and uniform honeycombs in 4-space: