Triangular tiling honeycomb 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 cells. Each edge of the honeycomb is surrounded by three cells, and each vertex is ideal with infinitely many cells meeting there. Its vertex figure is a hexagonal tiling. It has two lower reflective symmetry constructions, as an alternated order-6 hexagonal tiling honeycomb, ↔ , and as from , which
5-demicubic honeycomb for n≥5) and it Voronoi tessellation is a tritruncated 5-cubic honeycomb, , containing all with bitruncated 5-orthoplex, Voronoi cells. There are three uniform construction symmetries of this tessellation. Each symmetry can be represented by arrangements of different colors on the 32 5-demicube facets around each vertex. Regular and uniform honeycombs in 5-space: 5-demicubic honeycomb The 5-demicube honeycomb, or demipenteractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 5-space. It is constructed as an alternation of the regular 5-cube honeycomb. It is the first tessellation in the demihypercube honeycomb family which, with all the next ones, is not regular,