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
2 22 honeycomb types of cells: octahedron, 0, and tetrahedron, 0. The 2 honeycomb, is fourth in a dimensional series of uniform polytopes, expressed by Coxeter as k series. The final is a paracompact hyperbolic honeycomb, 3. Each progressive uniform polytope is constructed from the previous as its vertex figure. The 2 honeycomb is third in another dimensional series 2. 2 22 honeycomb In geometry, the 2 honeycomb is a uniform tessellation of the six-dimensional Euclidean space. It can be represented by the Schläfli symbol {3,3,3}. It is constructed from 2 facets and has a 1 vertex figure, with 54 2 polytopes around