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
Cubic-octahedral honeycomb in a rectangular pyramid vertex figure. It has a Coxeter diagram . The omnitruncated cubic-octahedral honeycomb is a compact uniform honeycomb, constructed from truncated cuboctahedron cells, in a rhombic disphenoid vertex figure. It has a Coxeter diagram with [2,2] (order 4) extended symmetry in its rhombic disphenoid vertex figure. Cubic-octahedral honeycomb In the geometry of hyperbolic 3-space, the cube-octahedron honeycomb is a compact uniform honeycomb, constructed from cube, octahedron, and cuboctahedron cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram, , and is named by its two regular cells. Wide-angle perspective views: It contains a subgroup H2