Hexagonal tiling honeycomb The half-symmetry construction alternate two types of tetrahedra. The truncated hexagonal tiling honeycomb, t{6,3,3}, has tetrahedral and truncated hexagonal tiling facets, with a tetrahedral vertex figure. It is similar to the 2D hyperbolic truncated order-3 apeirogonal tiling, t{∞,3} with apeirogonal and triangle faces: The bitruncated hexagonal tiling honeycomb or bitruncated order-6 tetrahedral honeycomb, t{6,3,3}, has truncated tetrahedra and hexagonal tiling cells, with a tetrahedral vertex figure. The cantellated hexagonal tiling honeycomb, t{6,3,3}, has octahedral and rhombitrihexagonal tiling cells, with a triangular prism vertex figure. The cantitruncated hexagonal tiling honeycomb, t{6,3,3}, has truncated tetrahedron and truncated trihexagonal tiling cells, with a
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