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
Tetrahedral-octahedral honeycomb in 3 of 4 hyperplanes of the [4,3], formula_4 Coxeter group. Cells are irregular pyramids and can be seen as 1/12 of a cube, or 1/24 of a rhombic dodecahedron, each defined with three corner and the cube center. A related uniform skew apeirohedron exists with the same vertex arrangement, but triangles and square removed. It can be seen as truncated tetrahedra and truncated cubes augmented together. The gyrated tetrahedral-octahedral honeycomb or gyrated alternated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of octahedra and tetrahedra in a ratio of 1:2. It is vertex-uniform with