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
Cubic honeycomb uniform honeycombs constructed by the formula_1 Coxeter group. The symmetry can be multiplied by the symmetry of rings in the Coxeter–Dynkin diagrams: <HR> The rectified cubic honeycomb or rectified cubic cellulation is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of octahedra and cuboctahedra in a ratio of 1:1. John Horton Conway calls this honeycomb a cuboctahedrille, and its dual an oblate octahedrille. The "rectified cubic honeycomb" can be orthogonally projected into the euclidean plane with various symmetry arrangements. There are four uniform colorings for the cells of this honeycomb with reflective symmetry, listed by their