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
5-cell honeycomb honeycomb. The cyclotruncated 4-simplex honeycomb or cyclotruncated 5-cell honeycomb is a space-filling tessellation honeycomb. It can also be seen as a birectified 5-cell honeycomb. It is composed of 5-cells, truncated 5-cells, and bitruncated 5-cells facets in a ratio of 2:2:1. Its vertex figure is an Elongated tetrahedral antiprism, with 8 equilateral triangle and 24 isosceles triangle faces, defining 8 5-cell and 24 truncated 5-cell facets around a vertex. It can be constructed as five sets of parallel hyperplanes that divide space into two half-spaces. The 3-space hyperplanes contain quarter cubic honeycombs as a collection facets. The truncated 4-simplex honeycomb or