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
Order-8-3 triangular honeycomb construction as a uniform honeycomb, Schläfli symbol {∞,(8,∞,8)}, Coxeter diagram, , with alternating types or colors of cells. Order-8-3 triangular honeycomb In the geometry of hyperbolic 3-space, the order-8-3 triangular honeycomb (or 3,8,3 honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,8,3}. It has three order-8 triangular tiling {3,8} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many triangular tilings existing around each vertex in an octagonal tiling vertex figure. It is a part of a sequence of regular honeycombs with order-8 triangular tiling cells: {3,8,"p"}. It is a part of