Triangular tiling honeycomb The omnitruncated triangular tiling honeycomb, , has truncated trihexagonal tiling and hexagonal prism cells, with a tetrahedron vertex figure. The runcisnub triangular tiling honeycomb, , has trihexagonal tiling, triangular tiling, triangular prism, and triangular cupola cells. It is vertex-transitive, but not uniform, since it contains Johnson solid triangular cupola cells. Triangular tiling honeycomb The triangular tiling honeycomb is one of 11 paracompact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. It is called "paracompact" because it has infinite cells and vertex figures, with all vertices as ideal points at infinity. It has Schläfli symbol {3,6,3}, being composed of triangular tiling
Cubic honeycomb around a vertex, making a chiral octahedral symmetry that can be stacked in all 3-dimensions: Individual cells have 2-fold rotational symmetry. In 2D orthogonal projection, this looks like a mirror symmetry. The truncated square prismatic honeycomb or tomo-square prismatic cellulation is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of octagonal prisms and cubes in a ratio of 1:1. It is constructed from a truncated square tiling extruded into prisms. It is one of 28 convex uniform honeycombs. <HR> The snub square prismatic honeycomb or simo-square prismatic cellulation is a space-filling tessellation (or honeycomb) in Euclidean 3-space.