Triangular tiling honeycomb truncated hexagonal tiling cells, with a tetrahedral vertex figure. The cantellated triangular tiling honeycomb, , has truncated hexagonal tiling and triangular prism cells, with a triangular prism vertex figure. It can also be constructed as a half-symmetry form, cantic snub triangular tiling honeycomb, , symmetry [3,6,3]. The cantitruncated triangular tiling honeycomb, , has rhombitrihexagonal tiling and hexagonal prism cells, with a tetrahedron vertex figure. The runcinated triangular tiling honeycomb, , has hexagonal tiling and triangular prism cells, with a hexagonal antiprism vertex figure. The runcitruncated triangular tiling honeycomb, , has hexagonal tiling, rhombitrihexagonal tiling, triangular prism, and dodecagonal prism cells.
Tetragonal disphenoid honeycomb rectified cubic honeycomb with octahedral and cuboctahedral cells: The phyllic disphenoidal honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. John Horton Conway calls this an "Eighth pyramidille". A cell can be see as 1/48 of a translational cube with vertices positioned: one corner, one edge center, one face center, and the cube center. The edge colors and labels specify how many cells exist around the edge. It is dual to the omnitruncated cubic honeycomb: Tetragonal disphenoid honeycomb The tetragonal disphenoid tetrahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of identical tetragonal disphenoidal