Order-6 hexagonal tiling honeycomb . The "cantellated order-6 hexagonal tiling honeycomb", t{6,3,6}, has trihexagonal tiling and rhombitrihexagonal tiling cells, with a triangular prism vertex figure. The "cantitruncated order-6 hexagonal tiling honeycomb", t{6,3,6}, has hexagonal tiling and truncated trihexagonal tiling cells, with a triangular prism vertex figure. The runcinated order-6 hexagonal tiling honeycomb, t{6,3,6}, has hexagonal tiling and hexagonal prism cells, with a triangular antiprism vertex figure. It is analogous to the 2D hyperbolic rhombihexahexagonal tiling, rr{6,6}, with square and hexagonal faces: The runcitruncated order-6 hexagonal tiling honeycomb, t{6,3,6}, has Truncated hexagonal tiling, rhombitrihexagonal tiling, hexagonal prism, and dodecagonal prism cells. The omnitruncated order-6 hexagonal
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