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.
Tetrahedral-octahedral honeycomb the vertex arrangement of the disphenoid tetrahedral honeycomb, dual honeycomb of the uniform bitruncated cubic honeycomb: It is also the body centered cubic, the union of two cubic honeycombs in dual positions. The kissing number of the D lattice is 8 and its Voronoi tessellation is a bitruncated cubic honeycomb, , containing all truncated octahedral Voronoi cells, . The [4,3,4], , Coxeter group generates 15 permutations of uniform honeycombs, 9 with distinct geometry including the alternated cubic honeycomb. The expanded cubic honeycomb (also known as the runcinated tesseractic honeycomb) is geometrically identical to the cubic honeycomb. The [4,3], , Coxeter