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 edge. It can be seen as a cubic honeycomb with each cube subdivided by a center point into 6 square pyramid cells. The original cubic honeycomb walls are removed, joining pairs of square pyramids into square bipyramids (octahedra). Its vertex and edge framework is identical to the hexakis cubic honeycomb. There is one type of plane with faces: a flattended triangular tiling with half of the triangles as "holes". These cut face-diagonally through the original cubes. There are also square tiling plane that exist as nonface "holes" passing through the centers of the octahedral cells. It is dual to the