Hexagonal tiling honeycomb tetrahedron vertex figure. The runcinated hexagonal tiling honeycomb, t{6,3,3}, has tetrahedron, rhombitrihexagonal tiling hexagonal prism, triangular prism cells, with a octahedron vertex figure. The runcitruncated hexagonal tiling honeycomb, t{6,3,3}, has cuboctahedron, Triangular prism, Dodecagonal prism, and truncated hexagonal tiling cells, with a quad-pyramid vertex figure. The runcicantellated hexagonal tiling honeycomb or runcitruncated order-6 tetrahedral honeycomb, t{6,3,3}, has truncated tetrahedron, hexagonal prism, hexagonal prism, and rhombitrihexagonal tiling cells, with a quad-pyramid vertex figure. The omnitruncated hexagonal tiling honeycomb or omnitruncated order-6 tetrahedral honeycomb, t{6,3,3}, has truncated octahedron, hexagonal prism, dodecagonal prism, and truncated trihexagonal tiling cells, with a quad-pyramid vertex figure.
Tetrahedral-octahedral honeycomb Conway calls this honeycomb a 3-RCO-trille, and its dual quarter cubille. The dual of a "runcic cubic honeycomb" is called a quarter cubille, with Coxeter diagram , with faces in 2 of 4 hyerplanes of the formula_3, [4,3] symmetry fundamental domain. Cells can be seen as 1/4 of dissected cube, using 4 vertices and the center. Four cells exist around 6 edges, and 3 cells around 3 edges. It is related to the runcinated cubic honeycomb, with quarter of the cubes alternated into tetrahedra, and half expanded into rhombicuboctahedra. This honeycomb can be divided on truncated square tiling planes, using