Rhombic dodecahedral honeycomb cells. The vertices with the acute rhombic face angles have 6 cells. The rhombic dodecahedron can be twisted on one of its hexagonal cross-sections to form a trapezo-rhombic dodecahedron, which is the cell of a somewhat similar tessellation, the Voronoi diagram of hexagonal close-packing. The "rhombic dodecahedral honeycomb" can be dissected into a trigonal trapezohedral honeycomb with each rhombic dodecahedron dissected into 4 trigonal trapezohedrons. Each rhombic dodecahedra can also be dissected with a center point into 12 rhombic pyramids of the rhombic pyramidal honeycomb. The trapezo-rhombic dodecahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It consists
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