Dodecahedral-icosahedral honeycomb square antiprism vertex figure. It has a Coxeter diagram . The cyclotruncated icosahedral-dodecahedral honeycomb is a compact uniform honeycomb, constructed from dodecahedron, truncated icosahedron cells, in a triangular antiprism vertex figure. It has a Coxeter diagram . It can be see as somewhat analogous to the pentahexagonal tiling with pentagonal and hexagonal faces: The truncated dodecahedral-icosahedral honeycomb is a compact uniform honeycomb, constructed from truncated icosahedron, truncated dodecahedron, rhombicosidodecahedron, truncated icosidodecahedron cells, in a trapezoidal pyramid vertex figure. It has a Coxeter diagram . The omnitruncated dodecahedral-icosahedral honeycomb is a compact uniform honeycomb, constructed from truncated icosidodecahedron cells, in a
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