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
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