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
Cubic honeycomb uniform honeycombs constructed by the formula_1 Coxeter group. The symmetry can be multiplied by the symmetry of rings in the Coxeter–Dynkin diagrams: <HR> The rectified cubic honeycomb or rectified cubic cellulation is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of octahedra and cuboctahedra in a ratio of 1:1. John Horton Conway calls this honeycomb a cuboctahedrille, and its dual an oblate octahedrille. The "rectified cubic honeycomb" can be orthogonally projected into the euclidean plane with various symmetry arrangements. There are four uniform colorings for the cells of this honeycomb with reflective symmetry, listed by their