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
Bitruncated cubic honeycomb the Coxeter–Dynkin diagrams: This honeycomb can be alternated, creating pyritohedral icosahedra from the truncated octahedra with disphenoid tetrahedral cells created in the gaps. There are three constructions from three related Coxeter-Dynkin diagrams: , , and . These have symmetry [4,3,4], [4,(3)] and [3] respectively. The first and last symmetry can be doubled as <nowiki></nowiki>4,3,4 and [[3]]. The dual honeycomb is made of cells called ten-of-diamonds decahedra. This honeycomb is represented in the boron atoms of the α-rhombihedral crystal. The centers of the icosahedra are located at the fcc positions of the lattice. Bitruncated cubic honeycomb The bitruncated cubic honeycomb is