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,(31,1)⁺] and [3]⁺ respectively.
The first and last symmetry can be doubled as [[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.
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,(31,1)⁺] and [3]⁺ respectively. The first and last symmetry can be doubled as [[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