in 3D

Tessellating space with truncated octahedra

the following video is a grasshopper definition that shows how the cuboctahedron and the truncated octahedron can be modelled from the regular octahedron. The definition also shows that truncated octahedra fill space by translation of their replicas, since the sum of the amplitude of the dihedral angles of truncated octahedra, placed in a certain position, adds up to 360º.

This and other examples are included in my Doctoral Thesis.

tessellating space with truncated octahedra (by vera viana)