A Packing of Polyhedra

Truncated octahedra, truncated cuboctahedra, and cubes pack together in the ratio 1:1:3 to fill space. Here are a number of polyhedra, taken from the packing, which can be used for study and amusement. The edge lengths of the faces are the same as those used for the blocks derived from the packing of truncated octahedra. thing:2479574 - Truncated Octahedra as Children's Blocks

A simple representation of the packing uses a half truncated octahedral cage - "block_six.stl" and a truncated cuboctahedron - "basic_t_cuboctahedron.stl". Two half cages completely surround the truncated cuboctahedron illustrating the packing. See image above.

Six other combinations of the three polyhedra are provided. There are many ways to join them together to fill space. For example a checker board arrangement of "block_twenty.stl" and "block_four.stl" makes layers which nest layers of truncated cuboctahedra.

OpenSCAD code is included.