A Packing of Polyhedra

thingiverse

Truncated octahedra, truncated cuboctahedra, and cubes pack together in a precise ratio of 1:1:3 to fill space efficiently. A collection of polyhedra, carefully extracted from the packing, offers numerous study and amusement opportunities for kids. The edge lengths of these faces are identical to those used for blocks derived from the packing of truncated octahedra. A simplified representation of the packing employs a half-truncated octahedral cage - "block_six.stl" and a truncated cuboctahedron - "basic_t_cuboctahedron.stl". Two complete cages fully surround the truncated cuboctahedron, demonstrating the packing arrangement. See the image above. Six additional combinations of these three polyhedra are provided. There are many creative ways to connect them together to fill space effectively. For instance, a checkerboard arrangement of "block_twenty.stl" and "block_four.stl" creates layers that nest perfectly with layers of truncated cuboctahedra. OpenSCAD code is included for convenience.