The stella octangula can be seen as either an octahedron with a tetrahedron placed on each face, or as the union of two overlapping tetrahedra. In combination with with the octahedron the stella octangula can fill space. The stella octangula has 24 equilateral triangle faces; The octahedron has 8 equilateral triangle faces. The three-sided laser-cut pieces used here represent those faces.

Material: laser-cut plywood

The truncated octahedron has eight regular hexagon faces and six square faces. The six-sided and four-sided pieces used here represent those faces.

Material: laser-cut plywood

The rhombic dodecahedron has twelve rhombus-shaped faces. The four-sided pieces used here represent those faces.

Material: laser-cut plywood

The pieces are all the same, but only some of them represent the faces of the cubes; the others serve as connectors. Because the cube space packing is a self-dual, one may also observe that duality here by exchanging which pieces one views as faces versus connectors.

Material: laser-cut plywood