Cubes are aligned side by side and then slid along their faces. Since the cube is divided into an octet part and a tet part, it is possible to show how octahedra and tetrahedra can be slid along one another. Also, the same arrangement is valid for rhombohedra, if one diagonal of the cube is varied, possibly even to zero.
Potentially, this Demonstration can be used for exploring possible crystal structures. There may also be applications in architecture, for example, tiling.