There are 28 such tessellations. See B. Grünbaum, Uniform tilings of 3-space. Geombinatorics 4(1994), 49 - 56.

The tiling of octahedra and tetrahedra is of special importance since its vertices form a cubic close-packing of spheres. All of these are found in crystal arrangements.

Some important examples are:

- The tiling of cubes
- The tiling of octahedra and cuboctahedra
- The tiling of truncated octahedra
- The tiling of octahedra and tetrahedra
- The tiling of tetrahedra and truncated tetrahedra

- The Uniform Polyhedra
- Virtual Reality Polyhedra The Encyclopedia of Polyhedra