On the real combinations of cubes and octahedra

All the real combinations of cubes and octahedra (77657 in total) are enumerated and characterized by facet symbols and symmetry point groups. The most symmetrical polyhedra (with automorphism group orders not less than 6, 163 in total) are shown. It is assumed that they represent the most probable forms of natural diamond crystals. The results are discussed with respect to the Curie dissymmetry principle.