
Figure 3
Splitting of the cubic face form {123}_{cub} (hexakisoctahedron, point group 4/m2/m, 48 faces) into four rhombohedral subforms (12 faces each) of point group 2/m with their rhombohedral axes along [111]_{cub} and rhombohedral angle = 90° (cf. Appendix B). (a) {123}_{rh} (hexagonal dipyramid), (b) {23}_{rh} (ditrigonal scalenohedron), (c) {13}_{rh} (ditrigonal scalenohedron) and (d) {12}_{rh} (dihexagonal prism), (e) combination of these forms yields the cubic hexakisoctahedron. [Note that the central distances of the faces are different for the four rhombohedral forms, but equal in the combination (e).] 