Figure 3
Splitting of the cubic face form {123}cub (hexakisoctahedron, point group 4/m[\overline 3]2/m, 48 faces) into four rhombohedral subforms (12 faces each) of point group [\overline 3]2/m with their rhombohedral axes along [111]cub and rhombohedral angle [alpha] = 90° (cf. Appendix B[link]). (a) {123}rh (hexagonal dipyramid), (b) {[\overline 1]23}rh (ditrigonal scalenohedron), (c) {1[\overline 2]3}rh (ditrigonal scalenohedron) and (d) {12[\overline 3]}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).]  [article HTML]

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