The application of eigensymmetries of face forms to X-ray diffraction intensities of crystals twinned by `reticular merohedry'

Klapper, H.; Hahn, Th.

doi:10.1107/S0108767311032454

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

). (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).]