Figure 2
(a) Stereographic projection of a general {hkl} form in point group m. (b) Reflection across the (010) plane applied to (a). The two projections have point group m.. (c) Fourfold vertical rotation applied to (a). (d) Fourfold vertical rotation applied to (b). The two projections have point group .m. (e) Overlap of (a) and (b) leading to a form with point group mm2. (f) Overlap of (c) and (d) leading to a form with point group mm2. The operations in mm2 not contained in .m. map directly (a) to (b) and the operations in mm2 not contained in m.. map directly (c) to (d); they map by conjugation the respective point groups, which in this case do not coincide. (g) Overlap of (a) and (c). (h) Overlap of (b) and (d). (i) Overlap of (a) and (d). (j) Overlap of (b) and (c). These four forms have as nontrivial symmetry operation a reflection across a diagonal plane: the reflections in the original forms as well as the fourfold rotation do not appear in the point group of the compound form because they act only as partial operations. |