Figure 1
(a) Stereographic projection of a general {hkl} form in point group ..2. (b) Reflection across the (010) plane applied to (a). (c) Fourfold vertical rotation applied to (a). (d) Fourfold vertical rotation applied to (b). The four projections all have point group ..2. (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 ..2 map directly (a) to (b) and (c) to (d) and map by conjugation the respective point groups, which in this case coincide. (g) Overlap of (a) and (c) leading to a form with point group 4. (h) Overlap of (b) and (d) leading to a form with point group 4. The operations in 4 not contained in ..2 map directly (a) to (c) and (b) to (d) and map by conjugation the respective point groups, which coincide. (i) Overlap of (a) and (d) leading to a form with point group 2.mm. (j) Overlap of (b) and (c) leading to a form with point group 2.mm. The operations in 2.mm not contained in ..2 map directly (a) to (d) and (b) to (c) and map by conjugation the respective point groups, which coincide. (k) Overlap of (a), (b), (c) and (d) leading to a form with point group 4mm. The operations in 4mm not contained in ..2 map directly (a) to (b), (c) and (d) and map by conjugation the respective point groups, which coincide. |