International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 |
International Tables for Crystallography (2010). Vol. B, ch. 1.5, p. 192
https://doi.org/10.1107/97809553602060000762 Appendix A1.5.1. Reciprocal-space groups^{a}Departamento de Fisíca de la Materia Condensada, Facultad de Cienca y Technología, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain , and ^{b}Institut für Kristallographie, Universität, D-76128 Karlsruhe, Germany |
This table is based on Table 1 of Wintgen (1941).
In order to obtain the Hermann–Mauguin symbol of from that of , one replaces any screw rotations by rotations and any glide reflections by reflections. The result is the symmorphic space group . For most space groups , the reciprocal-space group is isomorphic to , i.e. and belong to the same arithmetic crystal class. In the following cases is isomorphic to a symmorphic space group which is different from . Thus the arithmetic crystal classes of and are different, i.e. can not be obtained in this simple way:
References
Wintgen, G. (1941). Zur Darstellungstheorie der Raumgruppen. Math. Ann. 118, 195–215.