International
Tables for Crystallography Volume A Space-group symmetry Edited by M. I. Aroyo © International Union of Crystallography 2015 |
International Tables for Crystallography (2015). Vol. A, ch. 1.4, pp. 42-73
https://doi.org/10.1107/97809553602060000922 Chapter 1.4. Space groups and their descriptions
B. Souvignier,^{d} H. Wondratschek,^{e}^{‡} M. I. Aroyo,^{a}^{*} G. Chapuis^{b} and A. M. Glazer^{c}
^{a}Departamento de Física de la Materia Condensada, Universidad del País Vasco (UPV/EHU), Bilbao, Spain,^{b}École Polytechnique Fédérale de Lausanne, BSP/Cubotron, CH-1015 Lausanne, Switzerland,^{c}Department of Physics, University of Oxford, Parks Road, Oxford, United Kingdom,^{d}Radboud University Nijmegen, Faculty of Science, Mathematics and Computing Science, Institute for Mathematics, Astrophysics and Particle Physics, Postbus 9010, 6500 GL Nijmegen, The Netherlands, and ^{e}Laboratorium für Applikationen der Synchrotronstrahlung (LAS), Universität Karlsruhe, Germany |
Footnotes
^{‡}Deceased.
^{2} The numbers listed are those for bipolar directions, for which direction and opposite direction are equivalent. For the corresponding polar directions in cubic space groups only the four equivalent polar directions or of the tetrahedron occur.
^{3} The `symmetry-element' interpretation of the constituents of the HM symbols (cf. footnote 1^{1}) results in the following modification of the `simplest-operation' rule [known as the `priority rule', cf. Section 4.1.2.3 of International Tables for Crystallography, Volume A (2002) (referred to as IT A5)]: When more than one kind of symmetry element exists in a given direction, the choice of the corresponding symbols in the space-group symbol is made in order of descending priority , and rotation axes before screw axes.
^{4} In the original HM symbols the constituent `1' was avoided by the use of different centred cells.
^{5} One usually chooses as the representative direction and not the equivalent direction [110], in analogy to the cases of trigonal and hexagonal space groups where is the representative of the set of tertiary symmetry directions, while (or [110]) belongs to the set of secondary symmetry directions, cf. Table 2.1.3.1 .
^{6} Note: `3' or `' directly after the lattice symbol denotes a trigonal or rhombohedral space group; `3' or `' in the third position (second position after the lattice symbol) is characteristic for cubic space groups.