International
Tables for Crystallography Volume A Space-group symmetry Edited by Th. Hahn © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. A. ch. 2.2, pp. 18-19
Section 2.2.4.1. Present symbols
a
Institut für Kristallographie, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany, and bLaboratorium voor Chemische Fysica, Rijksuniversiteit Groningen, The Netherlands |
Both the short and the full Hermann–Mauguin symbols consist of two parts: (i) a letter indicating the centring type of the conventional cell, and (ii) a set of characters indicating symmetry elements of the space group (modified point-group symbol).
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For the different crystal lattices, the Hermann–Mauguin space-group symbols have the following form:
Short and full Hermann–Mauguin symbols differ only for the plane groups of class m, for the monoclinic space groups, and for the space groups of crystal classes mmm, , , , and . In the full symbols, symmetry axes and symmetry planes for each symmetry direction are listed; in the short symbols, symmetry axes are suppressed as much as possible. Thus, for space group No. 62, the full symbol is and the short symbol is Pnma. For No. 194, the full symbol is and the short symbol is . For No. 230, the two symbols are and .
Many space groups contain more kinds of symmetry elements than are indicated in the full symbol (`additional symmetry elements', cf. Chapter 4.1 ). A complete listing of the symmetry elements is given in Tables 4.2.1.1 and 4.3.2.1 under the heading Extended full symbols. Note that a centre of symmetry is never explicitly indicated (except for space group ); its presence or absence, however, can be readily inferred from the space-group symbol.
References
Heesch, H. (1929). Zur systematischen Strukturtheorie. II. Z. Kristallogr. 72, 177–201.Google Scholar