Tables for
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.3, p. 790

Section Generalized symmetry

H. Burzlaffa and H. Zimmermannb*

aUniversität Erlangen–Nürnberg, Robert-Koch-Strasse 4a, D-91080 Uttenreuth, Germany, and bInstitut für Angewandte Physik, Lehrstuhl für Kristallographie und Strukturphysik, Universität Erlangen–Nürnberg, Bismarckstrasse 10, D-91054 Erlangen, Germany
Correspondence e-mail: Generalized symmetry

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The international symbols can be suitably modified to describe generalized symmetry, e.g. colour groups, which occur when the symmetry operations are combined with changes of physical properties. For the description of antisymmetry (or `black–white' symmetry), the symbols of the Bravais lattices are supplemented by additional letters for centrings accompanied by a change in colour. For symmetry operations that are not translations, a prime is added to the usual symbol if a change of colour takes place. A complete description of the symbols and a detailed list of references are given by Koptsik (1966[link]). The Shubnikov symbols have not been extended to colour symmetry.

An introduction to the structure, properties and symbols of magnetic subperiodic and magnetic space groups is given in Chapter 3.6[link] .


Koptsik, V. A. (1966). Shubnikov Groups. Moscow University Press. (In Russian.)

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