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

International Tables for Crystallography (2016). Vol. A, ch. 3.3, p. 777

Table 3.3.1.1 

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:  helmuth.zimmermann@krist.uni-erlangen.de

Table 3.3.1.1| top | pdf |
International (Hermann–Mauguin) and Shubnikov symbols for sym­metry elements

The first power of a symmetry operation is often designated by the symmetry-element symbol without exponent 1, the other powers of the operation carry the appropriate exponent.

 Symmetry elements
of the first kindof the second kind
Hermann–Mauguin 1 2 3 4 6 [\bar{1}\quad m\quad \bar{3}\quad \bar{4}\quad \bar{6}]
Shubnikov 1 2 3 4 6 [\tilde{2}\quad m\quad \tilde{6}\quad \tilde{4}\quad \tilde{3}]
According to a private communication from J. D. H. Donnay, the symbols for elements of the second kind were proposed by M. J. Buerger. Koptsik (1966[link]) used them for the Shubnikov method.