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. 779

Section 3.3.2.1. Introduction

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

3.3.2.1. Introduction

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Each space group is related to a crystallographic point group. Space-group symbols, therefore, can be obtained by a modification of point-group symbols. The simplest modification which merely gives an enumeration of the space-group types (cf. Section 1.3.4.1[link] ) has been used by Schoenflies. The Shubnikov and Hermann–Mauguin symbols, however, reveal the glide or screw components of the symmetry operations and are designed in such a way that the nature of the symmetry elements and their relative locations can be deduced from the symbol. [A detailed discussion and listings of computer-adapted space-group symbols implemented in crystallographic software, such as the so-called Hall symbols (Hall, 1981a[link],b[link]) or explicit symbols (Shmueli, 1984[link]), can be found in Chapter 1.4[link] of International Tables for Crystallography, Volume B (2008)[link].]

References

International Tables for Crystallography (2008). Vol. B, Reciprocal Space. Edited by U. Shmueli, 3rd ed. Heidelberg: Springer.
Hall, S. R. (1981a). Space-group notation with an explicit origin. Acta Cryst. A37, 517–525.
Hall, S. R. (1981b). Space-group notation with an explicit origin; erratum. Acta Cryst. A37, 921.
Shmueli, U. (1984). Space-group algorithms. I. The space group and its symmetry elements. Acta Cryst. A40, 559–567.








































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