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. 12.1, p. 818

Section 12.1.1. Introduction

H. Burzlaffa and H. Zimmermannb*

a Universität 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

12.1.1. Introduction

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For symbolizing space groups, or more correctly types of space groups, different notations have been proposed. The following three are the main ones in use today:

  • (i) the notation of Schoenflies (1891[link], 1923[link]);

  • (ii) the notation of Shubnikov (Shubnikov & Koptsik, 1972[link]), which is frequently used in the Russian literature;

  • (iii) the international notation of Hermann (1928)[link] and Mauguin (1931)[link]. It was used in IT (1935)[link] and was somewhat modified in IT (1952)[link].

In all three notations, the space-group symbol is a modification of a point-group symbol.

Symmetry elements occur in lattices, and thus in crystals, only in distinct directions. Point-group symbols make use of these discrete directions and their mutual relations.

References

First citation Internationale Tabellen zur Bestimmung von Kristallstrukturen (1935). I. Band, edited by C. Hermann. Berlin: Borntraeger. [Reprint with corrections: Ann Arbor: Edwards (1944). Abbreviated as IT (1935).]Google Scholar
 First citation International Tables for X-ray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press. [Revised editions: 1965, 1969 and 1977. Abbreviated as IT (1952).]Google Scholar
 First citation Hermann, C. (1928). Zur systematischen Strukturtheorie I. Eine neue Raumgruppensymbolik. Z. Kristallogr. 68, 257–287.Google Scholar
 First citation Mauguin, Ch. (1931). Sur le symbolisme des groupes de répetition ou de symétrie des assemblages cristallins. Z. Kristallogr. 76, 542–558.Google Scholar
 First citation Schoenflies, A. (1891). Krystallsysteme und Krystallstructur. Leipzig: Teubner. [Reprint: Berlin: Springer (1984).]Google Scholar
 First citation Schoenflies, A. (1923). Theorie der Kristallstruktur. Berlin: Borntraeger.Google Scholar
 First citation Shubnikov, A. V. & Koptsik, V. A. (1972). Symmetry in science and art. Moscow: Nauka. (In Russian.) [Engl. transl: New York: Plenum (1974).]Google Scholar








































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