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

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

Section 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: 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 (1928a[link]) and Mauguin (1931[link]). This was used in Internationale Tabellen zur Bestimmung von Kristallstrukturen (IT 1935[link]) and was some­what modified in International Tables for X-ray Crystallography (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.


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).]
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).]
Hermann, C. (1928a). Zur systematischen Strukturtheorie I. Eine neue Raumgruppensymbolik. Z. Kristallogr. 68, 257–287.
Mauguin, Ch. (1931). Sur le symbolisme des groupes de répetition ou de symétrie des assemblages cristallins. Z. Kristallogr. 76, 542–558.
Schoenflies, A. (1891). Krystallsysteme und Krystallstructur. Leipzig: Teubner. [Reprint: Berlin: Springer (1984).]
Schoenflies, A. (1923). Theorie der Kristallstruktur. Berlin: Borntraeger.
Shubnikov, A. V. & Koptsik, V. A. (1972). Symmetry in Science and Art. Moscow: Nauka. (In Russian.) [Engl. transl: New York: Plenum (1974).]

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