Chapter 12.3 Properties of the international symbols

Space-group symmetry

First Online Edition (2006)

Part 12. Space-group symbols and their use

  1. H. Burzlaff1,
  2. H. Zimmermann2

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000526

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Burzlaff, H. and Zimmermann, H. 2006. Properties of the international symbols. International Tables for Crystallography. A:12:12.3:823–832.

Author Information

  1. 1

    Universität Erlangen–Nürnberg, Robert-Koch-Strasse 4a, D-91080 Uttenreuth, Germany

  2. 2

    Institut für Angewandte Physik, Lehrstuhl für Kristallographie und Strukturphysik, Universität Erlangen–Nürnberg, Bismarckstrasse 10, D-91054 Erlangen, Germany

Publication History

  1. Published Online: 1 JAN 2006


The standard Schoenflies, Shubnikov and short and full international space-group symbols used in the present edition and the 1935 edition of International Tables are extensively tabulated. Examples are given of how to derive the space group from the short international symbol and how to derive the full symbol from the short symbol. The derivation of symmetry elements that are not given explicitly in the full symbol is described. Standardization rules for the short symbols are given, and systematic absences and generalized symmetry (e.g. colour groups) are briefly discussed.


  • space-group symbols;
  • international space-group symbols;
  • generators;
  • symmetry operations;
  • general position;
  • Hermann–Mauguin symbols;
  • Shubnikov symbols;
  • Schoenflies symbols;
  • systematic absences