Chapter 11.1 Point coordinates, symmetry operations and their symbols

Space‐group symmetry

First Online Edition (2006)

Part 11. Symmetry operations

  1. W. Fischer,
  2. E. Koch

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000522

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Fischer, W. and Koch, E. 2006. Point coordinates, symmetry operations and their symbols. International Tables for Crystallography. A:11:11.1:810–811.

Author Information

  1. Institut für Mineralogie, Petrologie und Kristallographie, Philipps‐Universität, D‐35032 Marburg, Germany

Publication History

  1. Published Online: 1 JAN 2006



Chapter 11.1 deals with the different ways of representing symmetry operations, e.g. as linear equations, as pairs of a 3 × 3 and a 3 × 1 matrix, and as coordinate triplets (cf. ‘General positions’ in Part 7). The notation used under the heading ‘Symmetry operations’ in Parts 6 and 7 is explained. This kind of symbol contains information on the type of the symmetry operation, on the location of the corresponding symmetry element and, if necessary, on the glide or screw vector.


  • point coordinates;
  • coordinate triplets;
  • symmetry operations;
  • symbols