Chapter 11.2 Derivation of symbols and coordinate triplets

Space-group symmetry

First Online Edition (2006)

Part 11. Symmetry operations

  1. W. Fischer,
  2. E. Koch

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000523

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Fischer, W. and Koch, E. 2006. Derivation of symbols and coordinate triplets. International Tables for Crystallography. A:11:11.2:812–816.

Author Information

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

Publication History

  1. Published Online: 1 JAN 2006


Chapter 11.2 describes a method for deriving the symbol of a symmetry operation (i.e. its type, the location of its symmetry element, and possibly its glide or screw vector) from its coordinate triplet as given in the ‘general position’ of a space group. The reverse procedure is also explained. A table shows the coordinate triplets and the 3 × 3 matrices for all symmetry operations of crystallographic point groups and for all orientations of the corresponding symmetry elements.


  • coordinate triplets;
  • symbols;
  • symmetry operations;
  • symmetry elements;
  • matrices for point-group symmetry operations