Chapter 14.2 Symbols and properties of lattice complexes

Space-group symmetry

First Online Edition (2006)

Part 14. Lattice complexes

  1. W. Fischer,
  2. E. Koch

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000531

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Fischer, W. and Koch, E. 2006. Symbols and properties of lattice complexes. International Tables for Crystallography. A:14:14.2:848–872.

Author Information

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

Publication History

  1. Published Online: 1 JAN 2006


The reference symbols of lattice complexes are described and the terms ‘degrees of freedom’ of a lattice complex, ‘limiting complex’, ‘comprehensive complex’ and ‘Weissenberg complex’ are defined and illustrated by examples. Then the descriptive symbols of lattice complexes are introduced, their properties are described and their interpretation is demonstrated by numerous examples. Tables and give the explicit assignment of the Wyckoff positions of all plane groups and space groups, respectively, to Wyckoff sets and to lattice complexes. For each Wyckoff position, the reference symbol of the corresponding lattice complex is tabulated. In addition, a descriptive symbol is given that describes the arrangement of points in the corresponding point configurations. It refers directly to the coordinate description of the Wyckoff position.


  • lattice complexes;
  • Wyckoff positions;
  • Wyckoff sets;
  • degrees of freedom;
  • limiting lattice complexes;
  • comprehensive lattice complexes;
  • Weissenberg complexes;
  • invariant lattice complexes