Chapter 14.3 Applications of the lattice-complex concept

Space-group symmetry

First Online Edition (2006)

Part 14. Lattice complexes

  1. W. Fischer,
  2. E. Koch

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000532

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Fischer, W. and Koch, E. 2006. Applications of the lattice-complex concept. International Tables for Crystallography. A:14:14.3:873–876.

Author Information

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

Publication History

  1. Published Online: 1 JAN 2006


Chapter 14.3 gives a short introduction to some applications of lattice complexes: (i) The knowledge of the assignment of the Wyckoff positions to lattice complexes considerably facilitates the study of geometrical properties of point configurations. (ii) Relations between crystal structures with different symmetries are often discernible because the corresponding Wyckoff positions either belong to the same lattice complex or because a limiting-complex relationship exists. (iii) Wyckoff positions belonging to the same lattice complex show analogous reflection conditions. (iv) If a phase transition of a crystal is connected with a group–subgroup degradation, comparison of the lattice complexes corresponding to the Wyckoff positions of the original space group on the one hand and of its various subgroups on the other hand very often shows which of these subgroups are suitable for the low-symmetry modification. (v) Many incorrect space-group assignments to crystal structures could be avoided by simply looking at the lattice complexes (and their descriptive symbols) that correspond to the Wyckoff positions occupied by the different kinds of atoms.


  • lattice complexes;
  • point configurations;
  • reflection conditions;
  • phase transitions;
  • relations between crystal structures;
  • space-group assignment