Chapter 1.5 Remarks on Wyckoff positions

Symmetry relations between space groups

Second Online Edition (2011)

Part 1. Space groups and their subgroups

  1. Ulrich Müller

Published Online: 15 DEC 2011

DOI: 10.1107/97809553602060000794

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Müller, U. 2011. Remarks on Wyckoff positions. International Tables for Crystallography. A1:1:1.5:41–43.

Author Information

  1. Fachbereich Chemie, Philipps‐Universität, D‐35032 Marburg, Germany

Publication History

  1. Published Online: 15 DEC 2011



The difference between crystallographic orbits, Wyckoff positions and Wyckoff sets is explained. Upon symmetry reduction of a space group to one of its subgroups, the Wyckoff positions of the space group will result in certain Wyckoff positions of the subgroup. The laws governing these kinds of relations are the subject of this chapter.


  • Euclidean normalizers;
  • affine normalizers;
  • Wyckoff positions;
  • Wyckoff sets;
  • group–subgroup relations;
  • multiplicities;
  • phase transitions;
  • splitting of Wyckoff positions;
  • Punktlage;
  • point configurations;
  • orbits;
  • derivative structures;
  • hettotypes;
  • aristotypes