Chapter 3.1 Guide to the tables

Symmetry relations between space groups

First Online Edition (2006)

Part 3. Relations between the Wyckoff positions

  1. Ulrich Müller

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000547

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Müller, U. 2006. Guide to the tables. International Tables for Crystallography. A1:3:3.1:428–433.

Author Information

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

Publication History

  1. Published Online: 1 JAN 2006


Group–subgroup relations among space groups imply definite relations between their Wyckoff positions and they often involve cell and coordinate transformations. This chapter describes the arrangement of the tables of relations given in Chapter 3.2. Aspects concerning the relations of the Wyckoff positions and the cell and coordinate transformations are discussed with the aid of several examples. Attention is drawn to details that have to be watched to avoid errors when using the tables. In particular, some intricate problems that can arise from origin shifts and from the use of nonconventional settings of space groups are pointed out.


  • interchange of Wyckoff labels;
  • Wyckoff positions;
  • cell transformations;
  • conjugate subgroups;
  • coordinate systems;
  • nonconventional settings;
  • orientational conjugation;
  • origin shift;
  • splitting of Wyckoff positions;
  • translational conjugation