Chapter 5.1 Transformations of the coordinate system (unit‐cell transformations)

Space‐group symmetry

First Online Edition (2006)

Part 5. Transformations in crystallography

  1. H. Arnold

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000510

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Arnold, H. 2006. Transformations of the coordinate system (unit‐cell transformations). International Tables for Crystallography. A:5:5.1:78–85.

Author Information

  1. Institut für Kristallographie, Rheinisch‐Westfälische Technische Hochschule, Aachen, Germany

Publication History

  1. Published Online: 1 JAN 2006



Transformations of the coordinate system are useful when nonconventional descriptions of a crystal structure are considered, for instance in the study of relations between different structures, of phase transitions and of group–subgroup relations. Unit‐cell transformations occur particularly frequently when different settings or cell choices of monoclinic, orthorhombic or rhombohedral space groups are to be compared or when ‘reduced cells’ are derived. In this chapter, matrix notation is used to describe a general transformation. Selected frequently occurring transformation matrices are tabulated and illustrated by diagrams.


  • coordinate systems;
  • unit‐cell transformations;
  • transformation matrices