Chapter 1.4 Arithmetic crystal classes and symmorphic space groups

Mathematical, physical and chemical tables

First Online Edition (2006)

Part 1. Crystal geometry and symmetry

  1. A. J. C. Wilson

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000575

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Wilson, A. J. C. 2006. Arithmetic crystal classes and symmorphic space groups. International Tables for Crystallography. C:1:1.4:15–22.

Author Information

  1. St John’s College, Cambridge CB2 1TP, England

Publication History

  1. Published Online: 1 JAN 2006


Arithmetic crystal classes have four main applications in practical crystallography: in the classification of space groups; in forming symbols for certain space groups in higher dimensions; in modelling the frequency of occurrence of space groups; and in establishing ‘equivalent origins’. Simple descriptions and complete enumerations of the arithmetic crystal classes in one, two and three dimensions are given in this chapter. Symmorphic space groups and the effect of dispersion on diffraction symmetry are also discussed.


  • anomalous dispersion;
  • arithmetic crystal classes;
  • classification;
  • crystal classes;
  • dispersion;
  • one-dimensional crystal classes;
  • space groups;
  • symmetry;
  • symmorphism;
  • three-dimensional crystal classes