Chapter 9.2 Reduced bases

Space-group symmetry

First Online Edition (2006)

Part 9. Crystal lattices

  1. P. M. de Wolff

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000518

International Tables for Crystallography

International Tables for Crystallography

How to Cite

de Wolff, P. M. 2006. Reduced bases. International Tables for Crystallography. A:9:9.2:750–755.

Author Information

  1. Laboratorium voor Technische Natuurkunde, Technische Hogeschool, Delft, The Netherlands

Publication History

  1. Published Online: 1 JAN 2006


In this chapter, reduced bases (reduced cells) are described. The treatment starts with the definition of the reduced basis and the reduced form in terms of the metric tensor and lists the conditions (both main and special) for reduced bases of type-I cells and type-II cells. This is followed by a detailed and systematic geometric explanation of these conditions. The resulting 44 lattice characters are defined and tabulated, and the relations between the lattice characters and the conventional cell parameters of the 14 Bravais lattices are listed and discussed.


  • reduced bases;
  • lattice characters;
  • unit cell;
  • lattices;
  • Bravais types;
  • transformations