Chapter 8.1 Basic concepts

Space-group symmetry

First Online Edition (2006)

Part 8. Introduction to space-group symmetry

  1. H. Wondratschek

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000514

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Wondratschek, H. 2006. Basic concepts. International Tables for Crystallography. A:8:8.1:720–725.

Author Information

  1. Institut für Kristallographie, Universität, D-76128 Karlsruhe, Germany

Publication History

  1. Published Online: 1 JAN 2006


Part 8 provides the theoretical background to the data in the tables and diagrams of Volume A. In Chapter 8.1, the basic concepts are treated, such as point and vector spaces; motions (isometries) and their description by matrices and augmented matrices; crystal patterns (as mathematical models of ideal crystals) with their point and vector lattices; crystallographic symmetry operations and symmetry groups as well as space groups (as symmetry groups of crystal patterns), point groups (as symmetry groups of macroscopic crystals) and their relations.


  • symmetry;
  • space groups;
  • point groups;
  • cosets;
  • coset decomposition;
  • crystal classes;
  • motions;
  • symmetry operations;
  • symmetry groups;
  • vector lattices;
  • point lattices;
  • crystal patterns;
  • unit cell;
  • symmetry elements