International
Tables for Crystallography Volume A1 Symmetry relations between space groups Edited by Hans Wondratschek and Ulrich Müller © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. A1. ch. 1.2, p. 8
Section 1.2.2.5. Isometries
a
Institut für Kristallographie, Universität, D-76128 Karlsruhe, Germany |
Isometries are special affine mappings, as in Definition 1.2.2.1.1. The matrix W of an isometry has to fulfil conditions which depend on the coordinate basis. These conditions are:
Algorithms for the determination of the kind of isometry from a given matrix–column pair and for the determination of the matrix–column pair for a given isometry can be found in IT A, Part 11 or in Hahn & Wondratschek (1994).
References
Hahn, Th. & Wondratschek, H. (1994). Symmetry of crystals. Introduction to International Tables for Crystallography, Vol. A. Sofia: Heron Press.Google Scholar