Tables for
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 1.7, pp. 132-139

Chapter 1.7. Topics on space groups treated in Volumes A1 and E of International Tables for Crystallography

H. Wondratschek,a U. Müller,b* D. B. Litvinc* and V. Kopskýd

aLaboratorium für Applikationen der Synchrotronstrahlung (LAS), Universität Karlsruhe, Germany,bFachbereich Chemie, Philipps-Universität, D-35032 Marburg, Germany,cDepartment of Physics, The Eberly College of Science, Penn State – Berks Campus, The Pennsylvania State University, PO Box 7009, Reading, PA 19610–6009, USA, and dBajkalska 1170/28, 100 00 Prague 10, Czech Republic
Correspondence e-mail:,



1 The point group determines both the symmetry of the physical properties of the macroscopic crystal and the symmetry of its ideal shape. Each space group belongs to a point group.

2 In the strict sense, two isotypic compounds do not have the same space group if their translation lattices (lattice dimensions) differ. However, such a strict treatment would render it impossible to apply group-theoretical methods in crystal chemistry and crystal physics. Therefore, we treat isotypic and homeotypic structures as if their translation lattices were the same or related by an integral enlargement factor. For more details see the second edition of IT A1 (2010[link]), Sections 1.2.7[link] and[link] . We prefer the term `misorder' instead of the usual `disorder' because there still is order in the `disordered' structure, although it is a reduced order.
3 A topotactic reaction is a chemical reaction in the solid state where the orientation of the product crystal is determined by the orientation of the educt crystal.