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

International Tables for Crystallography (2016). Vol. A, ch. 2.1, pp. 142-174

Chapter 2.1. Guide to the use of the space-group tables

Th. Hahn,a A. Looijenga-Vos,b M. I. Aroyo,c H. D. Flack,d K. Mommae and P. Konstantinovf

aInstitut für Kristallographie, RWTH Aachen University, 52062 Aachen, Germany,bLaboratorium voor Chemische Fysica, Rijksuniversiteit Groningen, The Netherlands,cDepartamento de Física de la Materia Condensada, Universidad del País Vasco (UPV/EHU), Bilbao, Spain,dChimie minérale, analytique et appliquée, University of Geneva, Geneva, Switzerland,eNational Museum of Nature and Science, 4–1-1 Amakubo, Tsukuba, Ibaraki 305–0005, Japan, and fInstitute for Nuclear Research and Nuclear Energy, 72 Tzarigradsko Chaussee, BG-1784 Sofia, Bulgaria



1 A space-group symbol is invariant under sign changes of the axes; i.e. the same symbol applies to the right-handed coordinate systems abc, [{\bf a}\overline{{\bf b}}\overline{{\bf c}}, \overline{{\bf a}}{\bf b}\overline{{\bf c}}, \overline{{\bf a}}\overline{{\bf b}}{\bf c}] and the left-handed systems [\overline{{\bf a}}{\bf bc}, {\bf a}\overline{{\bf b}}{\bf c}, {\bf ab}\overline{{\bf c}}, \overline{{\bf a}}\overline{{\bf b}}\overline{{\bf c}}].
2 The term Position (singular) is defined as a set of symmetry-equivalent points, in agreement with IT (1935)[link]: Point position; Punktlage (German); position (French). Note that in IT (1952)[link] the plural, equivalent positions, was used.
3 Often called point symmetry: Punktsymmetrie or Lagesymmetrie (German): symétrie ponctuelle (French).
4 The reflection conditions were called Auslöschungen (German), missing spectra (English) and extinctions (French) in IT (1935)[link] and `Conditions limiting possible reflections' in IT (1952)[link]; they are often referred to as `Systematic or space-group absences' (cf. Section 3.3.3[link] ).
5 These three vectors obey the `closed-triangle' condition [{\bf e} + {\bf f} + {\bf g} = {\bf 0}]; they can be considered as two-dimensional homogeneous axes.
6 In IT (1952)[link], the terms `1st setting' and `2nd setting' were used for `unique axis c' and `unique axis b'. In the present volume, as in the previous editions of this series, these terms have been dropped in favour of the latter names, which are unambiguous.