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. 2.1, p. 43   | 1 | 2 |

Section 2.1.2.3. Specification of the setting

Hans Wondratscheka* and Mois I. Aroyob

a Institut für Kristallographie, Universität, D-76128 Karlsruhe, Germany, and bDepartamento de Física de la Materia Condensada, Facultad de Ciencias, Universidad del País Vasco, Apartado 644, E-48080 Bilbao, Spain
Correspondence e-mail:  wondra@physik.uni-karlsruhe.de

2.1.2.3. Specification of the setting

| top | pdf |

All 17 plane-group types 1 and 230 space-group types are listed and described in IT A. However, whereas each plane-group type is represented exactly once, 44 space-group types, i.e. nearly 20%, are represented twice. This means that the conventional setting of these 44 space-group types is not uniquely determined and must be specified. The same settings underlie the data of this volume, which follows IT A as much as possible.

There are three reasons for listing a space-group type twice:

  • (1) Each of the 13 monoclinic space-group types is listed twice, with `unique axis b' and `unique axis c', where b or c is the direction distinguished by symmetry (monoclinic axis). The tables of this Part 2 always refer to the conventional cell choice, i.e. `cell choice 1', whereas in IT A for each setting three cell choices are shown. In the graphs, the monoclinic space groups are designated by their short HM symbols.

    Note on standard monoclinic space-group symbols : In this volume, as in IT A, the monoclinic space groups are listed for two settings. Nevertheless, the short symbol for the setting `unique axis b' has been always used as the standard (short) HM symbol. It does not carry any information about the setting of the particular description. As in IT A, no other short symbols are used for monoclinic space groups and their subgroups in the present volume.

  • (2) 24 orthorhombic, tetragonal or cubic space-group types are listed with two different origins. In general, the origin is chosen at a point of highest site symmetry (`origin choice 1'); for exceptions see IT A, Section 8.3.1[link] . If there are centres of inversion and if by this rule the origin is not at an inversion centre, then the space group is described once more with the origin at a centre of inversion (`origin choice 2').

  • (3) There are seven trigonal space groups with a rhombohedral lattice. These space groups are described in a hexagonal basis (`hexagonal axes') with a rhombohedrally centred hexagonal lattice as well as in a rhombohedral basis with a primitive lattice (`rhombohedral axes').

If there is a choice of setting for the space group [{\cal G}], the chosen setting is indicated under the HM symbol in the headline. If a subgroup [{\cal H} \,\lt\, {\cal G}] belongs to one of these 44 space-group types, its `conventional setting' must be defined. The rules that are followed in this volume are explained in Section 2.1.2.5[link].








































to end of page
to top of page