International
Tables for
Crystallography
Volume A1
Symmetry relations between space groups
Edited by Hans Wondratschek and Ulrich Müller

International Tables for Crystallography (2011). Vol. A1, ch. 2.1, p. 72   | 1 | 2 |

Section 2.1.1. Contents and arrangement of the subgroup tables

Hans Wondratscheka* and Mois I. Aroyob

aInstitut 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

2.1.1. Contents and arrangement of the subgroup tables

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In this chapter, the subgroup tables, the subgroup graphs and their general organization are discussed. In the following sections, the different types of data are explained in detail. For every plane group and every space group there is a separate table of maximal subgroups and minimal supergroups. The subgroup data are listed either individually, or as members of (infinite) series, or both. The supergroup data are not as complete as the subgroup data. However, most of them can be obtained by proper eval­uation of the subgroup data, as shown in Section 2.1.7[link]. In addition, there are graphs of translationengleiche and klassengleiche subgroups which contain for each space group all kinds of subgroups, not just the maximal ones.

The presentation of the plane-group and space-group data in the tables of Chapters 2.2[link] and 2.3[link] follows the style of the tables of Parts 6[link] (plane groups) and 7[link] (space groups) in Vol. A of International Tables for Crystallography (2005[link]), henceforth abbreviated as IT A. The data comprise:

  • Headline

  • Generators selected

  • General position

  • I Maximal translationengleiche subgroups

  • II Maximal klassengleiche subgroups

  • I Minimal translationengleiche supergroups

  • II Minimal non-isomorphic klassengleiche supergroups.

For the majority of groups, the data can be listed completely on one page. Sometimes two pages are needed. If the data extend less than half a page over one full page and data for a neighbouring space-group table `overflow' to a similar extent, then the two overflows are displayed on the same page. Such deviations from the standard sequence are indicated on the relevant pages by a remark Continued on…. The two overflows are separated by a solid line and are designated by their headlines.

The sequence of the plane groups and space groups [{\cal G}] in this volume follows exactly that of the tables of Part 6[link] (plane groups) and Part 7[link] (space groups) in IT A. The format of the subgroup tables has also been chosen to resemble that of the tables of IT A as far as possible. Graphs for translationengleiche and klassengleiche subgroups are found in Chapters 2.4[link] and 2.5[link] . Examples of graphs of subgroups can also be found in Section 10.1.4.3[link] of IT A, but only for subgroups of point groups. The graphs for the space groups are described in Section 2.1.8[link].

References

International Tables for Crystallography (2005). Vol. A, Space-Group Symmetry, edited by Th. Hahn, 5th ed. Heidelberg: Springer.








































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