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

International Tables for Crystallography (2011). Vol. A1, ch. 1.6, pp. 54-55

Section 1.6.7. Exercising care in the use of group–subgroup relations

Ulrich Müllera*

aFachbereich Chemie, Philipps-Universität, D-35032 Marburg, Germany
Correspondence e-mail:

1.6.7. Exercising care in the use of group–subgroup relations

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Using the tables of this volume or from other sources or using computer programs as offered by the Bilbao Crystallographic Server (see Chapter 1.7[link] ), it may be easy to search for group–subgroup relations between space groups of crystal structures. This should only be done bearing in mind and explicitly stating a crystallographic, physical or chemical context. It is senseless to construct relations in a purely formal manner, `just for fun', without a sound crystal-chemical or physical foundation. There exist no clear criteria to determine what is a `sound foundation', but crystallographic, chemical and physical common sense and knowledge should always be taken into consideration.

In addition, by experience we know that setting up trees of group–subgroup relations is susceptible to pitfalls. Some sources of errors are: not taking into account necessary origin shifts; wrong origin shifts; wrong basis and/or coordinate transformations; unnecessary basis transformations just for the sake of clinging on to standard space-group settings; lack of distinction between space groups and space-group types; lack of keeping track of the development of the atomic positions from group to subgroup; using different space-group or coordinate settings for like structures. If the group–subgroup relations are correct, but origin shifts or basis transformations have not been stated, this can cause subsequent errors and misunderstandings.


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