Tables for
Volume A
Space-group symmetry
Edited by Th. Hahn

International Tables for Crystallography (2006). Vol. A, ch. 4.2, p. 61

Section 4.2.4. Group–subgroup relations

E. F. Bertauta

aLaboratoire de Cristallographie, CNRS, Grenoble, France

4.2.4. Group–subgroup relations

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The following example illustrates the usefulness of multiple cells.

Example: p3m1 (14)

The symbol of this plane group, described by the triple cell h, is h31m, where the symmetry elements of the secondary and tertiary positions are interchanged. `Decentring' the h cell gives rise to maximal non-isomorphic k subgroups p31m of index [3], with lattice parameters [a\sqrt{3}, a\sqrt{3}] (cf. Section 4.3.5[link] ).

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