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. 3.1, p. 433   | 1 | 2 |

Section 3.1.5.2. Orientational conjugation

Ulrich Müllera*

a Fachbereich Chemie, Philipps-Universität, D-35032 Marburg, Germany
Correspondence e-mail: mueller@chemie.uni-marburg.de

3.1.5.2. Orientational conjugation

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In this case, the conjugate subgroups have differently oriented unit cells that are equivalent by a symmetry operation other than a translation of the space group. This occurs in the following cases: orthorhombic subgroups of hexagonal space groups; monoclinic subgroups of trigonal (including rhombohedral) space groups; rhombohedral and tetragonal subgroups of cubic space groups. In these cases, the corresponding cell and coordinate transformations are listed for all conjugate subgroups after the word `conjugate'. Their Wyckoff symbols, being the same for all conjugate subgroups, are not repeated.

Example 3.1.5.2.1

The cubic space group [P\, \overline{4}3m], No. 215, has three tetragonal conjugate subgroups [P\, \overline{4}2m]. Their tetragonal c axes correspond to the cubic a, b or c axes, respectively. In [P\, \overline{4}3m], a, b and c are symmetry-equivalent by the threefold rotation axes.








































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