International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.3, p. 777

Section 3.3.1.2. Schoenflies symbols

H. Burzlaffa and H. Zimmermannb*

aUniversität Erlangen–Nürnberg, Robert-Koch-Strasse 4a, D-91080 Uttenreuth, Germany, and bInstitut für Angewandte Physik, Lehrstuhl für Kristallographie und Strukturphysik, Universität Erlangen–Nürnberg, Bismarckstrasse 10, D-91054 Erlangen, Germany
Correspondence e-mail:  helmuth.zimmermann@krist.uni-erlangen.de

3.3.1.2. Schoenflies symbols

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Most Schoenflies symbols (Table 3.3.1.3[link], column 1) consist of the basic parts Cn, Dn,1 T or O, designating cyclic, dihedral, tetrahedral and octahedral rotation groups, respectively, with [n = 1, 2, 3, 4, 6]. The remaining point groups are described by additional symbols for mirror planes, if present. The subscripts h and v indicate mirror planes perpendicular and parallel to a main axis taken as vertical. For T, the three mutually perpendicular twofold axes and, for O, the three fourfold axes are considered to be the main axes. The index d is used for mirror planes that bisect the angle between two consecutive equivalent rotation axes, i.e. which are diagonal with respect to these axes. For the roto­inversion axes [\overline{1}, \overline{2} \equiv m, \overline{3}] and [\overline{4}], which do not fit into the general Schoenflies concept of symbols, other symbols [C_{i}, C_{s}, C_{3i}] and [S_{4}] are in use. The rotoinversion axis [\overline{6}] is equivalent to [3/m] and thus designated as [C_{3h}].

A detailed introduction to Schoenflies symbols of crystallographic point groups is given in Section 1.4.1.3[link] .








































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