International
Tables for Crystallography Volume A Space-group symmetry Edited by M. I. Aroyo © International Union of Crystallography 2016 |
International Tables for Crystallography (2016). Vol. A, ch. 3.3, p. 777
Section 3.3.1.2. Schoenflies symbols^{a}Universität Erlangen–Nürnberg, Robert-Koch-Strasse 4a, D-91080 Uttenreuth, Germany, and ^{b}Institut für Angewandte Physik, Lehrstuhl für Kristallographie und Strukturphysik, Universität Erlangen–Nürnberg, Bismarckstrasse 10, D-91054 Erlangen, Germany |
Most Schoenflies symbols (Table 3.3.1.3, column 1) consist of the basic parts C_{n}, D_{n},^{1} T or O, designating cyclic, dihedral, tetrahedral and octahedral rotation groups, respectively, with . 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 and , which do not fit into the general Schoenflies concept of symbols, other symbols and are in use. The rotoinversion axis is equivalent to and thus designated as .
A detailed introduction to Schoenflies symbols of crystallographic point groups is given in Section 1.4.1.3 .