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. 3.6, p. 854
Section 3.6.2.2.3. Standard set of coset representatives^{a}Department of Physics, The Eberly College of Science, Penn State – Berks Campus, The Pennsylvania State University, PO Box 7009, Reading, PA 19610–6009, USA |
The standard set of coset representatives of each representative group is listed on the right-hand side of the survey of magnetic group types, see e.g. Table 3.6.2.2. Each coset in the standard set of coset representatives is given in Seitz notation (Seitz, 1934, 1935a,b, 1936), i.e. {R∣τ} or {R∣τ}′. R denotes a proper or improper rotation (rotation-inversion), τ a non-primitive translation with respect to the non-primed translational subgroup of the magnetic group, and the prime denotes that {R∣τ} is coupled with time inversion. The subindex notation on R, denoting the orientation of the proper or improper rotation, is given in Table 1.4 of Litvin (2013). [Note that the Seitz notation used in Litvin (2013) predates and is different from the IUCr standard convention for Seitz symbolism, see Section 1.4.2.2 and Glazer et al. (2014).]
References
Glazer, A. M., Aroyo, M. I. & Authier, A. (2014). Acta Cryst. A70, 300–302.Litvin, D. B. (2013). Magnetic Group Tables, 1-, 2- and 3-Dimensional Magnetic Subperiodic Groups and Space Groups. Chester: International Union of Crystallography. Freely available from http://www.iucr.org/publ/978–0–9553602–2–0 .
Seitz, F. Z. (1934). A matrix-algebraic development of the crystallographic groups. Z. Kristallogr. 88, 433–459.
Seitz, F. Z. (1935a). A matrix-algebraic development of the crystallographic groups. Z. Kristallogr. 90, 289–313.
Seitz, F. Z. (1935b). A matrix-algebraic development of the crystallographic groups. Z. Kristallogr. 91, 336–366.
Seitz, F. Z. (1936). A matrix-algebraic development of the crystallographic groups. Z. Kristallogr. 94, 100–130.