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

International Tables for Crystallography (2016). Vol. A, ch. 3.6, p. 854

Section 3.6.2.2.3. Standard set of coset representatives

D. B. Litvina*

aDepartment of Physics, The Eberly College of Science, Penn State – Berks Campus, The Pennsylvania State University, PO Box 7009, Reading, PA 19610–6009, USA
Correspondence e-mail: u3c@psu.edu

3.6.2.2.3. Standard set of coset representatives

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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[link]. Each coset in the standard set of coset representatives is given in Seitz notation (Seitz, 1934[link], 1935a[link],b[link], 1936[link]), i.e. {Rτ} or {Rτ}′. 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 {Rτ} 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[link]). [Note that the Seitz notation used in Litvin (2013[link]) predates and is different from the IUCr standard convention for Seitz symbolism, see Section 1.4.2.2[link] and Glazer et al. (2014)[link].]

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.








































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