Designation of symmetry operations

Kopskyacute, V.; Litvin, D. B.

doi:10.1107/97809553602060000647

International
Tables for
Crystallography
Volume E
Subperiodic groups
Edited by V. Kopský and D. B. Litvin

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International Tables for Crystallography (2006). Vol. E. ch. 1.2, p. 15 | 1 | 2 |

Section 1.2.9.2. Designation of symmetry operations

V. Kopský^a and D. B. Litvin^b ^*

^a Department of Physics, University of the South Pacific, Suva, Fiji, and Institute of Physics, The Academy of Sciences of the Czech Republic, Na Slovance 2, PO Box 24, 180 40 Prague 8, Czech Republic, and ^bDepartment of Physics, Penn State Berks Campus, The Pennsylvania State University, PO Box 7009, Reading, PA 19610-6009, USA
Correspondence e-mail: u3c@psu.edu

1.2.9.2. Designation of symmetry operations

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The designation of symmetry operations for the subperiodic groups is the same as for the space groups. An entry in the block Symmetry operations is characterized as follows:

(i) A symbol denoting the type of the symmetry operation [cf. Chapter 1.2 of IT A (2005)], including its glide or screw part, if present. In most cases, the glide or screw part is given explicitly by fractional coordinates between parentheses. The sense of a rotation is indicated by the superscript + or −. Abbreviated notations are used for the glide reflections a(1/2, 0, 0) ≡ a; b(0, 1/2, 0) ≡ b; c(0, 0, 1/2) ≡ c. Glide reflections with complicated and unconventional glide parts are designated by the letter g, followed by the glide part between parentheses.
(ii) A coordinate triplet indicating the location and orientation of the symmetry element which corresponds to the symmetry operation. For rotoinversions the location of the inversion point is also given.

Details of this symbolism are given in Section 11.1.2 of IT A (2005).

References

International Tables for Crystallography (2005). Vol. A. Space-group symmetry, edited by Th. Hahn. Heidelberg: Springer. [Previous editions: 1983, 1987, 1992, 1995 and 2002. Abbreviated as IT A (2005).]Google Scholar

International Tables for Crystallography (2006). Vol. E. ch. 1.2, p. 15