International
Tables for Crystallography Volume E Subperiodic groups Edited by V. Kopský and D. B. Litvin © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. E, ch. 1.2, p. 22
Section 1.2.17.1. Frieze groups^{a}Freelance research scientist, Bajkalská 1170/28, 100 00 Prague 10, Czech Republic, and ^{b}Department of Physics, The Eberly College of Science, Penn State – Berks Campus, The Pennsylvania State University, PO Box 7009, Reading, PA 19610–6009, USA 
A list of sets of symbols for the frieze groups is given in Table 1.2.17.1. The information provided in this table is as follows:

Sets of symbols which are of a nonHermann–Mauguin (international) type are the set of symbols of the `black and white' symmetry type (column 3) and the sets of symbols in columns 6 and 7. The sets of symbols in columns 4, 5 and 11 do not follow the sequence of symmetry directions used for twodimensional space groups. The sets of symbols in columns 3, 4, 5 and 10 do not use a lowercase script to denote a onedimensional lattice. The set of symbols in column 9 uses parentheses and square brackets to denote specific symmetry directions. The symbol g is used in Part 1 to denote a glide line, a standard symbol for twodimensional space groups (IT A , 2005). A letter identical with a basisvector symbol, e.g. a or c, is not used to denote a glide line, as is done in the symbols of columns 5, 6, 7, 9 and 11, as such a letter is a standard notation for a threedimensional glide plane (IT A , 2005).
Columns 2 and 3 show the isomorphism between frieze groups and onedimensional magnetic space groups. The onedimensional space groups are denoted by and . The list of symbols in column 3, on replacing r with , is the list of onedimensional magnetic space groups. The isomorphism between these two sets of groups interexchanges the elements and 1′ of the onedimensional magnetic space groups and, respectively, the elements and , mirror lines perpendicular to the [10] and [01] directions, of the frieze groups.
References
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Lockwood, E. H. & Macmillan, R. H. (1978). Geometric Symmetry. Cambridge University Press.
Opechowski, W. (1986). Crystallographic and Metacrystallographic Groups. Amsterdam: North Holland.
Shubnikov, A. V. & Koptsik, V. A. (1974). Symmetry in Science and Art. New York: Plenum.
Vainshtein, B. K. (1981). Modern Crystallography I. Berlin: SpringerVerlag.