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Wallpaper Groups

The 17 Plane Symmetry Groups. Their symbols are p1, p2, pm, pg, cm, pmm, pmg, pgg, cmm, p4, p4m, p4g, p3, p31m, p3m1, p6, and p6m. For a description of the symmetry elements present in each space group, see Coxeter (1969, p. 413).


Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, 1969.

Hilbert, D. and Cohn-Vossen, S. Geometry and the Imagination. New York: Chelsea, 1952.

Joyce, D. E. ``Wallpaper Groups (Plane Symmetry Groups).''

Lee, X. ``The Discontinuous Groups of Rotation and Translation in the Plane.''

Schattschneider, D. ``The Plane Symmetry Groups: Their Recognition and Notation.'' Amer. Math. Monthly 85, 439-450, 1978.

Weyl, H. Symmetry. Princeton, NJ: Princeton University Press, 1952.

© 1996-9 Eric W. Weisstein