Abstract
When we say that a square is more symmetrical than a triangle, we mean that it has a greater number of symmetry operations, i.e., of congruent transformations that leave it invariant. The symmetry operations (including the identity) of any figure clearly form a group: the symmetry group of the figure. A completely irregular figure has a symmetry group of order 1. The group of order 2 arises when the figure has bilateral symmetry, or when it is transformed into itself by a half-turn (i. e., rotation through two right angles).
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© 1957 Springer-Verlag Berlin Heidelberg
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Coxeter, H.S.M., Moser, W.O.J. (1957). Abstract Crystallography. In: Generators and Relations for Discrete Groups. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-25739-5_4
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DOI: https://doi.org/10.1007/978-3-662-25739-5_4
Publisher Name: Springer, Berlin, Heidelberg
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