Chapter 3


 SIMILARITY
 SYMMETRY IN E2





A similarity symmetry group is any group of similarity transformations (H.S.M. Coxeter, 1969, pp. 72), at least one of which is not an isometry. According to the theorem on the existence of an invariant point of every discrete similarity transformation that is not an isometry (E.I. Galyarski, A.M. Zamorzaev, 1963; H.S.M. Coxeter, 1969), all the similarity symmetry groups of the plane E2 belong to the similarity symmetry groups with an invariant point. From the relationships: S2 = S20, S21 = S210, S210 S2, we can conclude that for a full understanding of the similarity symmetry groups of the plane E2, it is enough to analyze the similarity symmetry groups of the category S20. Owing to the existence of an invariant point, the similarity symmetry groups of the category S20 are also called the similarity symmetry groups of rosettes S20, and the corresponding figures possessing such a symmetry group are called similarity symmetry rosettes.


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