Harmonic analysis of dihedral groups
نویسنده
چکیده
The rotations are the symmetries preserving the (cyclic) ordering of vertices. Thus, a rotation g is determined by the image gv, so the subgroup N of rotations has n elements. A reflection is an order-2 symmetry reversing the ordering of vertices. Imbedding the n-gon in R, there are n axes through which the n-gon can be reflected, so there are n reflections. Since |G| = 2n, every symmetry is either a rotation or a reflection.
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