Detection of rotational and involutional symmetries and congruity of polyhedra

We propose a simple and efficient general algorithm for determining both rotational and involutional symmetries of polyhedra. It requiresO(m2) time and usesO(m) space, wherem is the number of edges of the polyhedron. As this is the lower bound of the symmetry detection problem for the considered output form, our algorithm is optimal. We show that a slight modification of our symmetry detection algorithm can be used to solve the related conguity problem of polyhedra.

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