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The grid method has been used to calculate the frequencies of the different vertices and corresponding Voronoi polygons occurring in generalized Penrose patterns. A simplified purely geometrical description of the importance of the Σ γj = 0 (mod 1) relation for Penrose patterns that obey certain necessary matching conditions is given. In n-grids with n odd, local 2n-fold symmetry occurs only if the inequality n cos α/(1 + cos α) (mod 1) < Σ γj < n/(l + cos α) (mod 1), where α = π/n, is fulfilled. n-grids and their corresponding rhombus patterns show global 2n-fold symmetry if Σ γj = 1/2 (mod 1), where γj = 1/2 (mod 1).
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