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This short exposition presents an algorithm for an exact calculation of patchfrequencies for the rhombic Penrose tiling. We recall a construction of Penrosetilings via dualisation, and by extending the known method for obtaining vertexconfigurations, we obtain the desired algorithm. It is then used to determinethe frequencies of several particular large patches which appear in theliterature. The analogous approach is also explained for the Ammann-Beenkertiling.

Patch frequencies in Penrose rhombic tilings