  This short exposition presents an algorithm for an exact calculation of patch
frequencies for the rhombic Penrose tiling. We recall a construction of Penrose
tilings via dualisation, and by extending the known method for obtaining vertex
configurations, we obtain the desired algorithm. It is then used to determine
the frequencies of several particular large patches which appear in the
literature. The analogous approach is also explained for the Ammann-Beenker
tiling.
