We present experimental results on the structure of Ag thin films grown on high-symmetry surfaces of both quasicrystals and approximants. For coverages above ten monolayers, Ag form fcc nanocrystals with (111) plane parallel to the surface plane. Depending on the substrate surface symmetry, the Ag nanocrystals exist in one, two or five different orientations, rotated by a multiple of 2π/30. The orientation relationship between crystalline films and substrates appears to be determined by the following principles: high atomic density rows of the adsorbate are aligned along high atomic density rows of the substrate.