Remarks on Penrose Tilings

This paper will cover some details on Penrose tilings presented in lectures over the years but never published in print before. The main topics are: (i) the characterizability of Penrose tilings by means of a local rule that does not refer to arrows on the edges of the tiles, and (ii) the fact that the Ammann quasigrid of the inflation of a Penrose tiling is topologically equivalent to the pentagrid that generates the original tiling.