The Baake construction, based on generating a set of vertices of Penrose tilings as a model set, is refined. An algorithm and a corresponding computer program for constructing an uncountable set of locally indistinguishable Penrose tilings are developed proceeding from this refined construction. Based on an analysis of the parameters of tiling vertices, 62 versions of rhomb combinations at the tiling center are determined. The combinatorial structure of Penrose tiling worms is established. A concept of flip transformations of tilings is introduced that makes it possible to construct Penrose tilings that cannot be implemented in the Baake construction.
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