Penrose tiling approximants

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Abstract
The modification of the Penrose tiling into a periodic structure is considered. Detailed analysis of the strip method and the dual transformation which yield approximants of the perfect tiling is presented in such a way that a complete classification of approximants is provided. The defects introduced to change the aperiodic order into a periodic one are discussed, their number per unit cell is derived, and the tile density is calculated. Our model implies also a fundamental similarity between the partial dislocations of the approximants and the elementary dislocations of quasi-crystals, which might result in comparable plasticity properties