Abstract
A method for constructing a 2D quasi-periodic Rauzy tiling Til as a section of some 3D periodic tiling Til3D is considered. The translation lattice of the tiling Til3D and its connectivity graph are constructed using the discrete modeling of packings. The calculation of the layer-by-layer growth polyhedron for the tiling Til3D made it possible to estimate from upper the shape of a growth polygon for the tiling Til. As a result, the growth shape in six out of eight growth sectors has been rigorously proven. A set of quasi-periodic tilings (locally indistinguishable from the Rauzy tiling Til), including seven centrosymmetric tilings, has been obtained.
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