Abstract
In this paper an overview of the so-called cut-and-project method is presented together with new results on the construction of a cut-and-project set with a given linear diagonalizable self-similarity A. Such a construction is illustrated on a two-dimensional mathematical quasicrystal related to the Pisot number . This model is described in detail and the associated Voronoi tilling is discussed. Moreover, it is shown that there exists a connection between the planar quasicrystal and higher-dimensional quasicrystal with 7-fold symmetry.
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