Abstract
The coordinates and parameters of vertices of a Rauzy tiling are calculated and the fractal character of tiling boundaries is described on the basis of complex and real parametrizations of Rauzy tiles. For a half-group of similarity transformations, which map tiling boundaries into themselves, an infinite system of generatrices is found. It is proven that a punctured Rauzy tiling has a central symmetry. Infinite helical stars with centers at the tiling vertices and rays formed by tiling boundaries are found and described; the set of similarity transformations for such stars forms a group. The set of such infinite stars covers all Rauzy tiling boundaries.
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Original Russian Text © V.G. Zhuravlev, A.V. Maleev, 2009, published in Kristallografiya, 2009, Vol. 54, No. 3, pp. 400–409.