Abstract

In this paper, we study arithmetical and topological properties for a class of Rauzy fractals Ra given by the polynomial x3−ax2+x−1 where a≥2 is an integer. In particular, we prove the number of neighbors of Ra in the periodic tiling is equal to 8. We also give explicitly an automaton that generates the boundary of Ra. As a consequence, we prove that R2 is homeomorphic to a topological disk.

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