Abstract
In this paper, we study a class of Rauzy fractals ${\mathcal R}_a$ given by the polynomial $x^3- ax^2+x-1$ where $a \geq 2$ is an integer. In particular, we give explicitly an automaton that generates the boundary of ${\mathcal R}_a$ and using an unusual numeration system we prove that ${\mathcal R}_a$ is homeomorphic to a topological disk.
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