  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 exotic numeration system we prove that ${\mathcal R}_a$ is
homeomorphic to a topological disk.
