  In this paper, we study arithmetical and topological properties for 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 prove the number of neighbors
of ${\mathcal R}_a$ in the periodic tiling is equal to $8$. We also give
explicitly an automaton that generates the boundary of ${\mathcal R}_a$. As a
consequence, we prove that ${\mathcal R}_2$ is homeomorphic to a topological
disk.
