In this paper, we study arithmetical and topological properties for a class of Rauzy fractals R a given by the polynomial x 3 - a x 2 + x - 1 where a ? 2 is an integer. In particular, we prove the number of neighbors of R a in the periodic tiling is equal to 8. We also give explicitly an automaton that generates the boundary of R a . As a consequence, we prove that R 2 is homeomorphic to a topological disk.
['João Francisco Pereira [Unesp] Bastos', 'Ali Messaoudi', 'Tatiane Maria [Unesp] Rodrigues', 'Daniel Smania']
A class of cubic Rauzy fractals