A class of cubic Rauzy fractals

Abstract

In this paper, we study arithmetical and topological properties for a class of Rauzy fractals Ragiven by the polynomial 'X POT.3'−a'X POT.2'+x −1 where a ≥ 2 is an integer. In particular, we prove the number of neighbors of 'R IND.A' in the periodic tiling is equal to 8. We also give explicitly an automaton that generates the boundary of 'R IND.A'. As a consequence, we prove that 'R IND.2' is homeomorphic to a topological disk.