Abstract

In this paper we describe explicitly the identifications on the boundary of the Rauzy fractal that makes it a fundamental domain of the two-dimensional torus, for the action of the lattice Z(2) on the plane. Using these identifications, we give a new way to compute the Hausdorff dimension of the Rauzy fractal. Also, we compute the Hausdorff dimension of the realization of the boundary of the Rauzy fractal on the interval.