Rauzy fractals are compact sets with fractal boundary that can be associated with anyunimodular Pisot irreducible substitution. These fractals can be defined as the Hausdorfflimit of a sequence of compact sets, where each set is a renormalized projection of afinite union of faces of unit cubes. We exploit this combinatorial definition to prove theconnectedness of the Rauzy fractal associated with any finite product of three-letterArnoux–Rauzy substitutions.