  We consider primitive substitution tilings on R^d whose expansion maps are
unimodular. We assume that all the eigenvalues of the expansion maps are
algebraic conjugates with the same multiplicity. In this case, we can construct
a cut-and-project scheme with a Euclidean internal space. Under some additional
condition, we show that if the substitution tiling has pure discrete spectrum,
then the corresponding representative point sets are regular model sets in that
cut-and-project scheme.
