  In this paper, we give a necessary condition for an infinite word defined by
a non-degenerate interval exchange on three intervals (3iet word) to be
invariant by a substitution: a natural parameter associated to this word must
be a Sturm number. We deduce some algebraic consequences from this condition
concerning the incidence matrix of the associated substitution. As a by-product
of our proof, we give a combinatorial characterization of 3iet words.
