Exchange of three intervals: Substitutions and palindromicity

We study purely morphic words coding symmetric non-degenerate three interval exchange transformation which are known to be palindromic, i.e., they contain infinitely many palindromes. We prove that such words are fixed by a conjugate to a morphism of class P, that is, a morphism such that each letter a is mapped to ppa where p and pa are both palindromes. We thus provide a new family of palindromic infinite words satisfying the conjecture of Hof, Knill and Simon. Given a morphism fixing such word, we give a formula to determine the parameters of the underlying three interval exchange and the intercept of the word.