2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174062We consider words coding exchange of three intervals with permutation (3,2,1), here called 3iet words. Recently, a characterization of substitution invariant 3iet words was provided. We study the opposite question: what are the morphisms fixing a 3iet word? We reveal a narrow connection of such morphisms and morphisms fixing Sturmian words using the new notion of amicability.13 pages, 5 figuresCombinatorics68R15; 08A50text