2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145226We prove that a certain family of flat surfaces in genus 3 does not fulfill Veech's Dichotomy. These flat surfaces provide uncountably many minimal but nonergodic directions. The conditions on this family are a combinatorical one and an irrationality condition. The Arnoux-Yoccoz surface fulfills this conditions.10 pages, 3 figuresDynamical Systems37D40; 37E35text