2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169678We answer a question of Vorobets by showing that the lattice property for flat surfaces is equivalent to the existence of a positive lower bound for the areas of affine triangles. We show that the set of affine equivalence classes of lattice surfaces with a fixed positive lower bound for the areas of triangles is finite and we obtain explicit bounds on its cardinality. We deduce several other characterizations of the lattice property.Dynamical Systemstext