2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63396If the system S of contracting similitudes on $ R^2$ satisfies open convex set condition, then the set F of extreme points of the convex hull $\tilde{K}$ of it's invariant self-similar set K has Hausdorff dimension 0 . If, additionally, all the rotation angles of the similitudes are commensurable with $π$, then the set F is finite and the convex hull $\tilde{K}$ is a convex polygon.10 pages, 3 figures, Latex2eMetric GeometryDynamical Systems28A80text