  If 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 $\pi$, then the set F is finite and the convex hull
$\tilde{K}$ is a convex polygon.
