On convex hulls of self-similar sets

Let $S=\{s_1,\dots,s_m\}$ be a system of contraction similitudes in Banach space and $K(S)$ it's invariant set. We obtain the conditions for the convex hull $H(K)$ of the invariant set to be a finite-sided polyhedron and give an exact estimate for the diameter of $K(S)$ in terms of contraction coefficients of $s_i$.