Isomorphic Steiner symmetrization

This paper proves that there exist 3n Steiner symmetrizations that transform any convex set K subset of R-n into an isomorphic Euclidean ball; i.e. if vol(K)=vol(D-n) where D-n is the standard Euclidean unit ball, then K can be transformed into a body (K) over tilde such that c(1)D(n) subset of (K) over tilde c(2)D(n), where c(1), c(2) are numerical constants. Moreover, for any c>2, cn symmetrizations are also enough.