Isomorphic Steiner symmetrization

This paper proves that there exist 3n Steiner symmetrizations that transform any convex set Kⁿ 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 such that c₁D_nKc₂D_n, where c₁,c₂ are numerical constants. Moreover, for any c>2, cn symmetrizations are also enough.