  We prove that for every convex body $K$ with the center of mass at the origin
and every $\varepsilon\in \left(0,\frac{1}{2}\right)$, there exists a convex
polytope $P$ with at most $e^{O(d)}\varepsilon^{-\frac{d-1}{2}}$ vertices such
that $(1-\varepsilon)K\subset P\subset K$.
