  Given a stationary and isotropic Poisson hyperplane process and a convex body
$K$ in ${\mathbb R}^d$, we consider the random polytope defined by the
intersection of all closed halfspaces containing $K$ that are bounded by
hyperplanes of the process not intersecting $K$. We investigate how well the
expected mean width of this random polytope approximates the mean width of $K$
if the intensity of the hyperplane process tends to infinity.
