  The deviation of a general convex body with twice differentiable boundary and
an arbitrarily positioned polytope with a given number of vertices is studied.
The paper considers the case where the deviation is measured in terms of the
surface areas of the involved sets, more precisely, by what is called the
surface area deviation. The proof uses arguments and constructions from
probability, convex and integral geometry. The bound is closely related to
$p$-affine surface areas.
