  Let $\Pi$ be a random polytope defined as the convex hull of the points of a
Poisson point process. Identities involving the moment generating function of
the measure of $\Pi$, the number of vertices of $\Pi$ and the number of
non-vertices of $\Pi$ are proven. Equivalently, identities for higher moments
of the mentioned random variables are given.
  This generalizes analogous identities for functionals of convex hulls of
i.i.d points by Efron and Buchta.
