  The convex hull $P_{n}$ of a Gaussian sample $X_{1},...,X_{n}$ in $R^{d}$ is
a Gaussian polytope. We prove that the expected number of facets $E f_{d-1}
(P_n)$ is monotonically increasing in $n$. Furthermore we prove this for random
polytopes generated by uniformly distributed points in a $d$-dimensional ball.
