Let \(X_1,X_2, \dots\) be an iid sequence of random points in \(\mathbb{R}^d\). In this interesting paper, the authors consider centered empirical measures \(\varphi_n\), \(n\in\mathbb{N}\), defined as \[ \varphi_n= \sum^n_{i=1}\|X_i -\overline X_n\|\delta \left(\cdot- {X_i-\overline X_n\over\|X_i-\overline X_n\|}\right) \] (here \(\overline X_n={1\over n} \sum^n_{i=1}X_i\) and \(\delta\) is the Dirac measure at 0). Under mild regularity conditions on the distribution of the \(X_i\), the measures \(\varphi_n\) fulfill Minkowski's existence theorem, hence there is a convex polytope \(P_n\) with surface area measure \(\varphi_n\). The authors show a law of large numbers for the random polytopes \(P_n\), namely they converge a.s. to a convex body \(K\) (and the measures \(\varphi_n\) converge weakly to the surface area measure \(\varphi\) of \(K)\). In addition, they prove a central limit theorem for the integrals \(\int gd\varphi_n\) of smooth functions \(g\).