This is an announcement for the paper "On the approximation of a polytope by its dual $L_{p}$-centroid bodies" by Grigoris Paouris and Elisabeth M. Werner. Abstract: We show that the rate of convergence on the approximation of volumes of a convex symmetric polytope P in R^n by its dual L_{p$-centroid bodies is independent of the geometry of P. In particular we show that if P has volume 1, lim_{p\rightarrow \infty} \frac{p}{\log{p}} \left( \frac{|Z_{p}^{\circ}(P)|}{|P^{\circ}|} -1 \right) = n^{2} . We provide an application to the approximation of polytopes by uniformly convex sets. Archive classification: math.FA Submitted from: elisabeth.werner@case.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1107.3683 or http://arXiv.org/abs/1107.3683