  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}}
(\frac{|Z_{p}^{\circ}(P)|}{|P^{\circ}|} -1) = n^{2}.
  We provide an application to the approximation of polytopes by uniformly
convex sets.
