On the approximation of a polytope by its dual $L_{p}$-centroid bodies Grigoris PaourisElisabeth Werner 52A2053A15centroid bodiesfloating bodiespolytopes$L_p$ Brunn Minkowski theory We show that the rate of convergence on the approximation of volumes of a convex symmetric polytope $P\in\mathbb{R}^n$ by its dual $L_p$-centroid bodies is independent of the geometry of $P$. In particular, we show that if $P$ has volume $1$, \[ \lim_{p\to\infty}\frac{p}{\log p}\left(\frac{|Z_p^{\circ}(P)|}{|P^{\circ}|}-\right)=n^2. \] We provide an application to the approximation of polytopes by uniformly convex sets. Indiana University Mathematics Journal 2013 text pdf 10.1512/iumj.2013.62.4875 10.1512/iumj.2013.62.4875 en Indiana Univ. Math. J. 62 (2013) 235 - 248 state-of-the-art mathematics http://iumj.org/access/