The error of polytopal approximation with respect to the symmetric difference metric and the L-p metric

Let M be a convex body in R-d with C-+(3) boundary. Polytopal approximation of M with respect to the symmetric difference metric (or the L-p metric) i s considered, if the approximating polytope has at most n facets (or at mos t n vertices). The asymptotic behavior of the distance of the best approxim ating polytope is well-known; it is of order n(-2/d-1). This (-2/d-1) paper provides an estimate of order n(-2/d-1 + -1/8d2) for the error term.