Restricted hyperplane sections of the cross‐polytope and the simplex

Source abstract

Abstract We give a new proof of Webb's theorem on maximal central hyperplane sections of the regular ‐simplex , viewed in its standard embedding in . A similar method also yields sharp maximal estimates for noncentral sections of whose distance from the barycenter is small, namely . Moreover, we obtain sharp volume estimates for central hyperplane sections of the cross‐polytope that pass through the barycenter of a facet.