%0 Journal Article
%T Sections of the regular Simplex - Volume formulas and estimates
%A Hauke Dirksen
%J Mathematics
%D 2015
%I arXiv
%X We state a general formula to compute the volume of the intersection of the regular $n$-simplex with some $k$-dimensional subspace. It is known that for central hyperplanes the one through the centroid containing $n-1$ vertices gives the maximal volume. We show that, for fixed small distances of a hyperplane to the centroid, the hyperplane containing $n-1$ vertices is still volume maximizing. The proof also yields a new and short argument for the result on central sections. Finally we give a partial result for the minimal central section.
%U http://arxiv.org/abs/1509.06408v1