Barycenters of points that are constrained to a polytope skeleton

Abstract

We give a short and simple proof of a recent result of Dobbins that any point in an $nd$-polytope is the barycenter of $n$ points in the $d$-skeleton. This new proof builds on the constraint method that we recently introduced to prove Tverberg-type results.

2 pages. This manuscript is now part of arXiv:1510.07984

References in corpus (1)

• A point in a $nd$-Polytope is the barycenter of $n$ points in its $d$-faces

Cited by in corpus (1)

• A center transversal theorem for an improved Rado depth