Barycenters of points that are constrained to a polytope skeleton

Pavle V. M. Blagojević, Florian Frick, Günter M. Ziegler

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…