Barycenters of points that are constrained to a polytope skeleton
  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. 
Pavle V. M. Blagojevi\'c, Florian Frick, G\"unter M. Ziegler
math.MG math.CO