Continuous barycenter functions on convex polytopes
The author reviews two results by Fuglede on barycentric functions, and he gives variant proofs and supplements. He further shows that Fuglede's results are equivalent to some obvious triangulation-theorems as e.g.: Let P be a convex polytope with vertices \(x_ 1,...,x_ m\). Then for each \(i\in \{1,...,n\}\) there is a proper triangulation into d-simplices \(T_ 1,...,T_ m\) of P such that the vertex \(x_ i\) is a vertex of each \(T_ j\).
scientific article; zbMATH DE number 3951445