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Letting $P$ be a convex polytope in $\mathbb{R}^d$ with $n>d$ vertices, westudy geometric and analytical properties of the set of generalized barycentriccoordinates relative to any point $p\in P$. We prove that such sets arepolytopes in $\mathbb{R}^n$ with at most $n-d-1$ vertices, and provide resultsabout continuity and differentiability for the corresponding set-valued maps.

Set-Valued Analysis of Generalized Barycentric Coordinates and Their Geometric Properties