Unisolvency for multivariate polynomial interpolation in Coatmèlec configurations of nodes

A new and straightforward proof of the unisolvability of the problem of multivariate poly- nomial interpolation based on Coatmèlec con?gurations of nodes, a class of properly posed set of nodes de?ned by hyperplanes, is presented. The proof generalizes a previous one for the bivariate case and is based on a recursive reduction of the problem to simpler ones fol- lowing the so-called Radon–Bézout process.