GC-sets are subsets T of \mathbbR^d\mathbb{R}^d of the appropriate cardinality dimP_n\dim\Pi_n for which, for each τ ∈ T, there are n hyperplanes whose union contains all of T except for τ, thus making interpolation to arbitrary data on T by polynomials of degree ≤ n uniquely possible. The existing bivariate theory of such sets is extended to the general multivariate case and the concept of a maximal hyperplane for T is highlighted, in hopes of getting more insight into existing conjectures for the bivariate case.