Multivariate polynomial interpolation : A GC 2 - set in R 4 without a maximal hyperplane

A set T ⊂ R at which interpolation from Π≤n(R ) (polynomials of degree ≤ n) is uniquely possible is a GCn-set if the associated Lagrange fundamental polynomials have only linear factors. For such GCn-sets T in the plane, Gasca and Maeztu conjectured the existence of a line containing n + 1 points from T. It is shown here that, already in R, there exist GC2-sets T without any hyperplanes containing dimΠ≤2(R ) points from T.