Configurations of nodes with defects greater than three

The Geometric characterization identifies the sets of nodes such that the Lagrange polynomials are products of linear factors. In order to classify sets satisfying the geometric characterization in the plane, the defect was introduced. A complete description has been given for sets of defect 0, 1, 2, 3 and n−1. We will prove the impossibility of existence of sets of nodes with defect 4, for n≥6. We will also discuss higher defects in order to complete the classification.