New results on lower bounds for the number of -facets

Abstract: In this paper we present two different results dealing with the number of -facets of a set of points: [1.] We give structural properties of sets in the plane that achieve the optimal lower bound of -edges for a fixed ; and [2.] we show that, for , the number of -facets of a set of points in general position in is at least , and that this bound is tight in the given range of . [Copyright &y& Elsevier]