the convex hull of any finite set of points on the moment curve is a cyclic polytope. cyclic polytopes have the largest possible number of faces for a given number of vertices, and in dimensions four or more have the property that their edges form a complete graph. more strongly, they are neighborly polytopes, meaning that each set of at most "d"/2 vertices of the polytope forms one of its faces. sets of points on the moment curve also realize the maximum possible number of simplices, formula_2, among all possible delaunay triangulations of sets of "n" points in "d" dimensions.