Note on matrix M property and discretization methods

I Given a finite point set X ⊂ Rd . Then there exists simplicial a complex called Delaunay triangulation of this point set such that I X is the set of vertices of the triangulation I The union of all its simplices is the convex hull of X . I (Delaunay property): For any given d-simplex Σ ⊂ Ω belonging to the triangulation, the interior of its circumsphere does not contain any vertex xk ∈ X . I Assume that the points of X are in general position, i.e. no n + 2 points lie on one sphere. Then the Delaunay triangulation is unique.