Convexity/Convex polytopes

Diagonals Definition: A convex polytope is the convex hull of a finite number of points. Usually, there will be at least three non-collinear points. Theorem: A set is a convex polytope if and only if: It is not the empty set It is bounded It is the intersection of a finite number of closed half-spaces. A simplex in an n-dimensional vector space is the convex hull of n+1 points that do not all lie on the same hyperplane. If n=2, a simplex is a triangle; if n=3, it is a tetrahedron.