4.25 polytope

A rational convex polytope (in short "polytope") in R^n is the convex hull of rational points. It may or may not be bounded. It is internally realized as a cone in one dimension higher, intersected with the hyperplane x0=1, we will consider it embedded into the projective space through R^n -> P R^n, x -> (1,x). Each polytope is uniquely determined by a minimal set of finitely many points, which we will refer to as "vertices". Moreover, a polytope can be represented as a set of points satisfying certain homogeneous linear inequalities and equalities. And these are the two main ways of constructing non-trivial polytopes.

4.25.1 polytopeViaPoints
4.25.2 polytopeViaInequalities
4.25.3 polytope related functions