# Working with lattice polytopes

Given a polytope (Polyhedron) which is the convexHull of a given set of points we might ask if the polytope is a Cayley polytope
 i1 : V = matrix {{0,2,-2,0},{0,1,1,1},{1,2,3,4}} o1 = | 0 2 -2 0 | | 0 1 1 1 | | 1 2 3 4 | 3 4 o1 : Matrix ZZ <--- ZZ i2 : P = convexHull V o2 = P o2 : Polyhedron i3 : isCayley P o3 = true

We can also construct Cayley polytopes by taking the Cayley sum of several polytopes.

 i4 : P2 = convexHull matrix{{0,1,2,3},{0,5,5,5},{1,2,3,2}} o4 = P2 o4 : Polyhedron i5 : cayley(P,P2,2) o5 = Polyhedron{...1...} o5 : Polyhedron i6 : vertices oo o6 = | 0 2 -2 0 0 1 3 2 | | 0 1 1 1 0 5 5 5 | | 1 2 3 4 1 2 2 3 | | 0 0 0 0 2 2 2 2 | 4 8 o6 : Matrix QQ <--- QQ