Normaliz

Normaliz is a open source tool for computations in affine monoids, vector configurations, rational polyhedra and rational cones. Normaliz also computes algebraic polyhedra, i.e., polyhedra defined over real algebraic extensions of the rational numbers. 

Its computations include convex huls and vertices, Hilbert bases, Ehrhart series, volumes, lattice points, triangulations, face lattices, and automorphism groups.