Macaulay2 package FourierMotzkin -- for convex hull and vertex enumeration. A convex cone is polyhedral if it is a finite intersection of halfspaces. A convex cone is finitely generated if it is the set of all nonnegative linear combinations of a finite set of vectors. The fundamental theorem for cones states that a convex cone is polyhedral if and only if it is finitely generated. FourierMotzkin is a Macaulay2 implementation of the Double Description Method (of Fourier, Dines and Motzkin) for converting between these two basic representations for convex cones. For polytopes, this allows one to convert between the convex hull of a finite point set and the bounded intersection of halfspaces.