homIdealPolytope W
Given a list of vertices of a lattice polytope, the function outputs a homogeneous ideal of $k[x_1,\ldots,x_{n+1}]$ such that the polytope is the convex hull of the lattice points of the dehomogenization of a set of monomials that generates the ideal in $k[x_1,\ldots,x_n]$.
The following example computes the homogeneous ideal corresponding to a 2cross polytope.

The output can be used to compute the mixed volume of a collection of polytopes. A list of the output ideals, corresponding to the vertices of various polytopes, can be used as an input in the mMixedVolume function to compute the mixed volume of polytopes.
The object homIdealPolytope is a method function with options.