Suppose I have defined a convex set as the convex hull of a set of points. (I know that all these points are "extremal points" of the convex set.) I know want to translate this description of the convex set into description in terms of a set of facets, or inequalities. Is there a general theory for how to do this?
In case the problem is hard in general, what if the convex set is "very symmetric", and the number of facets is similar to the number of vertices.
