Consider a convex V-polytope generated by the origin and $n$ points $\mathbf{h}_1,\cdots,\mathbf{h}_n$ in $\mathbb{R}^r$. A Theorem in the area of convex geometry shows that each V-polytope is a H-polytope and vice versa.
My question is given $n$ points $\left\{\mathbf{h}_1,\cdots,\mathbf{h}_n \right\}$ how to express such a V-polytope by the intersection of least half spaces (i.e., in a form of a matrix inequality).
One-dimensional case is trivial.
