What is the Minkowski-Weyl theorem for convex polyhedra?

The Minkowski-Weyl Theorem states every polyhedron is finitely generated and every finitely generated set is a polyhedron. More precisely, for two subsets $P$ and $Q$ of $R^d$, $P+Q$ denotes the Minkowski sum of $P$ and $Q$:

$$P + Q = \{ p +q: p \in P q \in Q \}.$$

Theorem 5 (Minkowski-Weyl's Theorem)   For a subset $P$ of $R^d$, the following statements are equivalent:

(a)

P is a polyhedron, i.e., for some real (finite) matrix $A$ and real vector $b$, $P=\{ x : A x \le b \}$;

(b)

There are finite real vectors $v_1, v_2, \ldots, v_n$ and $r_1, r_2, \ldots, r_s$ in $R^d$ such that
$P = conv(v_1, v_2, \ldots, v_n) + nonneg(r_1, r_2, \ldots, r_s)$.

Thus, every polyhedron has two representations of type (a) and (b), known as (halfspace) H-representation and (vertex) V-representation, respectively. A polyhedron given by H-representation (V-representation) is called H-polyhedron (V-polyhedron).