Polyhedra are particular convex sets. Given a polyhedron P, we say that an element v of P is a vertex of P if it cannot be written as a convex combination of other elements in P.
We also say that a vector d of Rn is a direction of the polyhedron P if for each element x of P the ray pointed in x and having direction d is entirely contained in P. Moreover we say that d is an extreme direction of P if d cannot be written as a conic combinations of other directions in P. For example, represented in the figure is an unbounded polyhedron with two vertices corresponding to the two red points and two extreme directions represented by the red arrows. We can obtain a different characterization of polyhedra by saying that a polyhedron is any convex set having a finite number of vertices and extreme directions.