  Every polyhedron can be described by an H-representation H(P) consisting of
half spaces or equivalently by a V-representation V(P) as the convex hull of a
set of vertices and extreme rays. By a suitable encoding we can define a
polyhedron Q by setting H(Q)=V(P). We call P self-dual if V(Q) is isomorphic to
H(P). It is well known and often stated that polytopes that contain the origin
in their interior and pointed polyhedral cones are self-dual. It seems to be
less well known that, more generally, a polyhedron is self-dual if and only if
it contains the origin. We show this by using Minkowski's bipolar equation and
discuss its application to the H/V conversion problem.
