  We study polar orbitopes, i.e. convex hulls of orbits of a polar
representation of a compact Lie group. The face structure is studied by means
of the gradient momentum map and it is shown that every face is exposed and is
again a polar orbitope. Up to conjugation the faces are completely determined
by the momentum polytope. There is a tight relation with parabolic subgroups:
the set of extreme points of a face is the closed orbit of a parabolic subgroup
of G and for any parabolic subgroup the closed orbit is of this form.
