  We study the supremum of the volume of hyperbolic polyhedra with some fixed
combinatorics and with vertices of any kind (real, ideal or hyperideal). We
find that the supremum is always equal to the volume of the rectification of
the 1-skeleton.
  The theorem is proved by applying a sort of volume-increasing flow to any
hyperbolic polyhedron. Singularities may arise in the flow because some strata
of the polyhedron may degenerate to lower-dimensional objects; when this
occurs, we need to study carefully the combinatorics of the resulting
polyhedron and continue with the flow, until eventually we get a rectified
polyhedron.
