  We prove that every polytope described by algebraic coordinates is the face
of a projectively unique polytope. This provides a universality property for
projectively unique polytopes. Using a closely related result of Below, we
construct a combinatorial type of 5-dimensional polytope that is not realizable
as a subpolytope of any stacked polytope. This disproves a classical conjecture
in polytope theory, first formulated by Shephard in the seventies.
