Projection bodies and valuations

AbstractLet Π be the projection operator, which maps every polytope to its projection body. It is well known that Π maps the set of polytopes, Pn, in Rn into Pn, that it is a valuation, and that for every P∈Pn, ΠP is affinely associated to P. It is shown that these properties characterize the projection operator Π. This proves a conjecture by Lutwak