  With any integer convex polytope $P\subset\midR^n$ we associate a
multivariate hypergeometric polynomial whose set of exponents is $\midZ^{n}\cap
P.$ This polynomial is defined uniquely up to a constant multiple and satisfies
a holonomic system of partial differential equations of Horn's type. We prove
that the zero locus of any such polynomial is optimal in the sense of
Forsberg-Passare-Tsikh.
