  We obtain a recurrence relation for the f-polynomial of Gelfand-Zetlin
polytopes by analyzing geometric properties of a linear projection of the
Gelfand-Zetlin polytope onto a cube. We apply this recurrence relation to find
explicit formulas for the f-polynomials and h-polynomials of Gelfand-Zetlin
polytopes that belong to several simplest one-parameter families.
