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Stanley (1986) showed how a finite partially ordered set gives rise to twopolytopes, called the order polytope and chain polytope, which have the sameEhrhart polynomial despite being quite different combinatorially. We generalizehis result to a wider family of polytopes constructed from a poset P withintegers assigned to some of its elements.  Through this construction, we explain combinatorially the relationshipbetween the Gelfand-Tsetlin polytopes (1950) and the Feigin-Fourier-Littelmannpolytopes (2010), which arise in the representation theory of the speciallinear Lie algebra. We then use the generalized Gelfand-Tsetlin polytopes ofBerenstein and Zelevinsky (1989) to propose conjectural analogues of theFeigin-Fourier-Littelmann polytopes corresponding to the symplectic and oddorthogonal Lie algebras.

Gelfand-Tsetlin polytopes and Feigin-Fourier-Littelmann polytopes as marked poset polytopes