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Given a family of lattice polytopes, two common questions in Ehrhart Theoryare determining when a polytope has the integer decomposition property anddetermining when a polytope is reflexive. While these properties are ofindependent interest, the confluence of these properties is a source of activeinvestigation due to conjectures regarding the unimodality of the$h^\ast$-polynomial. In this paper, we consider the Newton polytopes arisingfrom two families of polynomials in algebraic combinatorics: Schur polynomialsand inflated symmetric Grothendieck polynomials. In both cases, we prove thatthese polytopes have the integer decomposition property by using the fact thatboth families of polynomials have saturated Newton polytope. Furthermore, inboth cases, we provide a complete characterization of when these polytopes arereflexive. We conclude with some explicit formulas and unimodality implicationsof the $h^\ast$-vector in the case of Schur polynomials.

Lattice polytopes from Schur and symmetric Grothendieck polynomials