A boundary analogue of the Sturmfels correspondence equates the h*-polynomial of lattice-polytope boundaries with the h-polynomial of regular unimodular triangulations, yielding Dehn-Sommerville relations and symmetry/unimodality characterizations.
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Boundary $h^\ast$-vectors and unimodular triangulations
A boundary analogue of the Sturmfels correspondence equates the h*-polynomial of lattice-polytope boundaries with the h-polynomial of regular unimodular triangulations, yielding Dehn-Sommerville relations and symmetry/unimodality characterizations.