Preorder polytopes generalize arbor polytopes as lattice polytopes with a proven duality between Ehrhart polynomials and zeta polynomials of their lattice point posets, plus combinatorial volume interpretations and formulas for Ehrhart and h*-polynomials.
Chapoton, On a q -analogue of the Zeta polynomial of posets, arXiv:2402.11979v2
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Polytopes and posets associated to preorders
Preorder polytopes generalize arbor polytopes as lattice polytopes with a proven duality between Ehrhart polynomials and zeta polynomials of their lattice point posets, plus combinatorial volume interpretations and formulas for Ehrhart and h*-polynomials.