A Note on Palindromic $\delta$-Vectors for Certain Rational Polytopes

Abstract

Let $P$ be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if $P$ is also a lattice polytope then the Ehrhart $\delta$-vector of $P$ is palindromic. Perhaps less well-known is that a similar result holds when $P$ is rational. We present an elementary lattice-point proof of this fact.