A note on palindromic $\delta$-vectors for certain rational polytopes
  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. 
Matthew H. J. Fiset and Alexander M. Kasprzyk