of a lattice polytope $\mathcal{P}$ is a combinatorial tool that enumerates the lattice points in dilations of $\mathcal{P}$. The $h^\ast$-vector of $\mathcal{P}$, denoted $h^\ast(\mathcal{P})$, records the coefficients in the numerator of the rational function representing the Ehrhart series. Understanding the $h^\ast$-vectors of reflexive polytopes has been a topic of extensive recent research [@Braun-Unimodality-Survey]. Hibi showed that reflexive polytopes have palindromic $h^\ast$-vectors [@Hibi--Palindromic].

A lattice polytope $\mathcal{P}$ is [**Gorenstein**]{} if some positive integer dilate of $\mathcal{P}$ is reflexive, and hence the Gorenstein property is a relaxation of reflexivity. The following conjecture is commonly attributed to Ohsugi and Hibi [@Ohsugi-Hibi] in the modern literature, though it is a special case of conjectures of Brenti [@Brenti--LogConcave] and of Stanley [@Stanley--LogConcave].

\[conj-unimodal\] If $\mathcal{P}$ is a Gorenstein polytope that has the integer decomposition property, then $h^\ast(\mathcal{P})$ is unimodal.

A prominent open question in Ehrhart Theory is whether the $h^\ast$-vector of every lattice polytope with IDP is unimodal [@Schepers-VanLangenhoven]; this is related to a conjecture of Stanley’s on the unimodality of $h$-vectors of Cohen-Macaulay and Gorenstein domains [@Stanley-Hilbert-Functions-CM]. Schepers and Van Langenhoven [@Schepers-VanLangenhoven] show that lattice parallelepipeds, which are among the simplest examples of polytopes that have IDP, also have unimodal $h^\ast$-vectors. We show ${\mathrm{Newt}}(s_\lambda)$ 