A [**(lattice) triangulation**]{} $\mathcal{T}$ of ${\mathcal{P}}$ is a decomposition of ${\mathcal{P}}$ as a lattice simplicial complex. We say that $\mathcal{T}$ is [**regular**]{} if the triangulation is induced as the domains of linearity of a piecewise-linear, convex function $\sigma:{\mathcal{P}}\to {\mathbb{R}}$. We say that $\mathcal{T}$ is [**unimodular**]{} if each maximal simplex $\Delta\in \mathcal{T}$ is a [**unimodular simplex**]{}, that is, if the vertices of $\Delta$ generate ${\mathbb{Z}}^d$. We say that ${\mathcal{P}}$ has the [**integer decomposition property (IDP)**]{} if for any positive integer $t$ and any lattice point $\p \in t\mathcal{P}\cap \mathbb{Z}^m$, there are $t$ lattice points $\bv_1, \ldots, \bv_t \in \mathcal{P}\cap \mathbb{Z}^m$ such that $\p= \bv_1+\cdots+\bv_t.$ The existence of a (regular) unimodular triangulation of ${\mathcal{P}}$ ensures that ${\mathcal{P}}$ has IDP. This implication is strict as one can construct examples of polytopes with IDP without a unimodular triangulation (see, e.g., [@Bruns-Gubeladze; @Firla-Ziegler]).

A sequence $a_0,a_1,\dots,a_n$ of real numbers is [**unimodal**]{} if there is some $0\leq j\leq n$ such that $a_0 \leq a_1 \leq \cdots \leq a_{j-1} \leq a_j \geq a_{j+1} \geq \cdots \geq a_n$. A common investigatory theme in Ehrhart theory is determining under what conditions one may ensure that coefficients of the $h^\ast$-vector form a unimodal sequence. The most notable sufficient result is 