Regular Unimodular Triangulations of Reflexive IDP 2-Supported Weighted Projective Space Simplices

For each integer partition q with d parts, we denote by Δ _(1,q) the lattice simplex obtained as the convex hull in R^d of the standard basis vectors along with the vector - q. For q with two distinct parts such that Δ _(1,q) is reflexive and has the integer decomposition property, we establish a characterization of the lattice points contained in Δ _(1,q). We then construct a Gröbner basis with a squarefree initial ideal of the toric ideal defined by these simplices. This establishes the existence of a regular unimodular triangulation for reflexive 2-supported Δ _(1,q) having the integer decomposition property. As a corollary, we obtain a new proof that these simplices have unimodal Ehrhart h^∗-vectors.