An interesting problem in Ehrhart theory is to identify lattice polytopes having a unimodal h*-vector. In this talk, we consider integrally closed reflexive simplices and discuss an operation that preserves reflexivity, integral closure, and unimodality of the h*-vector, providing one explanation for why unimodality occurs in this setting. We also discuss the failure of proving unimodality in this setting using an approach via Lefschetz elements. This is joint work with Robert Davis.