The $\delta$-vectors of reflexive polytopes and of the dual polytopes

Abstract

Let $\delta (\mathcal{P})$ be the $\delta$-vector of a reflexive polytope $\mathcal{P}\subset {\mathbb{R}}^d$ of dimension $d$ and $\delta ({\mathcal{P}}^{\vee })$ the $\delta$-vector of the dual polytope ${\mathcal{P}}^{\vee }\subset {\mathbb{R}}^d$. In general, $\delta (\mathcal{P})=\delta ({\mathcal{P}}^{\vee })$ does not hold. In this paper, we give a higher-dimensional construction of reflexive polytope whose $\delta$-vector equals the $\delta$-vector of the dual polytope. In particular, we consider the case that the reflexive polytope and the dual polytope are unimodularly equivalent.

10 pages

Cited by in corpus (2)

• Likelihood Geometry of Reflexive Polytopes
• Self dual reflexive simplices with Eulerian polynomials