Self dual reflexive simplices with Eulerian polynomials

Abstract

A lattice polytope $\mathcal{P}$ is called reflexive if its dual ${\mathcal{P}}^{\vee }$ is a lattice polytope. The property that $\mathcal{P}$ is unimodularly equivalent to ${\mathcal{P}}^{\vee }$ does not hold in general, and in fact there are few examples of such polytopes. In this note, we introduce a new reflexive simplex $Q_n$ which has this property. Additionally, we show that $\delta$-polynomalial of $Q_n$ is the Eulerian polynomial and show the existence of a regular, flag, unimodular triangulation.

final version. To appear in Graphs and Combinatorics JCCA 2016 Conference Proceedings

References in corpus (2)

• Generating functions and triangulations for lecture hall cones
• The $\delta$-vectors of reflexive polytopes and of the dual polytopes