Reflexive polytopes arising from edge polytopes

TL;DR

This paper introduces a new class of reflexive polytopes that contain edge polytopes of finite simple graphs as facets, extending the understanding of their geometric and normality properties.

Contribution

It constructs a new class of reflexive polytopes where every edge polytope is a facet, and extends normality characterization to these polytopes.

Findings

Edge polytopes are unimodularly equivalent to facets of new reflexive polytopes.

Normality characterization is extended to these reflexive polytopes.

Provides a positive answer to the question for a large family of (0,1)-polytopes.

Abstract

It is known that every lattice polytope is unimodularly equivalent to a face of some reflexive polytope. A stronger question is to ask whether every $(0,1)$-polytope is unimodularly equivalent to a facet of some reflexive polytope. A large family of $(0,1)$-polytopes are the edge polytopes of finite simple graphs. In the present paper, it is shown that, by giving a new class of reflexive polytopes, each edge polytope is unimodularly equivalent to a facet of some reflexive polytope. Furthermore, we extend the characterization of normal edge polytopes to a characterization of normality for these new reflexive polytopes.