Reflexive polytopes arising from edge polytopes
arXiv:1712.06078 · doi:10.1016/j.laa.2018.08.012
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 -polytope is unimodularly equivalent to a facet of some reflexive polytope. A large family of -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.
16 pages, to appear in Linear Algebra and its Applications