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arXiv · 1712.06078

Reflexive polytopes arising from edge polytopes

Takahiro Nagaoka·Akiyoshi Tsuchiya
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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.

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Takahiro Nagaoka, Akiyoshi Tsuchiya. 2017-12-17. Reflexive polytopes arising from edge polytopes. https://doi.org/10.1016/j.laa.2018.08.012

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