Reflexive polytopes arising from edge polytopes

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 fi...

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Bibliographic Details
Published inarXiv.org
Main Authors Nagaoka, Takahiro, Tsuchiya, Akiyoshi
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 08.08.2018
Subjects
Equivalence
Mathematics - Combinatorics
Normality
Polytopes
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1712.06078