Unconditional Reflexive Polytopes

Florian Kohl, McCabe C. Olsen, Raman Sanyal*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
127 Downloads (Pure)


A convex body is unconditional if it is symmetric with respect to reflections in all coordinate hyperplanes. We investigate unconditional lattice polytopes with respect to geometric, combinatorial, and algebraic properties. In particular, we characterize unconditional reflexive polytopes in terms of perfect graphs. As a prime example, we study the signed Birkhoff polytope. Moreover, we derive constructions for Gale-dual pairs of polytopes and we explicitly describe Gröbner bases for unconditional reflexive polytopes coming from partially ordered sets.

Original languageEnglish
Pages (from-to)427-452
Number of pages26
JournalDiscrete and Computational Geometry
Issue number2
Publication statusPublished - 1 Sep 2020
MoE publication typeA1 Journal article-refereed


  • Gale-dual pairs
  • Perfect graphs
  • Reflexive polytopes
  • Signed Birkhoff polytopes
  • Unconditional polytopes
  • Unimodular triangulations


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