Simion’s Type B Associahedron is a Pulling Triangulation of the Legendre Polytope

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5 Scopus citations


We show that the Simion type B associahedron is combinatorially equivalent to a pulling triangulation of the type A root polytope known as the Legendre polytope. Furthermore, we show that every pulling triangulation of the boundary of the Legendre polytope yields a flag complex. Our triangulation refines a decomposition of the boundary of the Legendre polytope given by Cho. Finally, we extend Cho’s cyclic group action to the triangulation in such a way that it corresponds to rotating centrally symmetric triangulations of a regular (2 n+ 2) -gon.

Original languageEnglish
Pages (from-to)98-114
Number of pages17
JournalDiscrete and Computational Geometry
Issue number1
StatePublished - Jul 1 2018

Bibliographical note

Funding Information:
Acknowledgements The authors thank the Princeton University Mathematics Department where this research was initiated. The first author was partially funded by the National Security Agency Grant H98230-13-1-028. This work was partially supported by grants from the Simons Foundation (# 429370 to Richard Ehrenborg, # 245153 and # 514648 to Gábor Hetyei, # 206001 and # 422467 to Margaret Readdy). The authors also thank the three anonymous referees for their comments.

Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.


  • Bott–Taubes polytope
  • Compressed polytopes
  • Cyclohedron
  • Flag complex
  • Stasheff polytope
  • Type A root polytope

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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