A Lower Bound Theorem for Centrally Symmetric Simplicial Polytopes

Steven Klee, Eran Nevo, Isabella Novik*, Hailun Zheng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Stanley proved that for any centrally symmetric simplicial d-polytope P with d≥ 3 , g2(P)≥(d2)-d. We provide a characterization of centrally symmetric simplicial d-polytopes with d≥ 4 that satisfy this inequality as equality. This gives a natural generalization of the classical Lower Bound Theorem for simplicial polytopes to the setting of centrally symmetric simplicial polytopes.

Original languageAmerican English
Pages (from-to)541-561
Number of pages21
JournalDiscrete and Computational Geometry
Issue number3
StatePublished - 15 Apr 2019

Bibliographical note

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


  • Centrally symmetric polytopes
  • Face numbers
  • Infinitesimal rigidity
  • Missing faces
  • Stacked spheres
  • Stresses


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