A Lower Bound Theorem for Centrally Symmetric Simplicial Polytopes

Steven Klee, Eran Nevo, Isabella Novik, Hailun Zheng

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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 languageEnglish
Pages (from-to)541-561
Number of pages21
JournalDiscrete and Computational Geometry
Volume61
Issue number3
DOIs
StatePublished - 15 Apr 2019
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

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

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