On the cone of f-vectors of cubical polytopes

Ron M. Adin, Daniel Kalmanovich, Eran Nevo, Patricia Hersh

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


What is the minimal closed cone containing all f-vectors of cubical d-polytopes? We construct cubical polytopes showing that this cone, expressed in the cubical g-vector coordinates, contains the nonnegative g-orthant, thus verifying one direction of the Cubical Generalized Lower Bound Conjecture of Babson, Billera, and Chan. Our polytopes also show that a natural cubical analogue of the simplicial Generalized Lower Bound Theorem does not hold.

Original languageEnglish
Pages (from-to)1851-1866
Number of pages16
JournalProceedings of the American Mathematical Society
Issue number5
StatePublished - 1 May 2019
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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