Almost simplicial polytopes: The lower and upper bound theorems

Eran Nevo, Guillermo Pineda-Villavicencio, Julien Ugon, David Yost

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


This is an extended abstract of the full version. We study n-vertex d-dimensional polytopes with at most one nonsimplex facet with, say, d + s vertices, called almost simplicial polytopes. We provide tight lower and upper bounds for the face numbers of these polytopes as functions of d, n and s, thus generalizing the classical Lower Bound Theorem by Barnette and Upper Bound Theorem by McMullen, which treat the case s = 0. We characterize the minimizers and provide examples of maximizers, for any d.

Original languageAmerican English
Pages (from-to)947-958
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2016
Event28th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2016 - Vancouver, Canada
Duration: 4 Jul 20168 Jul 2016

Bibliographical note

Publisher Copyright:
© 2014 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France


  • F-vector
  • Graph rigidity
  • LBT
  • Moment curve
  • Polytope
  • UBT


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