A Note on Kalai's $3^d$ Conjecture

  • Gregory R. Chambers
  • Elia Portnoy
DOI: https://doi.org/10.37236/13956

Abstract

Suppose that $C$ is a centrally symmetric $d$-dimensional convex polytope; in 1989 Kalai conjectured that $C$ has at least $3^d$ faces. We prove this result if there are $d$ hyperplanes with orthogonal normal vectors so that $C$ is symmetric about all of them.

Published
2026-08-07
How to Cite
Chambers, G., & Portnoy, E. (2026). A Note on Kalai’s $3^d$ Conjecture. The Electronic Journal of Combinatorics, 33(3), #P3.24. https://doi.org/10.37236/13956
Issue
Volume 33, Issue 3 (2026)
Article Number
P3.24