A Note on Kalai's $3^d$ Conjecture
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.
Fields of Study & Subjects
Point processes and geometric inequalities
Advanced Combinatorial Mathematics
Mathematical Inequalities and Applications
Publication details
- Journal / source
- The Electronic Journal of Combinatorics
- Volume
- 33
- Issue
- 3
- Publication date
- 7 August 2026
- Language
- EN