---
tag: 5CRY9ZK4Y2
kind: conjecture
name: Kalai's 3^d conjecture
aliases: [full-flag-conjecture, kalais-3d-conjecture]
sources:
  - wikipedia: en:39408412@r1364111300
    locator: Kalai's 3^d conjecture
    note: adopted
    mention: wikipedia://en/39408412
    sections: [Statement]
same_as:
  wikidata: Q17077841
  wikipedia: Kalai's 3^d conjecture
inventory: [S87DCMV9X3]
---

## Statement

In geometry, more specifically in polytope theory, **Kalai's 3<sup>*d*</sup> conjecture** is a conjecture on the polyhedral combinatorics of centrally symmetric polytopes, made by Gil Kalai in 1989. It states that every *d*-dimensional centrally symmetric polytope has at least 3<sup>*d*</sup> nonempty faces (including the polytope itself as a face but not including the [[empty set|0ECVK59Y03]]).