**Author:** Gil Kalai

**DOI:** __https://doi.org/10.1007/BF01788696__

A *d*-dimensional polytope (briefly, a *d*-polytope) *P* is centrally symmetric if *x *∈* P* implies *(-x) *∈* P*. Recall that the (proper) *faces* of *P* are the intersections of *P* with supporting hyperplanes. The empty set and *P* itself are regarded as trivial faces.

*Conjecture A*. Every centrally-symmetric *d*-polytope has at least 3^{d} non-empty faces.