Author: Gil Kalai
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 3d non-empty faces.