In geometry, **Kalai's 3**^{d}** conjecture** is a conjecture on the polyhedral combinatorics of centrally symmetric polytopes, made by Gil Kalai in 1989.^{[1]} It states that every *d*-dimensional centrally symmetric polytope has at least 3* ^{d}* nonempty faces (including the polytope itself as a face but not including the empty set).

**Unsolved problem in mathematics**:

*Does every d-dimensional centrally symmetric polytope have at least 3 ^{d} nonempty faces?*