Kalai's 3^d conjecture, in geometry and polytope theory, concerns the polyhedral combinatorics of centrally symmetric polytopes. Formulated in 1989 by the mathematician Gil Kalai, it states that every d-dimensional centrally symmetric polytope has at least 3^d nonempty faces.
Facts
StatementEvery d dimensional centrally symmetric polytope has at least 3 to the power d nonempty faces, including the polytope itself as a face but not including the empty set. 1 Proposed Year Progress Toward ResolutionKalai's 3^d conjecture is known to be true for d less than or equal to 4. 1 Classification
Resolution Status Prize Status
Prize Status (category) Sources
1. Kalai's 3^d Conjecture, Wikipedia
Introduction section
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).
Introduction section, second sentence
made by Gil Kalai in 1989.
Status section
The conjecture is known to be true for d <= 4.
- Lead section
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