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# On Kalai's conjectures about centrally symmetric polytopes

## Raman Sanyal and Axel Werner and Günter M. Ziegler – 2009

In 1989 Kalai stated the three conjectures A, B, C of increasing strength concerning face numbers of centrally symmetric convex polytopes. The weakest conjecture, A, became known as the $3^d$-conjecture''. It is well-known that the three conjectures hold in dimensions d \leq 3. We show that in dimension 4 only conjectures A and B are valid, while conjecture C fails. Furthermore, we show that both conjectures B and C fail in all dimensions d \geq 5.

Titel
On Kalai's conjectures about centrally symmetric polytopes
Verfasser
Raman Sanyal and Axel Werner and Günter M. Ziegler
Datum
2009
Erschienen in
Discrete Comput.\ Geometry, volume 41, pages 183-198
Art
Text