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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 Quelle/n Erschienen in Discrete Comput.\ Geometry, volume 41, pages 183-198 Art Text