Geodesic
Perfect Prismatoids and the Conjecture Concerning Face Numbers of Centrally Symmetric Polytopes
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 6, pp. 137-147.

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In this paper we introduce and study a class of centrally symmetric polytopes — perfect prismatoids — and some its properties related to the famous conjecture concerning face numbers of centrally symmetric polytopes are proved. It is proved that any Hanner polytope is a perfect prismatoid and any perfect prismatoid is affine equivalent to some $0/1$-polytope.
Keywords: polytopes, Hanner polytopes
Mots-clés : Kalai's conjecture. 
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M. A. Kozachok. Perfect Prismatoids and the Conjecture Concerning  Face Numbers of Centrally Symmetric Polytopes. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 6, pp. 137-147. http://geodesic.mathdoc.fr/item/MAIS_2012_19_6_a12/

[1] I. Barany, L. Lovasz, “On the numbers of faces of centrally-symmetric simplicial polytopes”, Graphs and Combinatorics, 3 (1987), 55–66 | MR

[2] O. Hanner, “Intersections of translates of convex body”, Math. Scand., 4 (1956), 67–89 | MR

[3] G. Kalai, “The Number of Faces of Centrally-symmetric Polytopes”, Graphs and Combinatorics, 5 (1989) | MR

[4] R. Sanyal, A. Werner, G. Ziegler, On Kalai’s conjectures concerning centrally symmetric polytopes, 2007, arXiv: 0708.3661v2 [math.CO] | MR

[5] R. Stanley, “Borsuk's theorem and the number of centrally symmetric polytopes”, Acta Math. Acad. Sci. Hungar., 40 (1982), 323–329 | MR

[6] G. Ziegler, Lectures on Polytopes, Springer-Verlag, New York, 1995 | MR

[7] M. S. Panov, “Critical Polyhedra”, Proceedings, Numgrid, 2008 | MR