Perfect Prismatoids and the Conjecture Concerning Face Numbers of Centrally Symmetric Polytopes
https://doi.org/10.18255/1818-1015-2012-6-137-147
Abstract
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.
About the Author
M. A. Kozachok
Математический институт им. В.А. Стеклова РАН;
Ярославский государственный университет им. П.Г. Демидова,
Международная лаборатория "Дискретная и вычислительная геометрия" им. Б.Н. Делоне
Russian Federation
Russian Federation
References
1. Barany I., Lovasz L. On the numbers of faces of centrally-symmetric simplicial polytopes // Graphs and Combinatorics. 1987. 3. P. 55–66.
2. Hanner O. Intersections of translates of convex body // Math. Scand. 1956. 4. P. 67–89.
3. Kalai G.The Number of Faces of Centrally-symmetric Polytopes // Graphs and Combinatorics. 1989. 5.
4. Sanyal R., Werner A., Ziegler G. On Kalai’s conjectures concerning centrally symmetric polytopes, 2007.
5. Stanley R. Borsuk’s theorem and the number of centrally symmetric polytopes // Acta Math. Acad. Sci. Hungar. 1982. 40. P. 323–329.
6. Ziegler G. Lectures on Polytopes. Springer-Verlag, New York, 1995.
7. Panov M.S. Critical Polyhedra, Proceedings, Numgrid, 2008.
Review
For citations:
Kozachok M.A. Perfect Prismatoids and the Conjecture Concerning Face Numbers of Centrally Symmetric Polytopes. Modeling and Analysis of Information Systems. 2012;19(6):137-147. (In Russ.) https://doi.org/10.18255/1818-1015-2012-6-137-147
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