Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T04:25:50.315Z Has data issue: false hasContentIssue false
  • English
  • Français

The lower bound theorem for centrally symmetric simple polytopes

Part of: Polytopes and polyhedra

Published online by Cambridge University Press:  26 February 2010

Isabella Novik
Isabella Novik
Affiliation:
Institute of Mathematics, The Hebrew University, Givat Ram, Jerusalem 91904, Israel.
Get access

Abstract

A new and more geometric proof is obtained of Stanley's lower bounds on the face numbers of centrally symmetric simple polytopes.

MSC classification

Secondary: 52B15: Symmetry properties of polytopes
Type
Research Article
Information
Mathematika , Volume 46 , Issue 2 , December 1999 , pp. 231 - 240
Copyright
Copyright © University College London 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. A'Campo-Neuen, A.. On generalized h-vectors of rational polytopes with symmetry of prime order. Discrete Comput. Geom., 22 (1999), 259–268.Google Scholar
2. Adin, R. M.. On h-vectors and symmetry. In Jerusalem Combinatorics '93, Coniemp. Math. 178 (1994), 1–20.CrossRefGoogle Scholar
3. Adin, R. M.. On face numbers of rational simplicial polytopes with symmetry. Adv. Math., 115 (1995), 268–285.Google Scholar
4. McMullen, P.. Representations of polytopes and polyhedral sets. Geom. Ded., 2 (1973), 83–89.CrossRefGoogle Scholar
5. McMullen, P.. On simple polytopes. Invent. Math., 113 (1993), 419–444.Google Scholar
6. McMullen, P.. Weights on polytopes. Discrete Comput. Geom., 15 (1996), 363–388.CrossRefGoogle Scholar
7. McMullen, P. and Shephard, G. C.. Diagrams for centrally symmetric polytopes. Mathematika 15 (1968), 123–138.Google Scholar
8. Stanley, R. P.. On the number of faces of centrally symmetric simplicial polytopes. Graphs and Combinatorics, 3 (1987), 55–66.CrossRefGoogle Scholar