Discrete & Computational Geometry

, Volume 6, Issue 1, pp 33–47

A new index for polytopes

  • Margaret M. Bayer
  • Andrew Klapper

DOI: 10.1007/BF02574672

Cite this article as:
Bayer, M.M. & Klapper, A. Discrete Comput Geom (1991) 6: 33. doi:10.1007/BF02574672


A new index for convex polytopes is introduced. It is a vector whose length is the dimension of the linear span of the flag vectors of polytopes. The existence of this index is equivalent to the generalized Dehn-Sommerville equations. It can be computed via a shelling of the polytope. The ranks of the middle perversity intersection homology of the associated toric variety are computed from the index. This gives a proof of a result of Kalai on the relationship between the Betti numbers of a polytope and those of its dual.

Copyright information

© Springer-Verlag New York Inc 1991

Authors and Affiliations

  • Margaret M. Bayer
    • 1
  • Andrew Klapper
    • 2
  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA
  2. 2.College of Computer ScienceNortheastern UniversityBostonUSA