Israel Journal of Mathematics

, Volume 47, Issue 4, pp 261–269

Two combinatorial properties of a class of simplicial polytopes

  • Carl W. Lee

DOI: 10.1007/BF02760600

Cite this article as:
Lee, C.W. Israel J. Math. (1984) 47: 261. doi:10.1007/BF02760600


Letf(Psd) be the set of allf-vectors of simpliciald-polytopes. ForP a simplicial 2d-polytope let Σ(P) denote the boundary complex ofP. We show that for eachff(Psd) there is a simpliciald-polytopeP withf(P)=f such that the 11 02 simplicial diameter of Σ(P) is no more thanf0(P)−d+1 (one greater than the conjectured Hirsch bound) and thatP admits a subdivision into a simpliciald-ball with no new vertices that satisfies the Hirsch property. Further, we demonstrate that the number of bistellar operations required to obtain Σ(P) from the boundary of ad-simplex is minimum over the class of all simplicial polytopes with the samef-vector. This polytopeP will be the one constructed to prove the sufficiency of McMullen's conditions forf-vectors of simplicial polytopes.

Copyright information

© Hebrew University 1984

Authors and Affiliations

  • Carl W. Lee
    • 1
    • 2
  1. 1.IBM Thomas J. Watson Research CenterYorktown HeightsUSA
  2. 2.Department of MathematicsUniversity of KentuckyLexingtonUSA

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