Advertisement

Discrete & Computational Geometry

, Volume 9, Issue 2, pp 159–163 | Cite as

The lower and upper bound problems for cubical polytopes

  • William Jockusch
Article

Abstract

We construct a family of cubical polytypes which shows that the upper bound on the number of facets of a cubical polytope (given a fixed number of vertices) is higher than previously suspected. We also formulate a lower bound conjecture for cubical polytopes.

Keywords

Convex Hull Discrete Comput Geom Boundary Complex Modeling Clay Simplicial Polytopes 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [A]
    E. A. Abbott,Flatland, a Romance of Many Dimensions, New York: Harper and Row, 1983.MATHGoogle Scholar
  2. [B1]
    D. W. Barnette, The minimum number of vertices of a simple polytope,Israel J. Math. 10 (1971), 121–125.MathSciNetCrossRefMATHGoogle Scholar
  3. [B2]
    D. W. Barnette, A proof of the lower bound conjecture for convex polytopes,Pacific J. Math. 46 (1973), 349–354.MathSciNetCrossRefMATHGoogle Scholar
  4. [BB]
    G. Blind and R. Blind, Convex Polytopes Without Triangular Faces,Israel J. Math. 71 (1990), 129–134.MathSciNetCrossRefMATHGoogle Scholar
  5. [M]
    P. McMullen, The maximum numbers of faces of a convex polytope,Mathematika 17 (1970), 179–184.MathSciNetCrossRefMATHGoogle Scholar
  6. [R]
    Rutgers University, Problems presented at the DIMACS Workshop on Polytopes and Convex Sets, 1990.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • William Jockusch
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

Personalised recommendations