Discrete & Computational Geometry

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

The lower and upper bound problems for cubical polytopes

  • William Jockusch


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.


Convex Hull Discrete Comput Geom Boundary Complex Modeling Clay Simplicial Polytopes 


  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

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