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Israel Journal of Mathematics

, Volume 6, Issue 4, pp 398–411 | Cite as

Some analogues of eberhard’s theorem on convex polytopes

  • B. Grünbaum
Article

Abstract

Letp k denote the number ofk-gonal faces of a simple 3-polytope. Euler’s relation leads to an equation between thep k ’s which does not involvep 6. Eberhard proved in 1891 that every sequence of non-negative integers (p 3,p 4,…) satisfying this equation corresponds to a polytope for suitable values ofp 6. In the present paper it is established that ifp 3=p 4=0 then every valuep 6≧8 is suitable.

Keywords

Planar Graph Nonnegative Integer Convex POLYTOPES Local Insertion Topological Disc 
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.

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References

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Copyright information

© Hebrew University 1968

Authors and Affiliations

  • B. Grünbaum
    • 1
  1. 1.University of WashingtonSeattle

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