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The minimum number of vertices of a simple polytope

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Abstract

Ad-polytope is ad-dimensional set that is the convex hull of a finite number of points. Ad-polytope is simple provided each vertex meets exactlyd edges. It has been conjectured that for simple polytopes {fx121-1} wheref i is the number ofi-dimensional faces of the polytope. In this paper we show that inequality (i) holds for all simple polytopes.

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References

  1. G. T. Sallee,Incidence Graphs of Polytopes, J. Combinatorial Theory2 (1967), 466–506.

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  2. B. Grünbaum,Convex Polytopes, Wiley and Sons, New York, 1967.

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Authors and Affiliations

  1. University of California, Davis

    David W. Barnette

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  1. David W. Barnette
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Research supported by N.S.F. Grant GP-19221.

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Barnette, D.W. The minimum number of vertices of a simple polytope. Israel J. Math. 10, 121–125 (1971). https://doi.org/10.1007/BF02771522

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  • DOI: https://doi.org/10.1007/BF02771522

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