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On a conjecture of lindenstrauss

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Abstract

It is proved that eachn-dimensional centrally symmetric convex polyhedron admits a 2-dimensional central section having at least 2n vertices. Some other related results are obtained and some unsolved problems are mentioned.

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References

  1. Bourbaki, N., 1955,Espaces vectoriels topologiques, Chaps. 3–5, A.S.I.,1229, Hermann, Paris.

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  2. Klee, V., 1959, Some characterizations of convex polyhedra,Acta. Math.,102, 79–107.

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  3. Klee, V., 1960, Polyhedral sections of convex bodies,Acta. Math.,103, 243–267.

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Authors and Affiliations

  1. University of Washington, Seattle, Washington, U.S.A.

    Victor Klee

Authors
  1. Victor Klee
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Additional information

Research supported in part by the National Science Foundation, U.S.A. (NSF-GP-378).

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Klee, V. On a conjecture of lindenstrauss. Israel J. Math. 1, 1–4 (1963). https://doi.org/10.1007/BF02759794

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  • DOI: https://doi.org/10.1007/BF02759794

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