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The polyhedral Tammes problem

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Abstract.

The central question of this paper is the following somewhat more general version of the well-known Tammes problem, which we call the polyhedral Tammes problem. For given integers \(n\geqq d+1\geqq 3\) find the maximum of the shortest distance between any two of the n vertices of a convex d-polytope with diameter 1 in E d. We study this question for large n, as well as for some small values of n for fixed d.

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Authors and Affiliations

  1. Cornell University, Department of Mathematics, Malott Hall, Ithaca, New York 14853-7901, USA, , , , , , US

    K. Bezdek

  2. 33 – 34 77th St. Apt. 5C, Flushing, NY 11372, USA, , , , , , US

    G. Blekherman

  3. Cornell University, Department of Mathematics, Malott Hall, Ithaca, New York 14853-7901, USA, , , , , , US

    R. Connelly

  4. Eötvös University, Institute of Mathematics II, Department of Geometry, H-1088 Budapest, Rákóczi út 5, Hungary, , , , , , HU

    B. Csikós

Authors
  1. K. Bezdek
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  2. G. Blekherman
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  3. R. Connelly
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  4. B. Csikós
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Received: 19.8.1999

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Bezdek, K., Blekherman, G., Connelly, R. et al. The polyhedral Tammes problem. Arch. Math. 76, 314–320 (2001). https://doi.org/10.1007/s000130050574

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  • DOI: https://doi.org/10.1007/s000130050574

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