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Periodica Mathematica Hungarica

, Volume 39, Issue 1–3, pp 7–15 | Cite as

DANZER-GRüNBAUM'S THEOREM REVISITED

  • Károly Bezdek
  • Grigoriy Blekherman
Article
  • 78 Downloads

Abstract

In this paper we prove some stronger versions of Danzer-Grünbaum's theorem including the following stability-type result. For 0 < α < 14π/27 the maximum number of vertices of a convex polyhedron in E 3 such that all angles between adjacent edges are bounded from above by α is 8. One of the main tools is the spherical geometry version of Pál's theorem.

Keywords

Main Tool Strong Version Spherical Geometry Convex Polyhedron Adjacent Edge 
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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Károly Bezdek
    • 1
  • Grigoriy Blekherman
    • 1
  1. 1.Department of GeometryEötvös UniversityHungary E-mail

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