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A Discrete Isoperimetric Inequality and Its Application to Sphere Packings

  • Peter Scholl
  • Achill Schürmann
  • Jörg M. Wills
Chapter
  • 723 Downloads
Part of the Algorithms and Combinatorics book series (AC, volume 25)

Abstract

We consider finite packings of equal spheres in Euclidean 3–space E3365体育网站. The convex hull of the sphere centers is the packing polytope. In the first part of the paper we prove a tight inequality between the surface area of the packing polytope and the number of sphere centers on its boundary, and investigate in particular the equality cases. The inequality follows from a more general inequality for cell complexes on packing polytopes.

Keywords

Parametric Density Boundary Complex Sphere Packing Sphere Center Lattice Packing 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Peter Scholl
    • 1
  • Achill Schürmann
    • 1
  • Jörg M. Wills
    • 1
  1. 1.Department of MathematicsUniversity of SiegenSiegenGermany

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