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Selected Proofs on Sphere Packings

  • Károly Bezdek
Chapter
Part of the CMS Books in Mathematics book series (CMSBM)

Abstract

Let B denote the unit ball centered at the origin o of \(\mathbb{E}^3\) and let \(\mathcal{P} : = {{\rm c}_1 + {\bf B}, {\rm c}_2 + {\bf c}, \cdots, {\rm c}_n + {\bf B}}\) denote the packing of n unit balls with centers c1; c2;… cn in \(\mathbb{E}^3\) having the largest number C(n) of touching pairs among all packings of n unit balls in \(\mathbb{E}^3\). (\(\mathcal{P}\) might not be uniquely determined up to congruence in which case \(\mathcal{P}\) stands for any of those extremal packings.) First, observe that Theorem 1.4.1 and Theorem 2.4.3 imply the following inequality in a straightforward way.

Keywords

Unit Ball Voronoi Cell Volume Force Sphere Packing Rigidity Matrix 
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 Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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