Selected Proofs on Sphere Packings

Part of the CMS Books in Mathematics book series (CMSBM)


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.


Unit Ball Voronoi Cell Volume Force Sphere Packing Rigidity Matrix 
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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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