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.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Keywords
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Bezdek, K. (2010). Selected Proofs on Sphere Packings. In: Classical Topics in Discrete Geometry. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0600-7_7
Download citation
DOI: https://doi.org/10.1007/978-1-4419-0600-7_7
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-0599-4
Online ISBN: 978-1-4419-0600-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)