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On Minimal Tilings with Convex Cells Each Containing a Unit Ball

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Part of the Fields Institute Communications book series (FIC, volume 69)

Abstract

We investigate the following problem that one can regard as a very close relative of the densest sphere packing problem. If the Euclidean 3-space is partitioned into convex cells each containing a unit ball, how should the shapes of the cells be designed to minimize the average edge curvature of the cells? In particular, we prove that the average edge curvature in question is always at least \(13.8564\ldots\).

Key words

Tiling Convex cell Unit sphere packing Average edge curvature Foam problem 

Subject Classifications

05B40 05B45 52B60 52C17 52C22 

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada
  2. 2.Department of MathematicsUniversity of PannoniaHungaryCanada

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