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ON A STRONG VERSION OF THE KEPLER CONJECTURE

Part of: Designs and configurations Polytopes and polyhedra Discrete geometry

Published online by Cambridge University Press:  01 August 2012

Károly Bezdek
Károly Bezdek*
Affiliation:
Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW Calgary, Canada T2N 1N4 Department of Mathematics, University of Pannonia, Veszprém, Hungary Institute of Mathematics, Eötvös University, Budapest, Hungary (email: bezdek@math.ucalgary.ca)

Abstract

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We raise and investigate the following problem which 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 surface area of the cells? In particular, we prove that the average surface area in question is always at least

MSC classification

Secondary: 05B40: Packing and covering 05B45: Tessellation and tiling problems 52B60: Isoperimetric problems for polytopes 52C17: Packing and covering in $n$ dimensions 52C22: Tilings in $n$ dimensions
Type
Research Article
Information
Mathematika , Volume 59 , Issue 1 , January 2013 , pp. 23 - 30
Copyright
Copyright © University College London 2012

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