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A proof of the Kepler conjecture
 Math. Intelligencer
, 1994
"... This section describes the structure of the proof of ..."
Abstract

Cited by 108 (11 self)
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This section describes the structure of the proof of
ON A STRONG VERSION OF THE KEPLER CONJECTURE
, 2013
"... 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 3space is partitioned into convex cells each containing a unit ball, how should the shapes of the cells be designed to minimize the average surface ar ..."
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 3space 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 √24 = 13.8564.... 3