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On a strong version of the Kepler conjecture
We raise and 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 surface area of the
cells? In particular, we prove that the average surface area in question is
always at least 13.8564... .Comment: 9 page
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