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On Minimal Tilings with Convex Cells Each Containing a Unit Ball
[chapter]
2013
Fields Institute Communications
Preserved Fulltext
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 : : :.
doi:10.1007/978-3-319-00200-2_4
fatcat:fcjxi7mirndypaczxs7jdn4pba