Hilbert's eighteenth problem

Hilbert's eighteenth problem is one of the 23 problems set out in a celebrated list compiled in 1900 by mathematician David Hilbert. It asks three separate questions on the space group in -dimensional Euclidean space, anisohedral tiling in three-dimensional Euclidean space, and the densest sphere packing in Kepler conjecture. Respectively, these questions were answered affirmatively by Ludwig Bieberbach, Karl Reinhardt, and Thomas Callister Hales.

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