The Hexagonal Honeycomb Conjecture

Morgan, Frank

doi:10.1090/S0002-9947-99-02356-9

The Hexagonal Honeycomb Conjecture
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Trans. Amer. Math. Soc. 351 (1999), 1753-1763 Request permission

Abstract:

It is conjectured that the planar hexagonal honeycomb provides the least-perimeter way to enclose and separate infinitely many regions of unit area. Various natural formulations of the question are not known to be equivalent. We prove existence for two formulations. Many questions remain open.

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