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The maximum area of the convex hull of a polyhex
A polyhex is an edge-connected set of n cells of the regular hexagonal tiling, where each cell has area one. We prove that the convex hull of a polyhex has area at most (1/6)*ceiling(n^2 + 14n/3), and we show that some polyhex reaches this bound for every n. This proves a conjecture of Kurz from 200
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