Note 4

No system of hexagons alone can enclose space; whether the hexagons be equal or unequal, regular or irregular, it is still under all circumstances mathematically impossible. The array of hexagons may be extended as far as you please, and over a surface either plane or curved, but it never closes in (D'ARCY THOMPSON, 1942, (abridged edition, 1975)). So although hexagons in, to cite an(other) example, the skeleton of the radiolarian Aulonia predominate, a certain number of facets are and must be other than hexagonal.

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