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There are three regular polygons you can use to tile a plane: triangles, squares, and hexagons. The regular hexagonal packing is the densest sphere packing in t
by jfarmer 13y ago
There are three regular polygons you can use to tile a plane: triangles, squares, and hexagons. The regular hexagonal packing is the densest sphere packing in the plane, so any time you have objects constrained to a plane which for the sake of maximizing or minimizing some force want to be equidistant from each other you'll get something close to a hexagon.
- jfarmer 13y agoI'll add that sometimes a shape like that might result from a more evolutionary process. In a 2D plane a circle is the structure which most equally distributes force, so it's the shape most able to hold up under pressure. But a tile of circles isn't so fortunate. Of all the possible tilings, the hexagonal tiling holds up the best precisely because it's the densest sphere packing in the plane. Other arrangements might appear, but over the course of time you're more likely to see hexagonal tilings since those are the ones that best survive external forces.