Zeke Freeman's The Buzz talks Tessellation.

Geometry
of Bees

Efficiency. Ever wonder why bees use hexagons to make beehives? There are two reasons—and good ones. First, bees want to enclose the largest possible space with the least amount of wax. With this in mind, a circle would almost seem best. But it isn't. So why don’t they use circular combs? Reason number two: hexagons are the shape with the most sides that “tesselate."

Tessellation is the process of creating a two-dimensional plane using the repetition of a geometric shape with no overlaps and no gaps. Tessellations frequently appeared in the art of M. C. Escher, who was inspired by studying the Moorish use of symmetry in the Alhambra tiles during a visit in 1922. Tessellations are seen throughout art history, from ancient architecture to modern art. In Latin, tessella is a small cubical piece of clay, stone or glass used to make mosaics. The word tessella means "small square" (from "tessera", square, which in its turn is from the Greek word for "four"). It corresponds with the everyday term tiling which refers to applications of tessellations, often made of glazed clay.

In other words, if you put a series of hexagons next to each other there will be no spaces between them. No shape with more than six sides will do this and no spaces in between means absolutely no wasted space. Efficiency, one of many unique qualities of the bee.—N.B.

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