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## George and His Gyrangle

Previously, I have discussed the art creations of George Hart, computer scientist and sculpture artist at Stony Brook University. He continues to make amazing things!

In 2011, George was involved with the first USA Science and Engineering Festival in washington, D.C. There, he coordinated a public "scupture-raising" of his new creation, the Gyrangle.

The Gyrangle is 38 inches tall, consisting of 490 hollow equilateral triangles (100 pounds), laser-cut from steel, bolted together in a mathematical way.

The Gyrangle is a discrete version of the Gyroid, first discovered by Alan Schoen in 1970. Now, in a mouth-ful, a gyroid is a "smooth, infinite, triply periodic, minimal surface." As to some additional properties, it contains no geometrically straight lines and does not have any reflectional symmetries. Channels run through it (i.e. the holes) in many cirections, connecting ot other channels at another angle, creating a spiral-effect.

Though a gyroid is a smooth, infinitely-large surface, George Hart discovered a way to triangulate it with equilateral triangles, calling his tetrahedral-slice the Gyrangle. Unlike the continuous version of the gyroid, George's model allows an infinite number of straight lines in multi-directions. Also, the faces formed by the equilateral triangles do not meet edge-to-edge, but rather each triangle shares half-edges with six neighboring triangles. Also, the triangles are each painted one of four colors based on the direction of their normal vectors.

On a page on his website, George further describes the sculpture, the assembly process, the underlying mathematical structure, alternate designs or views, the history of his gyrangle, and ways for you to make your own version of the model.

Two final notes. First, certain copolymers include gyroid structures, as in "the polymer phase diagram, the gyroid phase is between the lamellar and cylindrical phases." Also, using trig, a gyroid surface can be approximated by the surprisingly simple equation: cos(x)sin(y)+cos(y)sin(z)+cos(z)sin(x) = 0.

Source: Adapted from R. Sarhangi's "The Story of Gyrangle," Notices of the AMS, May 2011.