- Gyroid
A gyroid is an infinitely connected triply periodic
minimal surface discovered by Alan Schoen in 1970. [Alan H. Schoen, Infinite periodic minimal surfaces without self-intersections, NASA Technical Note TN D-5541 (1970).]The gyroid has
space group . Channels run through the gyroid labyrinths in the (100) and (111) directions; passages emerge perpendicular to any given channel as it is traversed, the direction at which they do so gyrating down the channel, giving rise to the name "gyroid".In 1986,
Osserman proved that it contains no straight lines, in 1996Große-Brauckmann andWohlgemuth [Karsten Große-Brauckmann and Meinhard Wohlgemuth, The gyroid is embedded and has constant mean curvature companions, Calc. Var. Partial Differential Equations 4 (1996), no. 6, 499–523.] proved that it is embedded, in 1997Große-Brauckmann proved that it has no reflectional symmetries.Other
In nature, gyroid structures are found in certain block
copolymer s. In the polymer phase diagram, the gyroid phase is between the lamellar and cylindrical phases.A gyroid is also a reference to a "gyrating clay figurine" which is unearthed in "
Animal Crossing ", avideo game byNintendo . In reality, these figurines are known asHaniwa .External links
* [http://www.bathsheba.com/math/gyroid/gyroid3d.html Rotatable picture of a gyroid's period]
* [http://mathworld.wolfram.com/Gyroid.html MathWorld entry on gyroids]
* [http://www.indiana.edu/~minimal/ Virtual Museum of Minimal Surfaces]
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