Gyroid

From Wikipedia, the free encyclopedia

A gyroid minimal surface, coloured to show the Gaussian curvature at each point.

A gyroid is an infinitely connected triply periodic minimal surface discovered by Alan Schoen in 1970^[1].

The gyroid has space group $Ia\bar{3}d$ . 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 1996 Große-Brauckmann and Wohlgemuth ^[2]proved that it is embedded, in 1997 Große-Brauckmann proved that it has no reflectional symmetries.

[edit] Other

In nature, gyroid structures are found in certain block copolymers. 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, a video game by Nintendo. In reality these figurines are known as Haniwa.

Gyroid is also a popular card in the Yu-Gi-Oh! trading card game. Gyroid is a 4 star Machine/WIND monster, that has 1000 Attack and 1000 Defense, and can survive destruction in battle once per turn.

^ Alan H. Schoen, Infinite periodic minimal surfaces without self-intersections, NASA Technical Note TN D-5541 (1970).
^ 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.