Gyroid
"Gyroid" redirects here. For the creature, see Animal Crossing (video game).
A gyroid is a certain infinitely connected triply periodic minimal surface discovered by Alan Schoen in 1970.[1]
The gyroid has space group Ia3d. Channels run through the gyroid labyrinths in the (100) and (111) directions; passages emerge at 70.5 degree angles 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.
A gyroid surface can be trigonometrically approximated by the equation:
[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.
[edit] References
- ^ Alan H. Schoen, Infinite periodic minimal surfaces without self-intersections, NASA Technical Note TN D-5541 (1970)[1].
- ^ 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.
[edit] External links
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