The Gyroid

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In 1970, Alan Schoen discovered gyroids, "infinite periodic minimal surfaces without self-intersections" [1]. One feature of this unusual surface is its many channels, which you can see by rotating the object.

Contributed by: Enrique Zeleny (September 2012)
Open content licensed under CC BY-NC-SA



The equation for the gyroid is


Unexpected applications of gyroidal shapes arise in liquid crystalline materials, biological systems, and in the manufacture of industrial products like soap, detergent, shampoo, and waxes. Such shapes arise frequently in the study of liquid mixtures (like ketchup) when they act like solids, where they are called mesophases.


[1] A. H. Schoen, Infinite Periodic Minimal Surfaces without Self-Intersections, NASA Technical Note TN D-5541, Washington, DC: National Aeronautics and Space Administration, 1970.

2. J. D. Enlow, "Mathematical Modelling of Surfactant Liquid Crystal X-ray Diffraction," Ph.D. thesis, Department of Philosphy, University of Otago, New Zealand, 2002.

3. B. Boghosian and P. Coveney. "Ketchup on the Grid with Joysticks." Projects in Scientific Computing, Pittsburgh Supercomputing Center, 2004.

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