Details

The equation for the gyroid is

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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.

References

[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. www.maths.otago.ac.nz/~jenlow/research/files/thesis.pdf.

3. B. Boghosian and P. Coveney. "Ketchup on the Grid with Joysticks." Projects in Scientific Computing, Pittsburgh Supercomputing Center, 2004. www.psc.edu/science/teragyroid.html.