The gyroid, illustrated above, is an infinitely connected periodic minimal surface containing no straight lines (Osserman 1986)
that was discovered by Schoen (1970). Große-Brauckmann and Wohlgemuth (1996)
proved that the gyroid is embedded.
The gyroid is the only known embedded triply periodic minimal surface with triple junctions. In addition, unlike the five triply periodic minimal surfaces studied
by Anderson et al. (1990), the gyroid does not have any reflectional symmetries
(Große-Brauckmann 1997).
The image above shows a metal print of the gyroid created by digital sculptor Bathsheba
Grossman (http://www.bathsheba.com/).
Anderson, D. M.; Davis, H. T.; Nitsche, J. C. C.; and Scriven,
L. E. Adv. Chem. Phys. 77, 337-396, 1990.
Garstecki, P. and Hołyst, R. "Scattering Patterns of Self-Assembled Gyroid Cubic Phases in Amphiphilic Systems." J. Chem. Phys. 115, 1095-1099,
2001.
Gòzdz, W. and Hołyst, R. "High Genus Periodic Gyroid Surfaces of Nonpositive Gaussian Curvature." Phys. Rev. Lett. 76, 2726-2729,
1996.
Große-Brauckmann, K. "Gyroids of Constant Mean Curvature." Experiment.
Math. 6, 33-50, 1997.
Große-Brauckmann, K. and Wohlgemuth, M. "The Gyroid Is Embedded and Has Constant Mean Curvature Companions." Calc. Var. Partial Differential Equations 4,
499-523, 1996.
Grossman, B. "The Gyroid." http://www.bathsheba.com/math/gyroid/.
Hyde, S. T.; Andersson, S.; Ericsson, B.; and Larsson, K. "A Cubic Structure Consisting of a Lipid Bilayer Forming an Infinite Periodic Minimal Surface of the
Gyroid Type in the Glycerolmonooleate Water System." Z. Kristallogr. 168,
213-219, 1984.
Hyde, S. T.; Andersson, S.; Blum, Z.; Lidin, S.; Larsson, K.; Landh, T.; and Ninham, B. W. The Language of Shape. Amsterdam, Netherlands: Elsevier,
1997.
Mackay, A. L. "Periodic Minimal Surfaces." Nature 314,
604-606, 1985.
Osserman, R. Frontispiece to A Survey of Minimal Surfaces. New York: Dover, 1986.
Schoen, A. H. "Infinite Periodic Minimal Surfaces Without Selfintersections." NASA Tech. Note No. D-5541. Washington, DC, 1970.
Terrones, H. "Computation of Minimal Surfaces." J. de Physique 51,
No. 23, Suppl. Colloq. C7, 345-362, 1990.
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