Triply Periodic Minimal Surfaces

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In 1865, H. A. Schwarz found two triply periodic minimal surfaces (P and D) [1] and his student Edwin Neovius found another one (N). Around 1970, Alan Schoen found the gyroid [2] and others; many other cases have been discovered [3, 4]. Such surfaces are relevant in biomaterials and the study of several compounds with cubic lattices [5, 6].


[5] Fiona Meldrum's Group. "Mechanical Properties of Bio-Inspired Materials." (Aug 7, 2013)

[6] P. J. F. Gandy and J. Klinowski, "The Equipotential Surfaces of Cubic Lattices,", Chemical Physics Letters, 360(5–6), 2002 pp. 543–551. doi:10.1016/S0009-2614(02)00864-3.


Contributed by: Enrique Zeleny (August 2013)
Open content licensed under CC BY-NC-SA




[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] E. Zeleny. "The Gyroid" from the Wolfram Demonstrations Project—A Wolfram Web Resource.

[3] The Scientific Graphics Project. "Minimal Surfaces." (Aug 7, 2013)

[4] K. Brakke. "Triply Periodic Minimal Surfaces." (Aug 7, 2013)

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