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[[File:Neovius' minimal surface.png|thumb|Neovius' minimal surface in a unit cell.]]

In [[differential geometry]], the '''Neovius surface''' is a [[Triply periodic minimal surface|triply periodic]] [[minimal surface]] originally discovered by Finnish mathematician Edwin Rudolf Neovius (the uncle of [[Rolf Nevanlinna]]).<ref>E. R. Neovius, "Bestimmung zweier spezieller periodischer Minimalflächen", Akad. Abhandlungen, Helsingfors, 1883. http://resolver.sub.uni-goettingen.de/purl?PPN591417707</ref><ref>Eric A. Lord, and Alan L. Mackay, Periodic minimal surfaces of cubic symmetry, Current science, vol. 85, no. 3, 10 August 2003</ref>

The surface has [[genus (mathematics)|genus]] 9, dividing space into two infinite non-equivalent labyrinths. Like many other triply periodic minimal surfaces it has been studied in relation to the microstructure of [[block copolymers]], [[surfactant]]-water mixtures,<ref>S. T. Hyde, Interfacial architecture in surfactant-water mixtures: Beyond spheres, cylinders and planes. Pure and Applied Chemistry, vol. 64, no. 11, pp. 1617–1622, 1992</ref> and crystallography of soft materials.<ref>AL Mackay, Flexicrystallography: curved surfaces in chemical structures, Current Science, 69:2 25 July 1995</ref>

It can be approximated with the level set surface<ref>Meinhard Wohlgemuth, Nataliya Yufa, James Hoffman, and Edwin L. Thomas. Triply Periodic Bicontinuous Cubic Microdomain Morphologies by Symmetries. Macromolecules, 2001, 34 (17), pp 6083–6089</ref>
:<math>3[\cos(x) + \cos(y) + \cos(z)] +  4 \cos(x)\cos(y)\cos(z) = 0</math>

In Schoen's categorisation it is called the C(P) surface, since it is the "complement" of the [[Schwarz_minimal_surface#Schwarz_P_.28.22Primitive.22.29|Schwarz P surface]].  It can be extended with further handles, converging towards the expanded regular octahedron (in Schoen's categorisation)<ref>Alan H. Schoen, Triply Periodic Minimal Surfaces (TPMS), http://schoengeometry.com/e_tpms.html</ref><ref>Ken Brakke, C-P Family of Triply Periodic Minimal Surfaces, http://www.susqu.edu/brakke/evolver/examples/periodic/cpfamily.html</ref>

==References==

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[[Category:Differential geometry]]
[[Category:Minimal surfaces]]