Neovius surface

Neovius' minimal surface in a unit cell.

In differential geometry, the Neovius surface is a triply periodic minimal surface originally discovered by Finnish mathematician Edvard Rudolf Neovius, an uncle of Rolf Nevanlinna.

The surface has 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, and crystallography of soft materials.

It can be approximated with the level set surface

3(cos⁡x+cos⁡y+cos⁡z)+4cos⁡xcos⁡ycos⁡z=0

In Schoen's categorisation it is called the C(P) surface, since it is the "complement" of the Schwarz P surface. It can be extended with further handles, converging towards the expanded regular octahedron (in Schoen's categorisation)

References

  1. ↑ E. R. Neovius, "Bestimmung zweier spezieller periodischer Minimalflächen" (in German), Akad. Abhandlungen, Helsingfors, 1883. http://resolver.sub.uni-goettingen.de/purl?PPN591417707
  2. ↑ Eric A. Lord, and Alan L. Mackay, Periodic minimal surfaces of cubic symmetry, Current science, vol. 85, no. 3, 10 August 2003 https://www.schoengeometry.com/e80-tpms-media/Lord_Mackay_gallery_of_surfaces.pdf Access date: 26 April 2026
  3. ↑ 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 https://www.degruyterbrill.com/document/doi/10.1351/pac199264111617/html?srsltid=AfmBOorVhtmz1YpZhuErYY4JgV_r9ZnttrnCTJdzdqBktdKCGIQMlocl Access date: 26 April 2026
  4. ↑ AL Mackay, Flexicrystallography: curved surfaces in chemical structures, Current Science, 69:2 25 July 1995 JSTOR 24097238
  5. ↑ 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 JSTOR 54577
  6. ↑ Alan H. Schoen, Triply Periodic Minimal Surfaces (TPMS), http://schoengeometry.com/e-tpms.html
  7. ↑ Ken Brakke, C-P Family of Triply Periodic Minimal Surfaces, http://www.susqu.edu/brakke/evolver/examples/periodic/cpfamily.html Archived 2015-07-16 at the Wayback Machine