Neovius surface

In differential geometry, the Neovius surface is a triply periodic minimal surface originally discovered by Finnish mathematician Edvard Rudolf Neovius (the uncle of Rolf Nevanlinna).^{[1] [2]}

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,^[3] and crystallography of soft materials.^[4]

It can be approximated with the level set surface^[5]

${\displaystyle 3(\cos x+\cos y+\cos z)+4\cos x\cos y\cos z=0}${\displaystyle 3(\cos x+\cos y+\cos z)+4\cos x\cos y\cos 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)^{[6] [7]}

• Differential geometry
• Minimal surfaces

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