Neovius surface

In <a href="/facts/Differential_geometry/c04XmyLu">differential geometry</a>, the Neovius surface is a <a href="/facts/Triply_periodic_minimal_surface/YBAmbd7N">triply periodic</a> <a href="/facts/Minimal_surface/Fy7VkrLQ">minimal surface</a> originally discovered by Finnish mathematician Edvard Rudolf Neovius (the uncle of <a href="/facts/Rolf_Nevanlinna/uUvNQvmb">Rolf Nevanlinna</a>).
The surface has <a href="/facts/Genus_(mathematics)/o1Yhf8ty">genus</a> 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 <a href="/facts/Block_copolymers/35D97DuV">block copolymers</a>, <a href="/facts/Surfactant/zgVX6g8o">surfactant</a>-water mixtures, and crystallography of soft materials.
It can be approximated with the <a href="/facts/Level_set/JUmNbdNh">level set</a> surface

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 <a href="/facts/Alan_Schoen/gRqjSEvb">Schoen's</a> categorisation it is called the C(P) surface, since it is the "complement" of the <a href="/facts/Schwarz_minimal_surface/MVDWwkHh">Schwarz P surface</a>. It can be extended with further handles, converging towards the expanded regular octahedron (in Schoen's categorisation)

Neovius surface open-in-new

Neovius surface