Gyroid

GYROID

Surface studied and named by A. H. Schoen in 1970.
Alan Hugh Schoen (1924-...): American Mathematician.
Websites:
English Wikipedia
Alan H. Schoen's page
meet the gyroid
Scherer's PhD thesis
bugman123.com/MinimalSurfaces/index.html

The gyroid is a triply periodic minimal surface the fundamental patch of which is reproduced opposite.
The two figures are based on the equation that gives a non-minimal surface close to the true gyroid.

The fundamental patch is composed of 8 isometric skew hexagons, six of which have a vertex at the center of the patch.

The complete gyroid separates the space into two isometric domains, like the Schwarz P surface.

Compare to the Neovius surface.

Gyroid intersected by a sphere, by Alain Esculier
Where?????

Similarities with the brain coral...
or with a shower flower brush...

Engravings of gyroids with curvature lines and asymptotic lines, by Patrice Jeener, with its generous authorization.

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The gyroid is a triply periodic minimal surface the fundamental patch of which is reproduced opposite. The two figures are based on the equation that gives a non-minimal surface close to the true gyroid.
The fundamental patch is composed of 8 isometric skew hexagons, six of which have a vertex at the center of the patch.