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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 www.susqu.edu/brakke/evolver/examples/periodic/gyroid/gyroid.html 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 nonminimal 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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© Robert FERRÉOL 2017