Gyroid Patch, TPMS, Minimal Surfaces

####Gyroid Patch

The gyroid (Schoen, 1970) is a beautiful 3D structure. It can be algebraically approached by the implicit equation: *sin(x) cos(y)+sin(y)cos(z)+sin(z)cos(x)=0*, which in itself is a pretty thing to ponder. In a recent effort to bring the gyroid to K-12 students, I need to make a few models to show the basic ideas behind the gyroid. The soap film on a skew hexagon is certainly a first step. Then I need to make some “fundamental patches” for a cubic unit cell.

The present design is generated using CalcPlot3D using the above equation in the first octant. So it is a pretty close approximation of the real gyroid patch. I imported it into Fusion 360 and rounded the corners for safety and printing. Interestingly, the joint surfaces align nicely with each other. Eight patches can be glued together (1-min or 5-min epoxy glue or similar adhesive) for a gyroid unit. By default, the patch is embedded in an 88mm-cube. The unit gyroid is about 164mm x 164mm x 164mm. Feel free to scale it up or down for specific needs. Support and raft are necessary for printing. It is time-consuming to print the patches; but the outcome is really satisfying! I am indebted to Mrs. Schoen for her passion about the gyroid and her encouragement and support in our K-12 outreach.

####References

1. Schoen, Alan. https://schoengeometry.com/e-tpms.html 2. DaveMakesStuff. https://www.thingiverse.com/thing:4838412 3. Weyhaupt, Adam. https://plus.maths.org/content/meet-gyroid 4. https://wewanttolearn.wordpress.com/2019/02/03/triply-periodic-minimal-surfaces/ 5. https://c3d.libretexts.org/CalcPlot3D/index.html