My next project (after finally finishing all the quadratic surfaces) was to make a helicoid. I spend some time on *Mathematica* creating different helicoids by changing the parameters of the formula. The helicoid is pararametrized by \(x=u\cos(t), y=u\sin(t),\) and \(z=u\), where \(u\in[-1,1] \) and \(t\in[0,2\pi]\).

Professor Denne and I decided to print two of the ones I created to start (we may print more!). I exported the following *Mathematica *files and imported them into Cinema 4D.

Professor Denne used these files (as well as others) to create another worksheet in *Mathematica. *It can be found here.

After making them the correct size I optimized the polygons and extruded them by 0.20 cm (a process I can now do very quickly after all my practice with the quadratic surfaces). I then printed each of them on the liquid printer and had fantastic results!

The .STL and .form files for both of these helicoids can be found on Thingiverse.

Later on, I made another helicoid, this one with \(u\in[0.25,1.25]\) and \(t\in[0,2\pi]\). This model can be found on Thingiverse here.