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.