The next quadratic surfaces I printed were an elliptic paraboloid and a regular paraboloid.

For the elliptic paraboloid I imported the surface from Mathematica.

I then optimized the polygons, extruded them by 0.20 cm to give the surface thickness. After that I used the boole tool to make the edge flat and added an equation through the surface.

I created the regular paraboloid from scratch in Cinema 4D using the same process as the cone.  I used the formula spline $$x(t)=t, y(t)=t^2, z(t)=0$$ and then used the lathe tool with 60 rotation segments to rotate it 360 degrees. I optimized the polygons and extruded them to give the surface thickness. I also made sure to “boole” the edge to make it flat and added an equation.

I printed both paraboloids on the same build bed with the MakerBot 2X printer. They can be found on Thingiverse here and here.