(3,2) Ribbon Torus Knot

thingiverse

This is a 3,2 ribbon torus knot created by Cathy Wang and refined by Dave Pfaff and myself for my Math 341 Introduction to Topology class in Fall 2014. Print Settings Notes: You may need to scale this object up by a factor of 10 using Makerware since it's sized in cm not mm. You might also need to move the knot onto the platform, I think it's just above it. The knot measures approximately 10cm x 11cm x 5cm in size. This knot was first printed on a Projet-260 3D Systems printer. How I Designed This The entire model was crafted in Cinema4D. The knot was generated using the Formula tool with parametrization x=(2+cos(2t))cos(3t), y=(2+cos(2t))sin(3t), z=-sin(2t) from t=-pi to t=pi. A triangulated surface was created by first adding in a small rectangle, then using the SweepNurbs (without caps). The width and height of the rectangle were adjusted so the band is not a constant size through the knot. Overlapping edges and small gaps were also corrected. Finally, the knot was colored with a stunning rainbow-gradient. (The color doesn't show in the .stl file.)