I’ve continued with my project to edit the 3D printed models my Fall 2014 Math 341 Introduction to Topology class made. Recently, I came across two of my favorite pieces. The first is a model that was designed by Emily Jaekle (’16) and is a ribbon version of the (3,5) torus knot.

This \((5,3)\) ribbon torus knot was designed entirely in Cinema4D. The curve was created using the *Formula* tool with parametrization \(x(t)=(2+\cos(5t))\cos(3t), y(t)=(2+\cos(5t))\sin(3t), z(t)=-\sin(5t)\) for \(t\in[-\pi, \pi]\). The trianglulated surface was created by first adding in a small rectangle, then using the *SweepNurbs* (without caps). The rectangle was also rotated 1800 degrees in the process. The small gap was fixed using the *Bridge* tool in *Edge mode*. This ribbon knot was originally printed in blue on the Projet-260 3D Systems printer. Later, I printed it on the FormLabs 1+ printer in black resin. You can find the model here on Thingiverse.

The second model was designed by Cathy Wang (’15) and is a ribbon version of the (3,2) trefoil knot with an amazing color scheme.

The entire model was designed in Cinema4D. The knot was created using the *Formula tool* with parametrization \(x(t)=(2+\cos(2t))\cos(3t), y(t)=(2+\cos(2t))\sin(3t), z(t)=-\sin(2t)\) for \(t\in[-\pi,\pi]\). The trianglulated surface was created by first adding in a small rectangle, then using the *SweepNurbs* (without caps). The width and height of the rectangle was adjusted so the band is not a constant size through the knot. The overlapping edges and small gaps were also fixed. Finally, the knot was colored with a beautiful rainbow-gradient. This ribbon knot was originally printed in rainbow colors on the Projet-260 3D Systems printer. Later, I printed it on the FormLabs 1+ printer in black resin. You can find the model here on Thingiverse.