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(3,2) Ribbon Torus Knot

by dennedesigns, published

(3,2) Ribbon Torus Knot by dennedesigns Apr 9, 2016
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Summary

This is a (3,2) ribbon torus knot designed by Cathy Wang and edited by Dave Pfaff and myself for my Math 341 Introduction to Topology class in Fall 2014.

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Notes:

You may need to rescale this object by a factor of 10 in Makerware since it is sized in cm not mm. You may also need to move the knot onto the platform, I think it is just above it. The knot is about 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 designed in Cinema4D. The knot was created 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. 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. (The color doesn't show in the .stl file.)

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