(5,3) Ribbon Torus Knot

by dennedesigns, published

(5,3) Ribbon Torus Knot by dennedesigns Apr 7, 2016
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298Views 90Downloads Found in Math


A (5,3) ribbon-like torus knot designed by Emily Jaekle and edited by Dave Pfaff and myself from my Math 341 Introduction to Topology class in Fall 2014.

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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 9cm x 10cm x 4cm in size.

This knot was first printed on a Project 260 3D Systems printer. Later it was printed on a FormLabs 1+ printer.

How I Designed This

This (5,3) ribbon torus knot was designed entirely in Cinema4D. The curve was created using the Formula tool with parametrization x=(2+cos(5t))cos(3t), y=(2+cos(5t))sin(3t), z=-sin(5t) 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 rectangle was also rotated 1800 degrees in the process. The small gap was fixed using the Bridge tool in Edge mode.

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