Three Interlocking Trefoil Knots

by dennedesigns, published

Three Interlocking Trefoil Knots by dennedesigns Apr 1, 2016
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Three interlocking trefoil knots designed by Hayley Archer-McClelland and edited by Dave Pfaff and myself as part of my Math 341 Introduction to Topology course in Fall 2014. Each trefoil knot is linked with the two others.

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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 model is about 9cm x 10cm x 5cm in size.

These knots were first printed on a Project 260 3D Systems printer. Later they were printed on a FormLabs 1+ printer using clear resin (02).

How I Designed This

Designed entirely in Cinema4D. The parametric equations of a trefoil knot are x(t)= (2+cos(3t))cos(2t), y=(2+cos(3t))sin(2t), z=-sin(3t) from t=-pi to t=pi.

We first made the curve with the Formula function from t=-3.14 to t=3.14. We added a SweepNurb (with no caps) consisting of a circle with radius 0.2cm around the curve. The choice of t meant there was a small gap between the ends of the tube. We sealed this using the Stitch and Sew tool in Edge mode.

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