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Three Interlocking Trefoil Knots

by dennedesigns, published

Three Interlocking Trefoil Knots by dennedesigns Apr 1, 2016
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723Views 132Downloads Found in Math

Summary

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.

Print Settings

Printer Brand:

Formlabs

Printer:

Form 1

Rafts:

Yes

Supports:

Yes

Resolution:

0.2

Infill:

10%


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 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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