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Trefoil Menagerie

by mathgrrl, published

Trefoil Menagerie by mathgrrl Jan 25, 2014
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Summary

Clockwise from the rectangular-looking one and then finishing inside with the five-pointed-looking one, these are the following conformations of the trefoil knot:

  • Cubic lattice trefoil
  • (3,2) Torus knot trefoil
  • Tritangentless trefoil
  • Fourier-(1,1,2) trefoil
  • Minimum rope length trefoil
  • Minimum stick number trefoil
  • (2,3) Torus knot trefoil
  • Petal knot trefoil

Special thanks to kitwallace who has developed code for efficiently producing STL files of parametrized curves!

For more information on the math and the OpenSCAD behind creating these knots, as well as slicing profiles, see these MakerHome posts:

Day 150 - Trefoil torus knots
Day 151 - Fourier and tritangentless trefoil knots
Day 152 - Petal and tight trefoil knots
Day 153 - Stick and lattice trefoil knots

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