Trefoil Cufflinks

The Trefoil Knot is a 3D curve totally drawn on a torus' surface. Part of the toroidal knots family, it is defined by the following parametric equations:

• x = (2 + cos 3t) cos 2t
• y = (2 + cos 3t) sin 2t
• z = sin 3t
  for t between 0 and 2*π

These cufflinks were modelled by twisting a square profile around a curve defined by the equations above. The shaft is composed of three curved square beams that make contact with the three middle points of the Knot.

A beautiful mathematic set of cufflinks inspired by ones that I have and that were crafted by an expert artisan in Taxco, Mexico (home of expert jewellers and silversmiths). The difference is that those are composed by three intertwined rings while these are defined by a parametric equation.

A couple of curious facts about these:

1. While touching one face, it takes four full turns around the axis to return to the starting position. That means that this knot is also a Möbius Strip and therefore is a solid with only one surface and one edge.
2. One cufflink is the mirror image of the other, but they are not topologically identical. That means that one can not be deformed into the other. Therefore there is a right-hand knot and a left-hand knot (Chirality).