Trefoil Earrings

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 earrings were modelled by twisting a square profile around a curve defined by the equations above.

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 earring 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).