A while back we looked at associating the number of strands in number theoretic braids with the size of the matrix operators in the Fourier transform, which is the same as the number of points on the circle (3 for mass). In the two strand case, the braids are easy to classify: copies of the only generator, . In other words, an integer labels all possible knots.

The homflypt polynomial for the torus knot is

for two parameters and . Specialisations include which results (effectively) in the Jones polynomial

Since the endpoints of braid diagrams lie on a circle, there are two circles bounding a diagram. For the 3-strand case, there are two sets of three points defining the boundary, which thus looks like a 6 point torus.