What is "stevedore knot"

The stevedore knot is a stopper knot, often tied near the end of a rope. It is more bulky and less prone to jamming than the closely related figure-eight knot.

In knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 6 knot and the 6 knot. The stevedore knot is listed as the 6 knot in the Alexander–Briggs notation, and it can also be described as a twist knot with four twists, or as the (5,−1,−1) pretzel knot.

The mathematical stevedore knot is named after the common stevedore knot, which is often used as a stopper at the end of a rope. The mathematical version of the knot can be obtained from the common version by joining together the two loose ends of the rope, forming a knotted loop.

The stevedore knot is invertible but not amphichiral. Its Alexander polynomial is

Δ(t) =  − 2t + 5 − 2t,  

its Conway polynomial is

∇(z) = 1 − 2z,  

and its Jones polynomial is

V(q) = q − q + 2 − 2q + q − q + q. 

The Alexander polynomial and Conway polynomial are the same as those for the knot 9, but the Jones polynomials for these two knots are different. Because the Alexander polynomial is not monic, the stevedore knot is not fibered.

The stevedore knot is a ribbon knot, and is therefore also a slice knot.

The stevedore knot is a hyperbolic knot, with its complement having a volume of approximately 3.16396.