Stevedore's Knot
The stevedore's knot is the 6-crossing prime knot 6_1. It is implemented in the Wolfram Language as KnotData ["Stevedore"].
It has braid word sigma_1^(-1)sigma_2sigma_1^(-1)sigma_3sigma_2^(-1)sigma_3sigma_2. It has Arf invariant 0 and is not amphichiral, although it is invertible. It is a slice knot (Rolfsen 1976, p. 225).
The Alexander polynomial Delta(x), BLM/Ho polynomial Q(x), Conway polynomial del (x), HOMFLY polynomial P(l,m), and Jones polynomial V(t) of Stevedore's knot are
Surprisingly, the knot 09-046 shares the same Alexander polynomial with the stevedore's knot. However, no knots on 10 or fewer crossings share the same BLM/Ho polynomial or Jones polynomial with it.
See also
Figure Eight Knot, Knot, Miller Institute Knot, Prime Knot, Solomon's Seal Knot, Trefoil KnotExplore with Wolfram|Alpha
References
Bar-Natan, D. "The Knot 6_1." https://katlas.org/wiki/6_1.Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 225, 1976.Referenced on Wolfram|Alpha
Stevedore's KnotCite this as:
Weisstein, Eric W. "Stevedore's Knot." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StevedoresKnot.html