Kinoshita-Terasaka Knot

The Knot with Braid Word

$${\sigma_1}^3{\sigma_3}^2\sigma_2{\sigma_3}^{-1}{\sigma_1}^{-2}\sigma_2{\sigma_1}^{-1}{\sigma_3}^{-1}{\sigma_2}^{-1}.$$

Its Jones Polynomial is

$$t^{-4}(-1+2t-2t^2+2t^3+t^6-2t^7+2t^8-2t^9+t^{10}),$$

the same as for Conway's Knot. It has the same Alexander Polynomial as the Unknot.

References

Kinoshita, S. and Terasaka, H. ``On Unions of Knots.'' Osaka Math. J. 9, 131-153, 1959.