|Common name||[[Figure-of-nine knot]]|
|Dowker notation||4, 8, 10, 2, 6|
|Last /Next||51 / 61|
|alternating, hyperbolic, prime, reversible, twist|
In knot theory, the three-twist knot is the twist knot with three-half twists. It is listed as the 52 knot in the Alexander-Briggs notation, and is one of two knots with crossing number five, the other being the cinquefoil knot.
its Conway polynomial is
and its Jones polynomial is
If the fibre of the knot in the initial image of this page were cut at the bottom right of the image, and the ends were pulled apart, it would result in a single-stranded figure-of-nine knot (not the figure-of-nine loop).
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