Three-twist knot

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Three-twist knot
Blue Three-Twist Knot.png
Arf invariant 0
Braid length 6
Braid no. 3
Bridge no. 2
Crosscap no. 2
Crossing no. 5
Genus 1
Hyperbolic volume 2.82812
Stick no. 8
Unknotting no. 1
Conway notation [32]
A-B notation 52
Dowker notation 4, 8, 10, 2, 6
Last /Next 5161
Other
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.

The three-twist knot is a prime knot, and it is invertible but not amphichiral. Its Alexander polynomial is

its Conway polynomial is

and its Jones polynomial is

[1]

Because the Alexander polynomial is not monic, the three-twist knot is not fibered.

The three-twist knot is a hyperbolic knot, with its complement having a volume of approximately 2.82812.

References[edit]