Three-twist knot

Three-twist knot
Common nameFigure-of-nine knot
Arf invariant0
Braid length6
Braid no.3
Bridge no.2
Crosscap no.2
Crossing no.5
Genus1
Hyperbolic volume2.82812
Stick no.8
Unknotting no.1
Conway notation[32]
A–B notation52
Dowker notation4, 8, 10, 2, 6
Last / Next5161
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[1] in the Alexander-Briggs notation, and is one of two knots with crossing number five, the other being the cinquefoil knot.

  1. ^ Pinsky, Tali (1 September 2017). "On the topology of the Lorenz system". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 473 (2205). The Royal Society: 20170374. doi:10.1098/rspa.2017.0374. PMC 5627380. PMID 28989313. Retrieved 26 August 2018. (b) the knot with three half-twists, called the 52 knot.