| Three-twist knot | |
|---|---|
 | |
| Common name | Figure-of-nine knot |
| 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 | 51 / 61 |
| 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.
- ^ 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.