Figure-eight knot (mathematics)
In knot theory, a figure-eight knot (also called Listing's knot) is the unique knot with a crossing number of four. This makes it the knot with the third-smallest possible crossing number, after the unknot and the trefoil knot. The figure-eight knot is a prime knot.
| Figure-eight knot | |
|---|---|
| Common name | Figure-eight knot |
| Arf invariant | 1 |
| Braid length | 4 |
| Braid no. | 3 |
| Bridge no. | 2 |
| Crosscap no. | 2 |
| Crossing no. | 4 |
| Genus | 1 |
| Hyperbolic volume | 2.02988 |
| Stick no. | 7 |
| Unknotting no. | 1 |
| Conway notation | [22] |
| A–B notation | 41 |
| Dowker notation | 4, 6, 8, 2 |
| Last / Next | 31 / 51 |
| Other | |
| alternating, hyperbolic, fibered, prime, fully amphichiral, twist | |
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