Figure-eight knot (mathematics)
Unique knot with a crossing number of four / From Wikipedia, the free encyclopedia
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This article is about the mathematical concept. For the knot, see Figure-eight knot. For other uses, see Figure 8.
In knot theory, a figure-eight knot (also called Listing's knot[1]) 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.
Quick Facts Common name, Arf invariant ...
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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