Figure-eight knot (mathematics)

Figure-eight knot
Common nameFigure-eight knot
Arf invariant1
Braid length4
Braid no.3
Bridge no.2
Crosscap no.2
Crossing no.4
Hyperbolic volume2.02988
Stick no.7
Unknotting no.1
Conway notation[22]
A–B notation41
Dowker notation4, 6, 8, 2
Last / Next3151
alternating, hyperbolic, fibered, prime, fully amphichiral, twist
Figure-eight knot of practical knot-tying, with ends joined

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.

  1. ^ "Listing knot - Encyclopedia of Mathematics". Retrieved 2020-06-25.

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