Cinquefoil knot
Mathematical knot with crossing number 5 / From Wikipedia, the free encyclopedia
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In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other being the three-twist knot. It is listed as the 51 knot in the Alexander-Briggs notation, and can also be described as the (5,2)-torus knot. The cinquefoil is the closed version of the double overhand knot.
Quick Facts Common name, Arf invariant ...
Cinquefoil | |
---|---|
Common name | Double overhand knot |
Arf invariant | 1 |
Braid length | 5 |
Braid no. | 2 |
Bridge no. | 2 |
Crosscap no. | 1 |
Crossing no. | 5 |
Genus | 2 |
Hyperbolic volume | 0 |
Stick no. | 8 |
Unknotting no. | 2 |
Conway notation | [5] |
A–B notation | 51 |
Dowker notation | 6, 8, 10, 2, 4 |
Last / Next | 41 / 52 |
Other | |
alternating, torus, fibered, prime, reversible |
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