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] 
AB notation  5_{1} 
Dowker notation  6, 8, 10, 2, 4 
Last /Next  4_{1} / 5_{2} 
Other  
alternating, torus, fibered, prime, reversible 
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 threetwist knot. It is listed as the 5_{1} knot in the AlexanderBriggs notation, and can also be described as the (5,2)torus knot. The cinquefoil is the closed version of the double overhand knot.
The cinquefoil is a prime knot. Its writhe is 5, and it is invertible but not amphichiral.^{[1]} Its Alexander polynomial is
 ,
its Conway polynomial is
 ,
and its Jones polynomial is
These are the same as the Alexander, Conway, and Jones polynomials of the knot 10_{132}. However, the Kauffman polynomial can be used to distinguish between these two knots.
The name “cinquefoil” comes from the fivepetaled flowers of plants in the genus Potentilla.
YouTube Encyclopedic

1/2Views:1 794893

Trefoil knot

magnet field
Transcription
See also
References
Further reading
 A Pentafoil Knot at the Wayback Machine (archived June 4, 2004)