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| {{Infobox knot theory
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| | name= Cinquefoil
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| | practical name= Double overhand knot
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| | image= Blue Cinquefoil Knot.png
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| | caption=
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| | arf invariant= 1
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| | braid length= 5
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| | braid number= 2
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| | bridge number= 2
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| | crosscap number= 1
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| | crossing number= 5
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| | hyperbolic volume= 0
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| | linking number=
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| | stick number= 8
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| | unknotting number= 2
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| | conway_notation= [5]
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| | ab_notation= 5<sub>1</sub>
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| | dowker notation= 6, 8, 10, 2, 4
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| | thistlethwaite=
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| | last crossing= 4
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| | last order= 1
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| | next crossing= 5
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| | next order= 2
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| | alternating= alternating
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| | class= torus
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| | fibered= fibered
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| | prime= prime
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| | slice=
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| | symmetry= reversible
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| | tricolorable=
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| }}
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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 (knot theory)|crossing number]] five, the other being the [[three-twist knot]]. It is listed as the '''5<sub>1</sub> 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]].
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| The cinquefoil is a [[prime knot]]. Its [[writhe]] is 5, and it is [[invertible knot|invertible]] but not [[amphichiral knot|amphichiral]].<ref>{{MathWorld|title=Solomon's Seal Knot|urlname=SolomonsSealKnot}}</ref> Its [[Alexander polynomial]] is
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| :<math>\Delta(t) = t^2 - t + 1 - t^{-1} + t^{-2}</math>,
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| its [[Conway polynomial]]{{dn|date=January 2014}} is
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| :<math>\nabla(z) = z^4 + 3z^2 + 1</math>,
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| and its [[Jones polynomial]] is
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| :<math>V(q) = q^{-2} + q^{-4} - q^{-5} + q^{-6} - q^{-7}.</math><ref>{{Knot Atlas|5_1}}</ref>
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| Surprisingly, these are the same as the Alexander, Conway, and Jones polynomials of the knot 10<sub>132</sub>. However, the [[Kauffman polynomial]] can be used to distinguish between these two knots.
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| The name “cinquefoil” comes from the five-petaled flowers of plants in the genus ''[[Potentilla]]''.
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| [[File:Cinquefoil Knot.jpg|right|thumb|Edible cinquefoil knot.]]
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| ==See also==
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| *[[Pentagram]]
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| *[[Trefoil knot]]
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| *[[7₁ knot]]
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| *[[Skein relation]]
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| ==References==
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| {{reflist}}
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| ==Further reading==
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| *{{Wayback|url=http://wwwhome.cs.utwente.nl/~jagersaa/Knopen/IndexP.html|title=A Pentafoil Knot|date=20040604232208}}
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| {{Knot theory|state=collapsed}}
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| {{knottheory-stub}}
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Welfare Worker Porter from Bloomfield, enjoys to spend time meditation, Dungeon Hunter 4 Hack and aquariums. Did a cruiseship experience that included passing by Hanseatic Town of Visby.
Also visit my website ... Dungeon Hunter 4 Cheats