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- Cinquefoil_knot abstract "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.The cinquefoil is a prime knot. Its writhe is 5, and it is invertible but not amphichiral. Its Alexander polynomial is,its Conway polynomial is,and its Jones polynomial isSurprisingly, these are the same as the Alexander, Conway, and Jones polynomials of the knot 10132. However, the Kauffman polynomial can be used to distinguish between these two knots.The name “cinquefoil” comes from the five-petaled flowers of plants in the genus Potentilla.".
- Cinquefoil_knot thumbnail Blue_Cinquefoil_Knot.png?width=300.
- Cinquefoil_knot wikiPageID "16856240".
- Cinquefoil_knot wikiPageRevisionID "605457196".
- Cinquefoil_knot abNotation "51".
- Cinquefoil_knot alternating "alternating".
- Cinquefoil_knot arfInvariant "1".
- Cinquefoil_knot braidLength "5".
- Cinquefoil_knot braidNumber "2".
- Cinquefoil_knot bridgeNumber "2".
- Cinquefoil_knot class "torus".
- Cinquefoil_knot conwayNotation "[5]".
- Cinquefoil_knot crosscapNumber "1".
- Cinquefoil_knot crossingNumber "5".
- Cinquefoil_knot date "20040604232208".
- Cinquefoil_knot dowkerNotation "681024".
- Cinquefoil_knot fibered "fibered".
- Cinquefoil_knot genus "2".
- Cinquefoil_knot hasPhotoCollection Cinquefoil_knot.
- Cinquefoil_knot hyperbolicVolume "0".
- Cinquefoil_knot lastCrossing "4".
- Cinquefoil_knot lastOrder "1".
- Cinquefoil_knot name "Cinquefoil".
- Cinquefoil_knot nextCrossing "5".
- Cinquefoil_knot nextOrder "2".
- Cinquefoil_knot practicalName "Double overhand knot".
- Cinquefoil_knot prime "prime".
- Cinquefoil_knot stickNumber "8".
- Cinquefoil_knot symmetry "reversible".
- Cinquefoil_knot title "A Pentafoil Knot".
- Cinquefoil_knot unknottingNumber "2".
- Cinquefoil_knot url "http://wwwhome.cs.utwente.nl/~jagersaa/Knopen/IndexP.html".
- Cinquefoil_knot subject Category:0_hyperbolic_volume_knots_and_links.
- Cinquefoil_knot comment "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.The cinquefoil is a prime knot. Its writhe is 5, and it is invertible but not amphichiral.".
- Cinquefoil_knot label "Cinquefoil knot".
- Cinquefoil_knot sameAs m.0408kdl.
- Cinquefoil_knot sameAs Q5121087.
- Cinquefoil_knot sameAs Q5121087.
- Cinquefoil_knot wasDerivedFrom Cinquefoil_knot?oldid=605457196.
- Cinquefoil_knot depiction Blue_Cinquefoil_Knot.png.
- Cinquefoil_knot isPrimaryTopicOf Cinquefoil_knot.