(Q168697)

English

figure-eight knot

unique knot with a crossing number of four

Listing's knot
4_1
4₁
4a_1
Figure-eight

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Statements

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Blue Figure-Eight Knot.png
1,584 × 1,800; 537 KB

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name

Listing's knot (English)

named after

Johann Benedict Listing

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figure-eight knot (English)

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defining formula

{\begin{pmatrix}x\\y\\z\end{pmatrix}}={\begin{pmatrix}\left(2+\cos {(2t)}\right)\cos {(3t)}\\\left(2+\cos {(2t)}\right)\sin {(3t)}\\\sin {(4t)}\end{pmatrix}}

1 reference

imported from Wikimedia project

German Wikipedia

3D model

Achterknoten 20230608 001.stl
5,120 × 2,880; 43.33 MB

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maintained by WikiProject

WikiProject Mathematics

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crossing number

4

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Alexander polynomial

-t+3-t^{-1}

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Conway polynomial

1-z^{2}

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Jones polynomial

q^{2}-q+1-q^{-1}+q^{-2}

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Alexander–Briggs notation

4_{1}

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Dowker-Thistlethwaite notation

4,6,8,2

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Dowker-Thistlethwaite name

4a_{1}

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Gauss notation

\{-1,2,-3,1,-4,3,-2,4\}

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Commons category

Figure-eight knots (knot theory)

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Identifiers

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28 October 2013

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1 reference

imported from Wikimedia project

English Wikipedia

Microsoft Academic ID

2777989480

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Sitelinks

Wikipedia(9 entries)

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Multilingual sites(1 entry)

commonswiki Category:Figure-eight knots (knot theory)