(−2,3,7) pretzel knot (Q4544970)

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type of mathematical knot

• Fintushel-Stern knot
• 12n242
• 12n₂₄₂
• 12n_242

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Language	Label	Description	Also known as
English	(−2,3,7) pretzel knot	type of mathematical knot	Fintushel-Stern knot 12n242 12n₂₄₂ 12n_242

Statements

instance of

prime knot

1 reference

stated in

KnotInfo

retrieved

June 2020

fibered knot

0 references

pretzel link

0 references

image

Pretzel knot.svg
283 × 312; 6 KB

0 references

maintained by WikiProject

WikiProject Mathematics

0 references

crossing number

12

0 references

Alexander polynomial

${\displaystyle t^{10}-t^{9}+t^{7}-t^{6}+t^{5}-t^{4}+t^{3}-t+1}$

1 reference

stated in

KnotInfo

retrieved

June 2020

Conway polynomial

${\displaystyle z^{10}+9z^{8}+27z^{6}+31z^{4}+12z^{2}+1}$

1 reference

stated in

KnotInfo

retrieved

June 2020

Jones polynomial

${\displaystyle -q^{13}+q^{12}-q^{11}+q^{7}+q^{5}}$

1 reference

stated in

KnotInfo

retrieved

June 2020

Dowker-Thistlethwaite notation

${\displaystyle 4,8,-16,2,-18,-20,-22,-24,-6,-10,-12,-14}$

1 reference

stated in

KnotInfo

retrieved

June 2020

Dowker-Thistlethwaite name

${\displaystyle 12n_{242}}$

0 references

Gauss notation

${\displaystyle \{1,-2,3,-1,-4,5,2,-3,-6,7,-8,9,-10,11,-12,4,-5,6,-7,8,-9,10,-11,12\}}$

0 references

Identifiers

Freebase ID

/m/02pwshb

0 references

Knot Atlas ID

K12n242

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Knotinfo ID

12n_242

0 references

 

Sitelinks

Wikipedia(1 entry)

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• enwiki (−2,3,7) pretzel knot

Wikibooks(0 entries)

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Wikinews(0 entries)

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Wikiquote(0 entries)

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Wikisource(0 entries)

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Wikiversity(0 entries)

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Wikivoyage(0 entries)

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Wiktionary(0 entries)

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Multilingual sites(0 entries)

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