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(Q4544970)
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English
(−2,3,7) pretzel knot
type of mathematical knot
Fintushel-Stern knot
12n242
12n₂₄₂
12n_242
In more languages
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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
t
10
−
t
9
+
t
7
−
t
6
+
t
5
−
t
4
+
t
3
−
t
+
1
{\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
z
10
+
9
z
8
+
27
z
6
+
31
z
4
+
12
z
2
+
1
{\displaystyle z^{10}+9z^{8}+27z^{6}+31z^{4}+12z^{2}+1}
1 reference
stated in
Knotinfo
retrieved
June 2020
Jones polynomial
−
q
13
+
q
12
−
q
11
+
q
7
+
q
5
{\displaystyle -q^{13}+q^{12}-q^{11}+q^{7}+q^{5}}
1 reference
stated in
Knotinfo
retrieved
June 2020
Dowker-Thistlethwaite notation
4
,
8
,
−
16
,
2
,
−
18
,
−
20
,
−
22
,
−
24
,
−
6
,
−
10
,
−
12
,
−
14
{\displaystyle 4,8,-16,2,-18,-20,-22,-24,-6,-10,-12,-14}
1 reference
stated in
Knotinfo
retrieved
June 2020
Dowker-Thistlethwaite name
12
n
242
{\displaystyle 12n_{242}}
0 references
Gauss notation
{
1
,
−
2
,
3
,
−
1
,
−
4
,
5
,
2
,
−
3
,
−
6
,
7
,
−
8
,
9
,
−
10
,
11
,
−
12
,
4
,
−
5
,
6
,
−
7
,
8
,
−
9
,
10
,
−
11
,
12
}
{\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
0 references
Knotinfo ID
12n_242
0 references
Sitelinks
Wikipedia
(1 entry)
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enwiki
(−2,3,7) pretzel knot
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Multilingual sites
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