12a
0172
(K12a
0172
)
A knot diagram
1
Linearized knot diagam
3 5 9 6 2 10 11 12 4 7 1 8
Solving Sequence
6,10
7 11
2,8
5 3 1 4 9 12
c
6
c
10
c
7
c
5
c
2
c
1
c
4
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.45180 × 10
120
u
73
+ 4.03952 × 10
120
u
72
+ ··· + 1.30235 × 10
121
b − 4.34074 × 10
120
,
6.05606 × 10
120
u
73
− 3.93278 × 10
121
u
72
+ ··· + 2.21400 × 10
122
a + 2.14853 × 10
123
,
u
74
− 3u
73
+ ··· − 105u − 34i
I
u
2
= hb
2
− b + 1, a + 1, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 84 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−1.45 × 10
120
u
73
+ 4.04 × 10
120
u
72
+ · · · + 1.30 × 10
121
b − 4.34 ×
10
120
, 6.06 × 10
120
u
73
− 3.93 × 10
121
u
72
+ · · · + 2.21 × 10
122
a + 2.15 ×
10
123
, u
74
− 3u
73
+ · · · − 105u − 34i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
11
=
u
−u
3
+ u
a
2
=
−0.0273534u
73
+ 0.177632u
72
+ ··· − 9.08897u − 9.70429
0.111475u
73
− 0.310170u
72
+ ··· + 0.717542u + 0.333299
a
8
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
0.0451659u
73
− 0.400611u
72
+ ··· − 29.8846u − 4.08994
−0.0475614u
73
+ 0.362089u
72
+ ··· + 24.0421u + 8.35798
a
3
=
−0.331234u
73
+ 1.03101u
72
+ ··· + 4.46259u + 4.44330
0.239159u
73
− 0.574819u
72
+ ··· − 2.80721u − 9.58086
a
1
=
−0.210920u
73
+ 0.849732u
72
+ ··· + 23.6544u + 14.0350
−0.147525u
73
+ 0.442629u
72
+ ··· + 7.67513u + 1.20613
a
4
=
−0.00239555u
73
− 0.0385226u
72
+ ··· − 5.84249u + 4.26805
−0.0475614u
73
+ 0.362089u
72
+ ··· + 24.0421u + 8.35798
a
9
=
−0.0354744u
73
+ 0.253948u
72
+ ··· + 6.90667u − 3.95032
0.217027u
73
− 0.765655u
72
+ ··· − 22.3956u − 12.1871
a
12
=
−0.361662u
73
+ 1.35032u
72
+ ··· + 39.2427u + 19.9087
−0.0399039u
73
+ 0.190967u
72
+ ··· + 4.64937u − 3.21561
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0808785u
73
+ 0.245428u
72
+ ··· − 15.6772u − 2.16608
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
74
+ 22u
73
+ ··· + 13u + 1
c
2
, c
5
u
74
+ 6u
73
+ ··· + 5u + 1
c
3
, c
9
u
74
+ u
73
+ ··· + 3072u
2
− 1024
c
6
, c
7
, c
10
u
74
− 3u
73
+ ··· − 105u − 34
c
8
, c
12
u
74
+ 3u
73
+ ··· − 2u − 1
c
11
u
74
− 43u
73
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
74
+ 66y
73
+ ··· + 1221y + 1
c
2
, c
5
y
74
+ 22y
73
+ ··· + 13y + 1
c
3
, c
9
y
74
− 55y
73
+ ··· − 6291456y + 1048576
c
6
, c
7
, c
10
y
74
− 85y
73
+ ··· + 17603y + 1156
c
8
, c
12
y
74
+ 43y
73
+ ··· − 2y + 1
c
11
y
74
− 21y
73
+ ··· − 54y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.792276 + 0.579163I
a = −0.405399 − 0.850260I
b = 0.218212 − 1.039340I
0.15163 − 5.92978I 0
u = −0.792276 − 0.579163I
a = −0.405399 + 0.850260I
b = 0.218212 + 1.039340I
0.15163 + 5.92978I 0
u = 0.141074 + 1.026160I
a = 0.741246 − 0.573106I
b = −0.754093 − 0.901400I
2.82540 + 5.08946I 0
u = 0.141074 − 1.026160I
a = 0.741246 + 0.573106I
b = −0.754093 + 0.901400I
2.82540 − 5.08946I 0
u = 0.247837 + 1.018910I
a = 0.476613 + 0.271184I
b = −0.759452 + 0.862977I
2.94401 − 0.64407I 0
u = 0.247837 − 1.018910I
a = 0.476613 − 0.271184I
b = −0.759452 − 0.862977I
2.94401 + 0.64407I 0
u = 0.738891 + 0.770167I
a = 1.42413 − 0.69452I
b = −0.768564 − 0.958680I
4.37578 + 6.45349I 0
u = 0.738891 − 0.770167I
a = 1.42413 + 0.69452I
b = −0.768564 + 0.958680I
4.37578 − 6.45349I 0
u = 0.819080 + 0.694478I
a = 0.395577 − 0.433900I
b = −0.809713 + 0.803977I
4.85168 + 0.52465I 0
u = 0.819080 − 0.694478I
a = 0.395577 + 0.433900I
b = −0.809713 − 0.803977I
4.85168 − 0.52465I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.833315 + 0.399088I
a = −2.05047 − 0.63615I
b = 0.684280 + 0.914822I
2.91943 + 5.78714I 0
u = 0.833315 − 0.399088I
a = −2.05047 + 0.63615I
b = 0.684280 − 0.914822I
2.91943 − 5.78714I 0
u = −0.833568 + 0.293621I
a = −0.491785 + 0.392953I
b = 0.641432 − 0.143331I
3.80185 − 3.25281I 12.99162 + 5.07017I
u = −0.833568 − 0.293621I
a = −0.491785 − 0.392953I
b = 0.641432 + 0.143331I
3.80185 + 3.25281I 12.99162 − 5.07017I
u = 0.536029 + 0.688679I
a = 1.157520 − 0.586197I
b = −0.016192 − 0.798494I
−1.03766 + 2.07310I 0. − 3.44701I
u = 0.536029 − 0.688679I
a = 1.157520 + 0.586197I
b = −0.016192 + 0.798494I
−1.03766 − 2.07310I 0. + 3.44701I
u = 0.749591 + 0.262619I
a = −2.06221 + 0.99351I
b = 0.705257 − 0.788110I
3.31170 + 0.45778I 9.93937 − 0.85994I
u = 0.749591 − 0.262619I
a = −2.06221 − 0.99351I
b = 0.705257 + 0.788110I
3.31170 − 0.45778I 9.93937 + 0.85994I
u = 1.273940 + 0.124542I
a = 1.174220 − 0.094574I
b = −0.227543 − 0.656454I
2.04447 + 1.01310I 0
u = 1.273940 − 0.124542I
a = 1.174220 + 0.094574I
b = −0.227543 + 0.656454I
2.04447 − 1.01310I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.059070 + 0.761879I
a = 1.57349 + 0.43998I
b = −0.764665 + 0.986007I
6.38008 − 11.03360I 0
u = −1.059070 − 0.761879I
a = 1.57349 − 0.43998I
b = −0.764665 − 0.986007I
6.38008 + 11.03360I 0
u = −0.645813 + 0.255567I
a = −0.114178 + 1.091410I
b = −0.851584 − 0.841956I
9.27124 + 2.13858I 13.72041 − 2.59497I
u = −0.645813 − 0.255567I
a = −0.114178 − 1.091410I
b = −0.851584 + 0.841956I
9.27124 − 2.13858I 13.72041 + 2.59497I
u = −1.113290 + 0.685903I
a = 0.659749 + 0.554990I
b = −0.825354 − 0.765471I
7.05334 − 5.07352I 0
u = −1.113290 − 0.685903I
a = 0.659749 − 0.554990I
b = −0.825354 + 0.765471I
7.05334 + 5.07352I 0
u = −0.089649 + 0.672839I
a = 0.88456 + 1.13933I
b = 0.095134 + 0.862320I
−1.96073 + 1.64413I −2.06231 − 4.26426I
u = −0.089649 − 0.672839I
a = 0.88456 − 1.13933I
b = 0.095134 − 0.862320I
−1.96073 − 1.64413I −2.06231 + 4.26426I
u = 0.358555 + 0.536553I
a = −0.04644 + 1.41724I
b = 0.197597 + 0.943333I
−1.56670 + 2.15882I −0.36505 − 4.88726I
u = 0.358555 − 0.536553I
a = −0.04644 − 1.41724I
b = 0.197597 − 0.943333I
−1.56670 − 2.15882I −0.36505 + 4.88726I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.545628 + 0.285450I
a = 2.12519 + 1.41592I
b = −0.813472 + 0.950753I
8.93340 − 4.05613I 13.18636 + 2.67213I
u = −0.545628 − 0.285450I
a = 2.12519 − 1.41592I
b = −0.813472 − 0.950753I
8.93340 + 4.05613I 13.18636 − 2.67213I
u = −0.538990 + 0.296954I
a = −1.66267 + 0.63971I
b = 0.413810 + 1.006280I
1.269800 + 0.465685I 10.92617 + 0.56708I
u = −0.538990 − 0.296954I
a = −1.66267 − 0.63971I
b = 0.413810 − 1.006280I
1.269800 − 0.465685I 10.92617 − 0.56708I
u = −1.392270 + 0.138352I
a = 1.157120 − 0.037316I
b = −0.289785 − 0.621402I
5.70309 − 3.30850I 0
u = −1.392270 − 0.138352I
a = 1.157120 + 0.037316I
b = −0.289785 + 0.621402I
5.70309 + 3.30850I 0
u = 0.590098
a = 0.115562
b = 0.437328
1.09942 9.14060
u = 0.275924 + 0.441037I
a = 1.129560 − 0.072563I
b = −0.142548 + 0.140247I
0.50148 + 1.32272I 5.11712 − 4.95919I
u = 0.275924 − 0.441037I
a = 1.129560 + 0.072563I
b = −0.142548 − 0.140247I
0.50148 − 1.32272I 5.11712 + 4.95919I
u = −1.48500 + 0.26000I
a = 1.120910 + 0.102882I
b = −0.255453 + 0.705274I
5.45005 − 5.59065I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48500 − 0.26000I
a = 1.120910 − 0.102882I
b = −0.255453 − 0.705274I
5.45005 + 5.59065I 0
u = −0.463679 + 0.155250I
a = −2.37623 + 0.65762I
b = 0.614271 − 0.862447I
0.59794 − 2.40390I 1.78729 + 3.32649I
u = −0.463679 − 0.155250I
a = −2.37623 − 0.65762I
b = 0.614271 + 0.862447I
0.59794 + 2.40390I 1.78729 − 3.32649I
u = −1.51959 + 0.08438I
a = −0.789869 − 0.291182I
b = 0.306865 − 1.151720I
4.67990 − 3.98112I 0
u = −1.51959 − 0.08438I
a = −0.789869 + 0.291182I
b = 0.306865 + 1.151720I
4.67990 + 3.98112I 0
u = −0.078329 + 0.427211I
a = −2.27926 + 0.07772I
b = 0.541612 − 0.940323I
0.26280 − 2.86416I 5.10786 − 1.03407I
u = −0.078329 − 0.427211I
a = −2.27926 − 0.07772I
b = 0.541612 + 0.940323I
0.26280 + 2.86416I 5.10786 + 1.03407I
u = 1.56928 + 0.03188I
a = −1.87634 − 0.78270I
b = 0.803759 + 0.892022I
7.70040 + 3.01101I 0
u = 1.56928 − 0.03188I
a = −1.87634 + 0.78270I
b = 0.803759 − 0.892022I
7.70040 − 3.01101I 0
u = 1.57468 + 0.06012I
a = −0.847918 − 0.235707I
b = 0.325364 − 1.160820I
8.54134 + 0.68666I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57468 − 0.06012I
a = −0.847918 + 0.235707I
b = 0.325364 + 1.160820I
8.54134 − 0.68666I 0
u = −1.58471
a = −0.992474
b = 0.861914
8.58805 0
u = 1.58785 + 0.09233I
a = 1.94370 + 0.00627I
b = −0.811458 − 1.037490I
16.3498 + 5.4804I 0
u = 1.58785 − 0.09233I
a = 1.94370 − 0.00627I
b = −0.811458 + 1.037490I
16.3498 − 5.4804I 0
u = 1.62114 + 0.06754I
a = 1.07652 − 0.93449I
b = −0.933998 + 0.760204I
17.2245 − 0.9450I 0
u = 1.62114 − 0.06754I
a = 1.07652 + 0.93449I
b = −0.933998 − 0.760204I
17.2245 + 0.9450I 0
u = −1.62817 + 0.07722I
a = −1.86464 − 0.79697I
b = 0.816768 + 0.882730I
11.54420 − 1.76278I 0
u = −1.62817 − 0.07722I
a = −1.86464 + 0.79697I
b = 0.816768 − 0.882730I
11.54420 + 1.76278I 0
u = −1.62013 + 0.22649I
a = 1.87179 + 0.02364I
b = −0.800729 + 1.038330I
12.2115 − 10.1477I 0
u = −1.62013 − 0.22649I
a = 1.87179 − 0.02364I
b = −0.800729 − 1.038330I
12.2115 + 10.1477I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.63229 + 0.17241I
a = −0.729730 + 0.249243I
b = 0.294541 + 1.166160I
8.34692 + 8.79923I 0
u = 1.63229 − 0.17241I
a = −0.729730 − 0.249243I
b = 0.294541 − 1.166160I
8.34692 − 8.79923I 0
u = −1.64023 + 0.18527I
a = 1.055260 + 0.872816I
b = −0.925763 − 0.748096I
13.12460 − 3.78419I 0
u = −1.64023 − 0.18527I
a = 1.055260 − 0.872816I
b = −0.925763 + 0.748096I
13.12460 + 3.78419I 0
u = 1.64954 + 0.09451I
a = −1.024770 − 0.042625I
b = 0.877470 + 0.021197I
12.40730 + 4.81921I 0
u = 1.64954 − 0.09451I
a = −1.024770 + 0.042625I
b = 0.877470 − 0.021197I
12.40730 − 4.81921I 0
u = −1.64916 + 0.12208I
a = −1.86517 + 0.76861I
b = 0.808404 − 0.906622I
11.46920 − 7.83965I 0
u = −1.64916 − 0.12208I
a = −1.86517 − 0.76861I
b = 0.808404 + 0.906622I
11.46920 + 7.83965I 0
u = 0.011633 + 0.252597I
a = −1.48519 − 3.25207I
b = 0.486901 + 0.619078I
1.18181 + 1.37684I 10.23383 − 4.11434I
u = 0.011633 − 0.252597I
a = −1.48519 + 3.25207I
b = 0.486901 − 0.619078I
1.18181 − 1.37684I 10.23383 + 4.11434I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73327 + 0.24468I
a = 1.83247 + 0.02129I
b = −0.798044 − 1.046890I
15.8035 + 15.1907I 0
u = 1.73327 − 0.24468I
a = 1.83247 − 0.02129I
b = −0.798044 + 1.046890I
15.8035 − 15.1907I 0
u = 1.73825 + 0.21069I
a = 1.096380 − 0.840577I
b = −0.932887 + 0.737413I
16.7780 + 8.8164I 0
u = 1.73825 − 0.21069I
a = 1.096380 + 0.840577I
b = −0.932887 − 0.737413I
16.7780 − 8.8164I 0
12
II. I
u
2
= hb
2
− b + 1, a + 1, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
11
=
u
−u
3
+ u
a
2
=
−1
b
a
8
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−b + 1
b − 1
a
3
=
0
b − 1
a
1
=
−1
0
a
4
=
0
b − 1
a
9
=
0
u
a
12
=
−u
3
+ 2u
−u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
4
b − 2u
3
b − 2u
2
b − 4u
3
+ 3bu + u
2
− 4b + 8u + 10
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
3
, c
9
u
10
c
6
, c
7
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
8
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
10
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
11
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
c
12
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
5
c
3
, c
9
y
10
c
6
, c
7
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
8
, c
12
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
11
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = −1.00000
b = 0.500000 + 0.866025I
2.40108 + 2.02988I 6.55976 − 4.16430I
u = −1.21774
a = −1.00000
b = 0.500000 − 0.866025I
2.40108 − 2.02988I 6.55976 + 4.16430I
u = −0.309916 + 0.549911I
a = −1.00000
b = 0.500000 + 0.866025I
0.329100 + 0.499304I 1.60756 + 0.92266I
u = −0.309916 + 0.549911I
a = −1.00000
b = 0.500000 − 0.866025I
0.32910 − 3.56046I 5.91654 + 9.74472I
u = −0.309916 − 0.549911I
a = −1.00000
b = 0.500000 + 0.866025I
0.32910 + 3.56046I 5.91654 − 9.74472I
u = −0.309916 − 0.549911I
a = −1.00000
b = 0.500000 − 0.866025I
0.329100 − 0.499304I 1.60756 − 0.92266I
u = 1.41878 + 0.21917I
a = −1.00000
b = 0.500000 + 0.866025I
5.87256 + 6.43072I 10.62344 − 8.02599I
u = 1.41878 + 0.21917I
a = −1.00000
b = 0.500000 − 0.866025I
5.87256 + 2.37095I 9.29269 + 1.50431I
u = 1.41878 − 0.21917I
a = −1.00000
b = 0.500000 + 0.866025I
5.87256 − 2.37095I 9.29269 − 1.50431I
u = 1.41878 − 0.21917I
a = −1.00000
b = 0.500000 − 0.866025I
5.87256 − 6.43072I 10.62344 + 8.02599I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
− u + 1)
5
)(u
74
+ 22u
73
+ ··· + 13u + 1)
c
2
((u
2
+ u + 1)
5
)(u
74
+ 6u
73
+ ··· + 5u + 1)
c
3
, c
9
u
10
(u
74
+ u
73
+ ··· + 3072u
2
− 1024)
c
5
((u
2
− u + 1)
5
)(u
74
+ 6u
73
+ ··· + 5u + 1)
c
6
, c
7
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
)(u
74
− 3u
73
+ ··· − 105u − 34)
c
8
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
)(u
74
+ 3u
73
+ ··· − 2u − 1)
c
10
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
74
− 3u
73
+ ··· − 105u − 34)
c
11
((u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
)(u
74
− 43u
73
+ ··· + 2u + 1)
c
12
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
)(u
74
+ 3u
73
+ ··· − 2u − 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
5
)(y
74
+ 66y
73
+ ··· + 1221y + 1)
c
2
, c
5
((y
2
+ y + 1)
5
)(y
74
+ 22y
73
+ ··· + 13y + 1)
c
3
, c
9
y
10
(y
74
− 55y
73
+ ··· − 6291456y + 1048576)
c
6
, c
7
, c
10
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
)(y
74
− 85y
73
+ ··· + 17603y + 1156)
c
8
, c
12
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
)(y
74
+ 43y
73
+ ··· − 2y + 1)
c
11
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
)(y
74
− 21y
73
+ ··· − 54y + 1)
18
