12n
0179
(K12n
0179
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 9 11 4 6 5 12 7 10
Solving Sequence
6,11 4,7
8 9 12 3 5 2 10 1
c
6
c
7
c
8
c
11
c
3
c
5
c
2
c
10
c
12
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.37190 × 10
18
u
22
− 7.99565 × 10
18
u
21
+ ··· + 2.02541 × 10
20
b − 2.79533 × 10
20
,
− 4.59710 × 10
19
u
22
− 4.62744 × 10
20
u
21
+ ··· + 3.44319 × 10
21
a − 1.63572 × 10
22
,
u
23
+ 2u
22
+ ··· + 52u + 17i
I
u
2
= h−5u
3
a
2
− 3a
2
u
2
+ 6u
3
a + 18a
2
u + 11u
2
a − 4u
3
− 4a
2
− 29au − 32u
2
+ 37b − 10a + 7u + 19,
2u
3
a
2
+ 2a
2
u
2
− u
3
a + a
3
+ a
2
u + 2u
3
− 2a
2
− au + 3u
2
+ 4u + 2, u
4
− u
2
+ 1i
I
u
3
= hu
3
− u
2
+ b + 1, u
4
− u
2
+ a + 2u + 1, u
5
− u
4
+ u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 40 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
= h1.37 × 10
18
u
22
− 8.00 × 10
18
u
21
+ · · · + 2.03 × 10
20
b − 2.80 ×
10
20
, −4.60 × 10
19
u
22
− 4.63 × 10
20
u
21
+ · · · + 3.44 × 10
21
a − 1.64 ×
10
22
, u
23
+ 2u
22
+ · · · + 52u + 17i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
0.0133513u
22
+ 0.134394u
21
+ ··· − 1.65131u + 4.75059
−0.00677343u
22
+ 0.0394767u
21
+ ··· − 0.213063u + 1.38013
a
7
=
1
u
2
a
8
=
−0.415260u
22
− 0.446011u
21
+ ··· − 13.3132u − 7.56780
−0.164479u
22
− 0.153676u
21
+ ··· − 4.53967u − 2.55254
a
9
=
−0.250781u
22
− 0.292335u
21
+ ··· − 8.77357u − 5.01526
−0.164479u
22
− 0.153676u
21
+ ··· − 4.53967u − 2.55254
a
12
=
−u
−u
3
+ u
a
3
=
−0.158366u
22
− 0.0384582u
21
+ ··· − 7.26516u + 1.53971
−0.184168u
22
− 0.141177u
21
+ ··· − 6.16412u − 1.51976
a
5
=
0.191837u
22
+ 0.133885u
21
+ ··· + 5.40801u + 3.14823
0.0435720u
22
+ 0.0231293u
21
+ ··· + 1.06482u + 0.103017
a
2
=
−0.0136483u
22
+ 0.162115u
21
+ ··· − 1.72543u + 5.96673
−0.0408799u
22
+ 0.00329935u
21
+ ··· − 0.954342u + 0.923420
a
10
=
u
3
u
5
− u
3
+ u
a
1
=
−u
5
− u
−u
7
+ u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
45183703312586503683
101270439284454752258
u
22
+
93456001880784428205
101270439284454752258
u
21
+ ··· +
880293744256233854306
50635219642227376129
u +
601972144725743861757
50635219642227376129
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
+ 28u
22
+ ··· − 74u + 1
c
2
, c
4
u
23
− 10u
22
+ ··· + 22u − 1
c
3
, c
7
u
23
− u
22
+ ··· − 64u − 32
c
5
, c
8
, c
9
u
23
− 2u
22
+ ··· − 238u − 49
c
6
, c
11
u
23
− 2u
22
+ ··· + 52u − 17
c
10
, c
12
u
23
+ 18u
22
+ ··· + 3418u + 289
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− 104y
22
+ ··· − 62214y −1
c
2
, c
4
y
23
− 28y
22
+ ··· − 74y −1
c
3
, c
7
y
23
+ 21y
22
+ ··· + 37376y −1024
c
5
, c
8
, c
9
y
23
+ 30y
21
+ ··· + 31556y −2401
c
6
, c
11
y
23
− 18y
22
+ ··· + 3418y −289
c
10
, c
12
y
23
− 18y
22
+ ··· + 2928914y −83521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.030250 + 0.133808I
a = 0.762093 + 1.177250I
b = −0.359850 + 0.929573I
3.40068 − 2.08292I −6.94504 + 2.82033I
u = −1.030250 − 0.133808I
a = 0.762093 − 1.177250I
b = −0.359850 − 0.929573I
3.40068 + 2.08292I −6.94504 − 2.82033I
u = 0.901962 + 0.543040I
a = 4.80515 + 0.32829I
b = 2.51685 + 4.97104I
−0.09172 − 2.05272I 13.5502 − 11.7426I
u = 0.901962 − 0.543040I
a = 4.80515 − 0.32829I
b = 2.51685 − 4.97104I
−0.09172 + 2.05272I 13.5502 + 11.7426I
u = −0.774138 + 0.517283I
a = −0.187723 − 0.729816I
b = −0.888501 − 0.210493I
1.78208 + 2.09879I 0.37186 − 4.32801I
u = −0.774138 − 0.517283I
a = −0.187723 + 0.729816I
b = −0.888501 + 0.210493I
1.78208 − 2.09879I 0.37186 + 4.32801I
u = −0.987737 + 0.455591I
a = 0.000748 − 1.386780I
b = 0.203991 − 0.922058I
3.17947 + 4.60678I −8.98911 − 4.52953I
u = −0.987737 − 0.455591I
a = 0.000748 + 1.386780I
b = 0.203991 + 0.922058I
3.17947 − 4.60678I −8.98911 + 4.52953I
u = 0.751562
a = −0.430119
b = 0.215899
−1.11111 −8.83030
u = 0.913312 + 0.995998I
a = −0.455968 − 0.165528I
b = 0.0273478 + 0.1092730I
8.77314 − 3.60069I −8.75891 + 4.90863I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.913312 − 0.995998I
a = −0.455968 + 0.165528I
b = 0.0273478 − 0.1092730I
8.77314 + 3.60069I −8.75891 − 4.90863I
u = −0.29230 + 1.39423I
a = 0.306239 − 0.296422I
b = 0.27422 − 1.73853I
−9.67128 − 5.78622I −6.43045 + 2.03811I
u = −0.29230 − 1.39423I
a = 0.306239 + 0.296422I
b = 0.27422 + 1.73853I
−9.67128 + 5.78622I −6.43045 − 2.03811I
u = 0.312134 + 0.458419I
a = −0.517712 − 0.280214I
b = 0.099441 + 0.699809I
−0.646445 − 1.161780I −6.90693 + 5.27856I
u = 0.312134 − 0.458419I
a = −0.517712 + 0.280214I
b = 0.099441 − 0.699809I
−0.646445 + 1.161780I −6.90693 − 5.27856I
u = −1.34978 + 0.77312I
a = −0.81654 + 1.45288I
b = 0.50785 + 1.97781I
−12.9726 + 13.2355I −7.13536 − 5.53565I
u = −1.34978 − 0.77312I
a = −0.81654 − 1.45288I
b = 0.50785 − 1.97781I
−12.9726 − 13.2355I −7.13536 + 5.53565I
u = −0.377835
a = 3.52955
b = 0.965970
−2.11000 0.409770
u = −1.59039 + 0.40688I
a = 0.35471 − 1.57413I
b = −0.18308 − 1.79179I
−6.97074 + 4.93755I −7.69369 − 2.56266I
u = −1.59039 − 0.40688I
a = 0.35471 + 1.57413I
b = −0.18308 + 1.79179I
−6.97074 − 4.93755I −7.69369 + 2.56266I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.78874
a = 0.851439
b = −0.299287
−10.2305 −8.74930
u = 1.81595 + 0.61002I
a = 0.714754 + 1.134980I
b = −0.13957 + 1.61563I
−16.2453 − 1.7569I −8.47765 + 0.68383I
u = 1.81595 − 0.61002I
a = 0.714754 − 1.134980I
b = −0.13957 − 1.61563I
−16.2453 + 1.7569I −8.47765 − 0.68383I
7
II.
I
u
2
= h−5u
3
a
2
+6u
3
a + · · · − 10a + 19, 2u
3
a
2
−u
3
a + · · · − 2a
2
+2, u
4
−u
2
+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
a
0.135135a
2
u
3
− 0.162162au
3
+ ··· + 0.270270a − 0.513514
a
7
=
1
u
2
a
8
=
−0.351351a
2
u
3
− 0.378378au
3
+ ··· + 0.297297a + 1.13514
−u
3
a
9
=
−0.351351a
2
u
3
− 0.378378au
3
+ ··· + 0.297297a + 1.13514
−u
3
a
12
=
−u
−u
3
+ u
a
3
=
−0.135135a
2
u
3
+ 0.162162au
3
+ ··· + 0.729730a + 0.513514
0.486486a
2
u
3
− 0.783784au
3
+ ··· − 1.02703a + 0.351351
a
5
=
0.108108a
2
u
3
+ 0.270270au
3
+ ··· + 0.216216a + 1.18919
1
a
2
=
0.0270270a
2
u
3
+ 0.567568au
3
+ ··· + 0.0540541a + 1.29730
−0.189189a
2
u
3
+ 0.0270270au
3
+ ··· − 0.378378a + 0.918919
a
10
=
u
3
0
a
1
=
−u
3
−u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
−
100
37
u
3
a
2
+
88
37
a
2
u
2
+
120
37
u
3
a+
64
37
a
2
u−
76
37
u
2
a−
80
37
u
3
−
80
37
a
2
−
136
37
au+
100
37
u
2
+
96
37
a+
140
37
u−
212
37
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)
4
c
2
(u
3
+ u
2
− 1)
4
c
3
, c
7
(u
6
− 3u
4
+ 2u
2
+ 1)
2
c
4
(u
3
− u
2
+ 1)
4
c
5
, c
8
, c
9
(u
2
+ 1)
6
c
6
, c
11
(u
4
− u
2
+ 1)
3
c
10
(u
2
− u + 1)
6
c
12
(u
2
+ u + 1)
6
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 3y
2
+ 2y −1)
4
c
2
, c
4
(y
3
− y
2
+ 2y −1)
4
c
3
, c
7
(y
3
− 3y
2
+ 2y + 1)
4
c
5
, c
8
, c
9
(y + 1)
12
c
6
, c
11
(y
2
− y + 1)
6
c
10
, c
12
(y
2
+ y + 1)
6
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 0.611376 + 1.168210I
b = 0.60113 + 1.32865I
4.66906 + 0.79824I −2.49024 + 0.48465I
u = 0.866025 + 0.500000I
a = −0.86134 − 1.84069I
b = −0.14373 − 1.45121I
4.66906 − 4.85801I −2.49024 + 6.44355I
u = 0.866025 + 0.500000I
a = 0.38394 − 3.55957I
b = 3.27465 − 0.87744I
0.53148 − 2.02988I −9.01951 + 3.46410I
u = 0.866025 − 0.500000I
a = 0.611376 − 1.168210I
b = 0.60113 − 1.32865I
4.66906 − 0.79824I −2.49024 − 0.48465I
u = 0.866025 − 0.500000I
a = −0.86134 + 1.84069I
b = −0.14373 + 1.45121I
4.66906 + 4.85801I −2.49024 − 6.44355I
u = 0.866025 − 0.500000I
a = 0.38394 + 3.55957I
b = 3.27465 + 0.87744I
0.53148 + 2.02988I −9.01951 − 3.46410I
u = −0.866025 + 0.500000I
a = 0.801323 + 0.635627I
b = −0.356011 − 0.161073I
4.66906 − 0.79824I −2.49024 − 0.48465I
u = −0.866025 + 0.500000I
a = −0.306233 − 0.883547I
b = 0.388851 + 0.038512I
4.66906 + 4.85801I −2.49024 − 6.44355I
u = −0.866025 + 0.500000I
a = 1.37094 − 0.52003I
b = 0.235109 − 0.877439I
0.53148 + 2.02988I −9.01951 − 3.46410I
u = −0.866025 − 0.500000I
a = 0.801323 − 0.635627I
b = −0.356011 + 0.161073I
4.66906 + 0.79824I −2.49024 + 0.48465I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.866025 − 0.500000I
a = −0.306233 + 0.883547I
b = 0.388851 − 0.038512I
4.66906 − 4.85801I −2.49024 + 6.44355I
u = −0.866025 − 0.500000I
a = 1.37094 + 0.52003I
b = 0.235109 + 0.877439I
0.53148 − 2.02988I −9.01951 + 3.46410I
12
III. I
u
3
= hu
3
− u
2
+ b + 1, u
4
− u
2
+ a + 2u + 1, u
5
− u
4
+ u
2
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
−u
4
+ u
2
− 2u − 1
−u
3
+ u
2
− 1
a
7
=
1
u
2
a
8
=
1
u
2
a
9
=
−u
2
+ 1
u
2
a
12
=
−u
−u
3
+ u
a
3
=
−u
4
+ u
2
− 2u − 1
−u
3
+ u
2
− 1
a
5
=
u
4
− u
2
+ 1
−u
4
a
2
=
−2u
4
+ 2u
2
− 2u − 2
u
4
− u
3
+ u
2
− 1
a
10
=
u
3
u
4
− u
3
− u
2
+ 1
a
1
=
−u
4
+ u
2
− 1
u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9u
4
+ u
3
+ 2u
2
− 4u − 17
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
7
u
5
c
4
(u + 1)
5
c
5
, c
10
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
6
u
5
− u
4
+ u
2
+ u − 1
c
8
, c
9
, c
12
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1
c
11
u
5
+ u
4
− u
2
+ u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
7
y
5
c
5
, c
8
, c
9
c
10
, c
12
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1
c
6
, c
11
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.758138 + 0.584034I
a = 1.47956 − 1.63976I
b = −1.10636 − 1.69341I
0.17487 + 2.21397I −6.59361 + 0.42541I
u = −0.758138 − 0.584034I
a = 1.47956 + 1.63976I
b = −1.10636 + 1.69341I
0.17487 − 2.21397I −6.59361 − 0.42541I
u = 0.935538 + 0.903908I
a = 0.044146 − 0.313338I
b = 0.532511 + 0.056433I
9.31336 − 3.33174I 3.61324 − 0.36944I
u = 0.935538 − 0.903908I
a = 0.044146 + 0.313338I
b = 0.532511 − 0.056433I
9.31336 + 3.33174I 3.61324 + 0.36944I
u = 0.645200
a = −2.04741
b = −0.852303
−2.52712 −20.0390
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
3
− u
2
+ 2u − 1)
4
(u
23
+ 28u
22
+ ··· − 74u + 1)
c
2
((u − 1)
5
)(u
3
+ u
2
− 1)
4
(u
23
− 10u
22
+ ··· + 22u − 1)
c
3
, c
7
u
5
(u
6
− 3u
4
+ 2u
2
+ 1)
2
(u
23
− u
22
+ ··· − 64u − 32)
c
4
((u + 1)
5
)(u
3
− u
2
+ 1)
4
(u
23
− 10u
22
+ ··· + 22u − 1)
c
5
((u
2
+ 1)
6
)(u
5
− u
4
+ ··· + 3u − 1)(u
23
− 2u
22
+ ··· − 238u − 49)
c
6
((u
4
− u
2
+ 1)
3
)(u
5
− u
4
+ u
2
+ u − 1)(u
23
− 2u
22
+ ··· + 52u − 17)
c
8
, c
9
((u
2
+ 1)
6
)(u
5
+ u
4
+ ··· + 3u + 1)(u
23
− 2u
22
+ ··· − 238u − 49)
c
10
(u
2
− u + 1)
6
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)
· (u
23
+ 18u
22
+ ··· + 3418u + 289)
c
11
((u
4
− u
2
+ 1)
3
)(u
5
+ u
4
− u
2
+ u + 1)(u
23
− 2u
22
+ ··· + 52u − 17)
c
12
(u
2
+ u + 1)
6
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
· (u
23
+ 18u
22
+ ··· + 3418u + 289)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
3
+ 3y
2
+ 2y −1)
4
(y
23
− 104y
22
+ ··· − 62214y −1)
c
2
, c
4
((y −1)
5
)(y
3
− y
2
+ 2y −1)
4
(y
23
− 28y
22
+ ··· − 74y −1)
c
3
, c
7
y
5
(y
3
− 3y
2
+ 2y + 1)
4
(y
23
+ 21y
22
+ ··· + 37376y −1024)
c
5
, c
8
, c
9
(y + 1)
12
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
· (y
23
+ 30y
21
+ ··· + 31556y −2401)
c
6
, c
11
(y
2
− y + 1)
6
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
· (y
23
− 18y
22
+ ··· + 3418y −289)
c
10
, c
12
(y
2
+ y + 1)
6
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
· (y
23
− 18y
22
+ ··· + 2928914y −83521)
18
