12n
0454
(K12n
0454
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 2 11 4 3 12 6 9 10
Solving Sequence
3,8
4
9,11
12 7 5 6 2 1 10
c
3
c
8
c
11
c
7
c
4
c
6
c
2
c
1
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.34392 × 10
24
u
30
+ 1.20403 × 10
25
u
29
+ ··· + 2.13898 × 10
24
b − 8.19442 × 10
25
,
− 5.24612 × 10
24
u
30
+ 1.21449 × 10
25
u
29
+ ··· + 2.13898 × 10
24
a − 6.53057 × 10
25
,
u
31
− 2u
30
+ ··· + 28u + 4i
I
u
2
= h3b − u − 2, 3a + 2u + 1, u
2
+ u + 1i
I
u
3
= hau + 3b − 4a + 2u + 1, 2a
2
− 3au + 2a + u − 3, u
2
+ 2i
I
v
1
= ha, b − v + 2, v
2
− 3v + 1i
* 4 irreducible components of dim
C
= 0, with total 39 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−5.34 × 10
24
u
30
+ 1.20 × 10
25
u
29
+ · · · + 2.14 × 10
24
b − 8.19 ×
10
25
, −5.25 × 10
24
u
30
+ 1.21 × 10
25
u
29
+ · · · + 2.14 × 10
24
a − 6.53 ×
10
25
, u
31
− 2u
30
+ · · · + 28u + 4i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
9
=
u
u
a
11
=
2.45262u
30
− 5.67789u
29
+ ··· + 112.994u + 30.5312
2.49834u
30
− 5.62900u
29
+ ··· + 123.421u + 38.3098
a
12
=
2.40875u
30
− 5.56826u
29
+ ··· + 108.882u + 29.9698
2.45447u
30
− 5.51937u
29
+ ··· + 119.309u + 37.7485
a
7
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
6
=
0.185869u
30
− 0.506326u
29
+ ··· + 8.73363u − 0.480369
0.954311u
30
− 2.13631u
29
+ ··· + 45.6943u + 14.8328
a
2
=
1.20265u
30
− 2.80559u
29
+ ··· + 57.4529u + 14.8908
−1.14984u
30
+ 2.60951u
29
+ ··· − 55.1167u − 16.9723
a
1
=
0.0528171u
30
− 0.196085u
29
+ ··· + 2.33621u − 2.08152
−1.14984u
30
+ 2.60951u
29
+ ··· − 55.1167u − 16.9723
a
10
=
−0.871927u
30
+ 2.04345u
29
+ ··· − 48.9524u − 11.3712
2.44025u
30
− 5.52900u
29
+ ··· + 118.778u + 35.8466
(ii) Obstruction class = −1
(iii) Cusp Shapes =
40150014847740772034704846
1604238713781269697683811
u
30
−
30333063294678849729282082
534746237927089899227937
u
29
+
··· +
642744006791888105510144570
534746237927089899227937
u +
616846322292496574153802580
1604238713781269697683811
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
+ 34u
30
+ ··· + 16249u + 361
c
2
, c
5
u
31
+ 4u
30
+ ··· − 17u + 19
c
3
, c
4
, c
7
c
8
u
31
+ 2u
30
+ ··· + 28u − 4
c
6
, c
10
u
31
+ 2u
30
+ ··· − 36u − 36
c
9
, c
11
, c
12
u
31
+ 6u
30
+ ··· + 5u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
− 74y
30
+ ··· + 131918441y −130321
c
2
, c
5
y
31
− 34y
30
+ ··· + 16249y −361
c
3
, c
4
, c
7
c
8
y
31
+ 40y
30
+ ··· + 272y −16
c
6
, c
10
y
31
+ 6y
30
+ ··· + 2232y −1296
c
9
, c
11
, c
12
y
31
− 20y
30
+ ··· + 223y −81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.150087 + 0.994909I
a = 0.49984 − 1.89088I
b = 1.130920 − 0.806791I
−3.71035 − 1.41787I 3.38804 + 1.32048I
u = −0.150087 − 0.994909I
a = 0.49984 + 1.89088I
b = 1.130920 + 0.806791I
−3.71035 + 1.41787I 3.38804 − 1.32048I
u = 0.949025 + 0.259341I
a = −0.072682 + 0.704869I
b = 0.582494 − 0.117627I
−3.71574 − 2.40842I 3.33618 + 2.66984I
u = 0.949025 − 0.259341I
a = −0.072682 − 0.704869I
b = 0.582494 + 0.117627I
−3.71574 + 2.40842I 3.33618 − 2.66984I
u = −0.761649 + 0.761026I
a = −0.101228 + 0.295647I
b = −0.778145 − 0.069572I
1.17088 − 2.70519I 1.34730 + 7.26275I
u = −0.761649 − 0.761026I
a = −0.101228 − 0.295647I
b = −0.778145 + 0.069572I
1.17088 + 2.70519I 1.34730 − 7.26275I
u = 0.801880 + 0.845490I
a = 0.192710 + 0.190905I
b = 1.308920 − 0.176651I
−5.44830 + 8.20678I 3.96431 − 6.25123I
u = 0.801880 − 0.845490I
a = 0.192710 − 0.190905I
b = 1.308920 + 0.176651I
−5.44830 − 8.20678I 3.96431 + 6.25123I
u = 0.518296 + 1.138380I
a = 0.075776 + 0.484959I
b = −0.478186 − 0.043766I
−8.10871 + 2.46499I 0
u = 0.518296 − 1.138380I
a = 0.075776 − 0.484959I
b = −0.478186 + 0.043766I
−8.10871 − 2.46499I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.239573 + 1.258650I
a = −0.049051 + 0.239996I
b = −0.174354 − 0.870729I
3.35227 − 2.03069I 6.00000 + 0.I
u = −0.239573 − 1.258650I
a = −0.049051 − 0.239996I
b = −0.174354 + 0.870729I
3.35227 + 2.03069I 6.00000 + 0.I
u = −0.049257 + 0.651330I
a = 0.031163 + 0.438228I
b = 0.636530 + 0.528351I
−1.02719 − 1.35876I 0.38562 + 5.54408I
u = −0.049257 − 0.651330I
a = 0.031163 − 0.438228I
b = 0.636530 − 0.528351I
−1.02719 + 1.35876I 0.38562 − 5.54408I
u = −0.01769 + 1.49068I
a = −1.84020 + 1.15884I
b = −2.05375 + 1.80415I
−4.97013 + 0.88940I 0
u = −0.01769 − 1.49068I
a = −1.84020 − 1.15884I
b = −2.05375 − 1.80415I
−4.97013 − 0.88940I 0
u = 0.146387 + 0.409089I
a = 0.10548 − 1.80116I
b = −1.016560 + 0.397771I
1.43804 + 0.67860I 5.66172 + 1.82882I
u = 0.146387 − 0.409089I
a = 0.10548 + 1.80116I
b = −1.016560 − 0.397771I
1.43804 − 0.67860I 5.66172 − 1.82882I
u = −0.333653
a = 4.41543
b = −0.313107
7.50433 24.5590
u = 0.06381 + 1.68753I
a = 1.345990 + 0.237815I
b = 1.82999 − 0.04669I
−9.31296 − 0.73241I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.06381 − 1.68753I
a = 1.345990 − 0.237815I
b = 1.82999 + 0.04669I
−9.31296 + 0.73241I 0
u = 0.26352 + 1.68744I
a = 1.67424 + 0.15516I
b = 2.20381 − 0.62844I
−13.9459 + 12.3803I 0
u = 0.26352 − 1.68744I
a = 1.67424 − 0.15516I
b = 2.20381 + 0.62844I
−13.9459 − 12.3803I 0
u = −0.18187 + 1.70595I
a = −1.372120 − 0.010334I
b = −1.81881 − 0.60789I
−7.53329 − 6.21670I 0
u = −0.18187 − 1.70595I
a = −1.372120 + 0.010334I
b = −1.81881 + 0.60789I
−7.53329 + 6.21670I 0
u = −0.283237
a = −1.71193
b = −0.227764
0.766548 14.0280
u = −0.03812 + 1.72844I
a = 1.237920 − 0.134015I
b = 1.67073 + 0.76279I
−13.51010 − 2.18010I 0
u = −0.03812 − 1.72844I
a = 1.237920 + 0.134015I
b = 1.67073 − 0.76279I
−13.51010 + 2.18010I 0
u = −0.260390
a = −0.560132
b = 2.58879
−0.450742 39.0360
u = 0.13397 + 1.76472I
a = −1.46619 − 0.05769I
b = −2.23420 − 0.13354I
−18.3679 + 5.2164I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.13397 − 1.76472I
a = −1.46619 + 0.05769I
b = −2.23420 + 0.13354I
−18.3679 − 5.2164I 0
8
II. I
u
2
= h3b − u − 2, 3a + 2u + 1, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u + 1
a
9
=
u
u
a
11
=
−
2
3
u −
1
3
1
3
u +
2
3
a
12
=
−
5
3
u −
1
3
−
2
3
u +
2
3
a
7
=
−u
u + 1
a
5
=
−u
u + 2
a
6
=
−u
u + 1
a
2
=
0
−u
a
1
=
−u
−u
a
10
=
−
2
3
u −
1
3
1
3
u +
2
3
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4
3
u + 7
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
u
2
+ u + 1
c
2
, c
7
, c
8
u
2
− u + 1
c
6
, c
10
u
2
c
9
(u + 1)
2
c
11
, c
12
(u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
y
2
+ y + 1
c
6
, c
10
y
2
c
9
, c
11
, c
12
(y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = − 0.577350I
b = 0.500000 + 0.288675I
1.64493 − 2.02988I 6.33333 + 1.15470I
u = −0.500000 − 0.866025I
a = 0.577350I
b = 0.500000 − 0.288675I
1.64493 + 2.02988I 6.33333 − 1.15470I
12
III. I
u
3
= hau + 3b − 4a + 2u + 1, 2a
2
− 3au + 2a + u − 3, u
2
+ 2i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
2
a
9
=
u
u
a
11
=
a
−
1
3
au +
4
3
a −
2
3
u −
1
3
a
12
=
2
3
au +
1
3
a +
4
3
u +
2
3
1
3
au +
2
3
a +
2
3
u +
1
3
a
7
=
−u
−u
a
5
=
−1
0
a
6
=
−
1
3
au +
1
3
a −
7
6
u −
4
3
−1
a
2
=
−
1
3
au +
1
3
a −
7
6
u −
1
3
−1
a
1
=
−
1
3
au +
1
3
a −
7
6
u −
4
3
−1
a
10
=
−au + a −
3
2
u − 2
−
2
3
au +
2
3
a −
1
3
u −
5
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
4
c
2
(u + 1)
4
c
3
, c
4
, c
7
c
8
(u
2
+ 2)
2
c
6
, c
11
, c
12
(u
2
+ u − 1)
2
c
9
, c
10
(u
2
− u − 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
7
c
8
(y + 2)
4
c
6
, c
9
, c
10
c
11
, c
12
(y
2
− 3y + 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 0.618034 + 0.270091I
b = 0.618034 − 0.874032I
2.30291 4.00000
u = 1.414210I
a = −1.61803 + 1.85123I
b = −1.61803 + 2.28825I
−5.59278 4.00000
u = − 1.414210I
a = 0.618034 − 0.270091I
b = 0.618034 + 0.874032I
2.30291 4.00000
u = − 1.414210I
a = −1.61803 − 1.85123I
b = −1.61803 − 2.28825I
−5.59278 4.00000
16
IV. I
v
1
= ha, b − v + 2, v
2
− 3v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
9
=
v
0
a
11
=
0
v − 2
a
12
=
2v − 1
v − 2
a
7
=
v
0
a
5
=
1
0
a
6
=
v
1
a
2
=
−v + 1
−1
a
1
=
−v
−1
a
10
=
−2v + 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
4
, c
7
c
8
u
2
c
5
(u + 1)
2
c
6
, c
9
u
2
− u − 1
c
10
, c
11
, c
12
u
2
+ u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
2
c
3
, c
4
, c
7
c
8
y
2
c
6
, c
9
, c
10
c
11
, c
12
y
2
− 3y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.381966
a = 0
b = −1.61803
−0.657974 −6.00000
v = 2.61803
a = 0
b = 0.618034
7.23771 −6.00000
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
2
+ u + 1)(u
31
+ 34u
30
+ ··· + 16249u + 361)
c
2
((u − 1)
2
)(u + 1)
4
(u
2
− u + 1)(u
31
+ 4u
30
+ ··· − 17u + 19)
c
3
, c
4
u
2
(u
2
+ 2)
2
(u
2
+ u + 1)(u
31
+ 2u
30
+ ··· + 28u − 4)
c
5
((u − 1)
4
)(u + 1)
2
(u
2
+ u + 1)(u
31
+ 4u
30
+ ··· − 17u + 19)
c
6
u
2
(u
2
− u − 1)(u
2
+ u − 1)
2
(u
31
+ 2u
30
+ ··· − 36u − 36)
c
7
, c
8
u
2
(u
2
+ 2)
2
(u
2
− u + 1)(u
31
+ 2u
30
+ ··· + 28u − 4)
c
9
((u + 1)
2
)(u
2
− u − 1)
3
(u
31
+ 6u
30
+ ··· + 5u + 9)
c
10
u
2
(u
2
− u − 1)
2
(u
2
+ u − 1)(u
31
+ 2u
30
+ ··· − 36u − 36)
c
11
, c
12
((u − 1)
2
)(u
2
+ u − 1)
3
(u
31
+ 6u
30
+ ··· + 5u + 9)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
6
)(y
2
+ y + 1)(y
31
− 74y
30
+ ··· + 1.31918 × 10
8
y − 130321)
c
2
, c
5
((y − 1)
6
)(y
2
+ y + 1)(y
31
− 34y
30
+ ··· + 16249y − 361)
c
3
, c
4
, c
7
c
8
y
2
(y + 2)
4
(y
2
+ y + 1)(y
31
+ 40y
30
+ ··· + 272y − 16)
c
6
, c
10
y
2
(y
2
− 3y + 1)
3
(y
31
+ 6y
30
+ ··· + 2232y − 1296)
c
9
, c
11
, c
12
((y − 1)
2
)(y
2
− 3y + 1)
3
(y
31
− 20y
30
+ ··· + 223y − 81)
22
