12a
0448
(K12a
0448
)
A knot diagram
1
Linearized knot diagam
3 6 10 9 7 2 12 5 4 1 8 11
Solving Sequence
3,10 4,6
2 7 1 11 9 5 8 12
c
3
c
2
c
6
c
1
c
10
c
9
c
4
c
8
c
12
c
5
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
17
+ 5u
16
+ ··· + 4b + 8, −2u
17
+ 9u
16
+ ··· + 4a + 4, u
18
− 5u
17
+ ··· − 16u + 4i
I
u
2
= h−u
22
a + 2u
22
+ ··· − 4a + 5, −u
22
a + u
22
+ ··· − 4a + 6, u
23
+ 2u
22
+ ··· + 4u + 2i
I
u
3
= h−au + b − u, 2a
2
+ au + 4a + u + 1, u
2
+ 2i
I
u
4
= hb
2
− b + 1, 2a − u + 2, u
2
+ 2i
I
v
1
= ha, b
2
+ b + 1, v + 1i
I
v
2
= ha, b − v + 1, v
2
− v + 1i
* 6 irreducible components of dim
C
= 0, with total 76 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−u
17
+5u
16
+· · ·+4b+8, −2u
17
+9u
16
+· · ·+4a+4, u
18
−5u
17
+· · ·−16u+4i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
1
2
u
17
−
9
4
u
16
+ ··· + 7u − 1
1
4
u
17
−
5
4
u
16
+ ··· + 6u − 2
a
2
=
−
1
4
u
16
+
5
4
u
15
+ ··· + 5u − 2
1
4
u
17
−
3
4
u
16
+ ··· + u − 1
a
7
=
−
1
4
u
17
+ u
16
+ ··· + u
3
+
5
2
u
2
−
1
4
u
17
+
5
4
u
16
+ ··· − 8u + 3
a
1
=
1
4
u
17
− u
16
+ ··· + 6u − 3
1
4
u
17
−
3
4
u
16
+ ··· + u − 1
a
11
=
−
1
4
u
16
+
3
4
u
15
+ ··· + 2u − 1
−
1
4
u
17
+
3
4
u
16
+ ··· −
7
2
u
3
+ 2u
2
a
9
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
12
=
−
3
4
u
16
+
9
4
u
15
+ ··· + 6u − 3
−
5
4
u
17
+
17
4
u
16
+ ··· − 6u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
17
+ 5u
16
− 25u
15
+ 46u
14
− 111u
13
+ 143u
12
− 191u
11
+
117u
10
+ 13u
9
− 240u
8
+ 433u
7
− 502u
6
+ 435u
5
− 247u
4
+ 94u
3
− 14u
2
+ 10u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
10
c
12
u
18
+ 5u
17
+ ··· + 9u + 1
c
2
, c
6
, c
7
c
11
u
18
− u
17
+ ··· − u + 1
c
3
, c
4
, c
8
c
9
u
18
− 5u
17
+ ··· − 16u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
10
c
12
y
18
+ 21y
17
+ ··· + 25y + 1
c
2
, c
6
, c
7
c
11
y
18
+ 5y
17
+ ··· + 9y + 1
c
3
, c
4
, c
8
c
9
y
18
+ 21y
17
+ ··· + 64y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.638269 + 0.881512I
a = −1.60019 − 0.74448I
b = 0.798989 − 0.998980I
7.85728 − 11.04010I 0.91859 + 8.54564I
u = 0.638269 − 0.881512I
a = −1.60019 + 0.74448I
b = 0.798989 + 0.998980I
7.85728 + 11.04010I 0.91859 − 8.54564I
u = 0.852606 + 0.090205I
a = 0.296474 − 0.662577I
b = −0.806782 − 0.920581I
5.47619 + 6.09265I −0.58572 − 4.92211I
u = 0.852606 − 0.090205I
a = 0.296474 + 0.662577I
b = −0.806782 + 0.920581I
5.47619 − 6.09265I −0.58572 + 4.92211I
u = 0.535129 + 1.029760I
a = −0.479909 − 0.577813I
b = 0.859278 + 0.833662I
8.92136 + 1.41173I 3.03885 − 1.48819I
u = 0.535129 − 1.029760I
a = −0.479909 + 0.577813I
b = 0.859278 − 0.833662I
8.92136 − 1.41173I 3.03885 + 1.48819I
u = 0.451443 + 0.440431I
a = 1.09739 + 1.26550I
b = −0.064887 + 0.931862I
−3.52462 − 1.59054I −11.07724 + 4.91257I
u = 0.451443 − 0.440431I
a = 1.09739 − 1.26550I
b = −0.064887 − 0.931862I
−3.52462 + 1.59054I −11.07724 − 4.91257I
u = −0.10451 + 1.44331I
a = −1.113270 + 0.030081I
b = 0.523980 + 0.536010I
5.86276 + 2.35783I 3.62999 − 2.31324I
u = −0.10451 − 1.44331I
a = −1.113270 − 0.030081I
b = 0.523980 − 0.536010I
5.86276 − 2.35783I 3.62999 + 2.31324I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.08738 + 1.48686I
a = −1.038310 − 0.257211I
b = 0.200297 − 0.935744I
2.79590 − 3.37304I −6.91564 + 4.05499I
u = 0.08738 − 1.48686I
a = −1.038310 + 0.257211I
b = 0.200297 + 0.935744I
2.79590 + 3.37304I −6.91564 − 4.05499I
u = −0.285768 + 0.364542I
a = 0.901755 − 0.405570I
b = −0.242963 − 0.416893I
−0.074410 + 0.940749I −1.49251 − 7.14224I
u = −0.285768 − 0.364542I
a = 0.901755 + 0.405570I
b = −0.242963 + 0.416893I
−0.074410 − 0.940749I −1.49251 + 7.14224I
u = 0.19312 + 1.68324I
a = 1.82710 + 0.07303I
b = −0.804956 + 1.067950I
16.6140 − 14.3108I 2.04409 + 7.60234I
u = 0.19312 − 1.68324I
a = 1.82710 − 0.07303I
b = −0.804956 − 1.067950I
16.6140 + 14.3108I 2.04409 − 7.60234I
u = 0.13233 + 1.72622I
a = 1.108960 + 0.785050I
b = −0.962956 − 0.771207I
18.5790 − 1.2471I 4.43961 − 1.42871I
u = 0.13233 − 1.72622I
a = 1.108960 − 0.785050I
b = −0.962956 + 0.771207I
18.5790 + 1.2471I 4.43961 + 1.42871I
6
II. I
u
2
=
h−u
22
a+2u
22
+· · ·−4a+5, −u
22
a+u
22
+· · ·−4a+6, u
23
+2u
22
+· · ·+4u+2i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
a
1
6
u
22
a −
1
3
u
22
+ ··· +
2
3
a −
5
6
a
2
=
−
2
3
u
22
a +
1
12
u
22
+ ··· −
1
6
a +
5
6
1
3
u
22
a +
1
3
u
22
+ ··· −
2
3
a −
1
6
a
7
=
−
1
6
u
22
a +
1
12
u
22
+ ··· +
5
6
a +
4
3
1
3
u
22
a −
1
6
u
22
+ ··· +
1
3
a −
1
6
a
1
=
−
1
3
u
22
a +
5
12
u
22
+ ··· −
5
6
a +
2
3
1
3
u
22
a +
1
3
u
22
+ ··· −
2
3
a −
1
6
a
11
=
−
1
6
u
22
a +
1
12
u
22
+ ··· −
7
6
a +
1
3
−
1
2
u
19
− u
18
+ ··· + 2u
3
− 1
a
9
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
12
=
−
1
6
u
22
a +
1
12
u
22
+ ··· −
7
6
a +
4
3
1
6
u
22
a +
1
6
u
22
+ ··· −
1
3
a −
4
3
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −u
22
−2u
21
−17u
20
−30u
19
−123u
18
−188u
17
−490u
16
−634u
15
−1160u
14
−1234u
13
−
1637u
12
−1380u
11
−1295u
10
−836u
9
−474u
8
−258u
7
−17u
6
−62u
5
+31u
4
−24u
3
−u
2
−10u−4
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
10
c
12
u
46
+ 14u
45
+ ··· + 143u + 9
c
2
, c
6
, c
7
c
11
u
46
− 2u
45
+ ··· − u + 3
c
3
, c
4
, c
8
c
9
(u
23
+ 2u
22
+ ··· + 4u + 2)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
10
c
12
y
46
+ 38y
45
+ ··· − 1657y + 81
c
2
, c
6
, c
7
c
11
y
46
+ 14y
45
+ ··· + 143y + 9
c
3
, c
4
, c
8
c
9
(y
23
+ 30y
22
+ ··· − 16y −4)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.101717 + 0.956988I
a = −1.60922 − 0.38645I
b = 0.711126 + 0.848084I
4.02906 + 2.70329I 3.85709 − 3.53932I
u = −0.101717 + 0.956988I
a = 0.226852 − 0.116990I
b = −0.646487 − 0.011771I
4.02906 + 2.70329I 3.85709 − 3.53932I
u = −0.101717 − 0.956988I
a = −1.60922 + 0.38645I
b = 0.711126 − 0.848084I
4.02906 − 2.70329I 3.85709 + 3.53932I
u = −0.101717 − 0.956988I
a = 0.226852 + 0.116990I
b = −0.646487 + 0.011771I
4.02906 − 2.70329I 3.85709 + 3.53932I
u = −0.590527 + 0.950438I
a = −0.372401 + 0.626274I
b = 0.877763 − 0.787116I
8.51760 + 4.81347I 2.29624 − 3.66244I
u = −0.590527 + 0.950438I
a = −1.57386 + 0.59427I
b = 0.814494 + 0.963779I
8.51760 + 4.81347I 2.29624 − 3.66244I
u = −0.590527 − 0.950438I
a = −0.372401 − 0.626274I
b = 0.877763 + 0.787116I
8.51760 − 4.81347I 2.29624 + 3.66244I
u = −0.590527 − 0.950438I
a = −1.57386 − 0.59427I
b = 0.814494 − 0.963779I
8.51760 − 4.81347I 2.29624 + 3.66244I
u = −0.851549
a = 0.318977 + 0.641567I
b = −0.822919 + 0.871364I
5.62987 −0.159510
u = −0.851549
a = 0.318977 − 0.641567I
b = −0.822919 − 0.871364I
5.62987 −0.159510
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.310581 + 0.724102I
a = 0.74445 + 1.33030I
b = −0.287866 + 1.056100I
0.71904 − 5.93181I −2.27026 + 8.51733I
u = 0.310581 + 0.724102I
a = −2.48407 − 0.16612I
b = 0.687979 − 0.915445I
0.71904 − 5.93181I −2.27026 + 8.51733I
u = 0.310581 − 0.724102I
a = 0.74445 − 1.33030I
b = −0.287866 − 1.056100I
0.71904 + 5.93181I −2.27026 − 8.51733I
u = 0.310581 − 0.724102I
a = −2.48407 + 0.16612I
b = 0.687979 + 0.915445I
0.71904 + 5.93181I −2.27026 − 8.51733I
u = −0.142481 + 0.697709I
a = 0.596174 − 1.278220I
b = −0.350478 − 1.020240I
1.074320 + 0.665738I −0.12924 − 2.13889I
u = −0.142481 + 0.697709I
a = −1.30149 + 1.63106I
b = 0.674450 − 0.798832I
1.074320 + 0.665738I −0.12924 − 2.13889I
u = −0.142481 − 0.697709I
a = 0.596174 + 1.278220I
b = −0.350478 + 1.020240I
1.074320 − 0.665738I −0.12924 + 2.13889I
u = −0.142481 − 0.697709I
a = −1.30149 − 1.63106I
b = 0.674450 + 0.798832I
1.074320 − 0.665738I −0.12924 + 2.13889I
u = 0.06498 + 1.43187I
a = −0.914346 − 0.030523I
b = 0.538898 + 0.948585I
4.71222 + 1.83282I −1.19119 − 3.38662I
u = 0.06498 + 1.43187I
a = −1.185950 + 0.041711I
b = 0.103552 − 0.462526I
4.71222 + 1.83282I −1.19119 − 3.38662I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.06498 − 1.43187I
a = −0.914346 + 0.030523I
b = 0.538898 − 0.948585I
4.71222 − 1.83282I −1.19119 + 3.38662I
u = 0.06498 − 1.43187I
a = −1.185950 − 0.041711I
b = 0.103552 + 0.462526I
4.71222 − 1.83282I −1.19119 + 3.38662I
u = 0.412009 + 0.257420I
a = 0.363474 − 0.843475I
b = −0.582313 − 0.938382I
−0.68358 + 3.35221I −7.56970 − 0.50241I
u = 0.412009 + 0.257420I
a = 2.42625 + 1.01899I
b = 0.239705 + 0.775765I
−0.68358 + 3.35221I −7.56970 − 0.50241I
u = 0.412009 − 0.257420I
a = 0.363474 + 0.843475I
b = −0.582313 + 0.938382I
−0.68358 − 3.35221I −7.56970 + 0.50241I
u = 0.412009 − 0.257420I
a = 2.42625 − 1.01899I
b = 0.239705 − 0.775765I
−0.68358 − 3.35221I −7.56970 + 0.50241I
u = −0.383099 + 0.261626I
a = 0.585655 − 0.689766I
b = −0.517899 − 0.693977I
0.093901 + 1.148620I −3.53575 − 5.49340I
u = −0.383099 + 0.261626I
a = 1.57410 + 0.04794I
b = 0.258543 − 0.493766I
0.093901 + 1.148620I −3.53575 − 5.49340I
u = −0.383099 − 0.261626I
a = 0.585655 + 0.689766I
b = −0.517899 + 0.693977I
0.093901 − 1.148620I −3.53575 + 5.49340I
u = −0.383099 − 0.261626I
a = 1.57410 − 0.04794I
b = 0.258543 + 0.493766I
0.093901 − 1.148620I −3.53575 + 5.49340I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.08026 + 1.64365I
a = −0.748904 − 0.268338I
b = 0.290120 − 1.211260I
9.00822 − 7.36719I −0.13452 + 5.65922I
u = 0.08026 + 1.64365I
a = 2.05640 − 0.46486I
b = −0.792060 + 0.953651I
9.00822 − 7.36719I −0.13452 + 5.65922I
u = 0.08026 − 1.64365I
a = −0.748904 + 0.268338I
b = 0.290120 + 1.211260I
9.00822 + 7.36719I −0.13452 − 5.65922I
u = 0.08026 − 1.64365I
a = 2.05640 + 0.46486I
b = −0.792060 − 0.953651I
9.00822 + 7.36719I −0.13452 − 5.65922I
u = −0.03421 + 1.64579I
a = −0.745240 + 0.215693I
b = 0.349052 + 1.200860I
9.38747 + 1.29678I 0.796324 − 0.636248I
u = −0.03421 + 1.64579I
a = 1.59194 − 1.02205I
b = −0.830675 + 0.831897I
9.38747 + 1.29678I 0.796324 − 0.636248I
u = −0.03421 − 1.64579I
a = −0.745240 − 0.215693I
b = 0.349052 − 1.200860I
9.38747 − 1.29678I 0.796324 + 0.636248I
u = −0.03421 − 1.64579I
a = 1.59194 + 1.02205I
b = −0.830675 − 0.831897I
9.38747 − 1.29678I 0.796324 + 0.636248I
u = −0.02383 + 1.69128I
a = −1.015700 + 0.009140I
b = 0.935462 + 0.040302I
13.36410 + 3.17654I 4.50027 − 2.52968I
u = −0.02383 + 1.69128I
a = 1.68568 + 0.63299I
b = −0.856758 − 0.910373I
13.36410 + 3.17654I 4.50027 − 2.52968I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.02383 − 1.69128I
a = −1.015700 − 0.009140I
b = 0.935462 − 0.040302I
13.36410 − 3.17654I 4.50027 + 2.52968I
u = −0.02383 − 1.69128I
a = 1.68568 − 0.63299I
b = −0.856758 + 0.910373I
13.36410 − 3.17654I 4.50027 + 2.52968I
u = −0.16619 + 1.70559I
a = 1.009680 − 0.837259I
b = −0.963165 + 0.726960I
17.6949 + 7.8244I 3.46049 − 3.10546I
u = −0.16619 + 1.70559I
a = 1.77155 + 0.04416I
b = −0.830523 − 1.049140I
17.6949 + 7.8244I 3.46049 − 3.10546I
u = −0.16619 − 1.70559I
a = 1.009680 + 0.837259I
b = −0.963165 − 0.726960I
17.6949 − 7.8244I 3.46049 + 3.10546I
u = −0.16619 − 1.70559I
a = 1.77155 − 0.04416I
b = −0.830523 + 1.049140I
17.6949 − 7.8244I 3.46049 + 3.10546I
14
III. I
u
3
= h−au + b − u, 2a
2
+ au + 4a + u + 1, u
2
+ 2i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−2
a
6
=
a
au + u
a
2
=
−au + a −
1
2
u + 2
au + u − 1
a
7
=
a +
1
2
u + 1
au + u − 1
a
1
=
a +
1
2
u + 1
au + u − 1
a
11
=
a + 1
au + 2u
a
9
=
u
−u
a
5
=
−1
0
a
8
=
0
−u
a
12
=
a + 1
au + 2a + 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8au − 8u + 4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
10
(u
2
− u + 1)
2
c
3
, c
4
, c
8
c
9
(u
2
+ 2)
2
c
6
, c
11
, c
12
(u
2
+ u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
10
c
11
, c
12
(y
2
+ y + 1)
2
c
3
, c
4
, c
8
c
9
(y + 2)
4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = −0.387628 − 0.353553I
b = 0.500000 + 0.866025I
4.93480 + 4.05977I 0. − 6.92820I
u = 1.414210I
a = −1.61237 − 0.35355I
b = 0.500000 − 0.866025I
4.93480 − 4.05977I 0. + 6.92820I
u = − 1.414210I
a = −0.387628 + 0.353553I
b = 0.500000 − 0.866025I
4.93480 − 4.05977I 0. + 6.92820I
u = − 1.414210I
a = −1.61237 + 0.35355I
b = 0.500000 + 0.866025I
4.93480 + 4.05977I 0. − 6.92820I
18
IV. I
u
4
= hb
2
− b + 1, 2a − u + 2, u
2
+ 2i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−2
a
6
=
1
2
u − 1
b
a
2
=
1
2
bu − b + 1
b − 1
a
7
=
1
2
bu
b − 1
a
1
=
1
2
bu
b − 1
a
11
=
1
2
bu −
1
2
u
u − 1
a
9
=
u
−u
a
5
=
−1
0
a
8
=
0
−u
a
12
=
1
2
bu −
1
2
u
bu − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
10
(u
2
− u + 1)
2
c
3
, c
4
, c
8
c
9
(u
2
+ 2)
2
c
6
, c
11
, c
12
(u
2
+ u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
10
c
11
, c
12
(y
2
+ y + 1)
2
c
3
, c
4
, c
8
c
9
(y + 2)
4
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = −1.000000 + 0.707107I
b = 0.500000 + 0.866025I
4.93480 0
u = 1.414210I
a = −1.000000 + 0.707107I
b = 0.500000 − 0.866025I
4.93480 0
u = − 1.414210I
a = −1.000000 − 0.707107I
b = 0.500000 + 0.866025I
4.93480 0
u = − 1.414210I
a = −1.000000 − 0.707107I
b = 0.500000 − 0.866025I
4.93480 0
22
V. I
v
1
= ha, b
2
+ b + 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
−1
0
a
4
=
1
0
a
6
=
0
b
a
2
=
1
−b − 1
a
7
=
b
b + 1
a
1
=
−b
−b − 1
a
11
=
0
−b
a
9
=
−1
0
a
5
=
1
0
a
8
=
−1
0
a
12
=
−b
−b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8b + 4
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
, c
11
u
2
− u + 1
c
2
, c
7
, c
12
u
2
+ u + 1
c
3
, c
4
, c
8
c
9
u
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
10
c
11
, c
12
y
2
+ y + 1
c
3
, c
4
, c
8
c
9
y
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −0.500000 + 0.866025I
− 4.05977I 0. + 6.92820I
v = −1.00000
a = 0
b = −0.500000 − 0.866025I
4.05977I 0. − 6.92820I
26
VI. I
v
2
= ha, b − v + 1, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
v
0
a
4
=
1
0
a
6
=
0
v − 1
a
2
=
1
−v
a
7
=
v − 1
v
a
1
=
−v + 1
−v
a
11
=
0
−1
a
9
=
v
0
a
5
=
1
0
a
8
=
v
0
a
12
=
−v + 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
, c
11
u
2
− u + 1
c
2
, c
7
, c
12
u
2
+ u + 1
c
3
, c
4
, c
8
c
9
u
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
10
c
11
, c
12
y
2
+ y + 1
c
3
, c
4
, c
8
c
9
y
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −0.500000 + 0.866025I
0 −6.00000
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 − 0.866025I
0 −6.00000
30
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
10
((u
2
− u + 1)
6
)(u
18
+ 5u
17
+ ··· + 9u + 1)(u
46
+ 14u
45
+ ··· + 143u + 9)
c
2
, c
7
((u
2
− u + 1)
4
)(u
2
+ u + 1)
2
(u
18
− u
17
+ ··· − u + 1)
· (u
46
− 2u
45
+ ··· − u + 3)
c
3
, c
4
, c
8
c
9
u
4
(u
2
+ 2)
4
(u
18
− 5u
17
+ ··· − 16u + 4)(u
23
+ 2u
22
+ ··· + 4u + 2)
2
c
6
, c
11
((u
2
− u + 1)
2
)(u
2
+ u + 1)
4
(u
18
− u
17
+ ··· − u + 1)
· (u
46
− 2u
45
+ ··· − u + 3)
c
12
((u
2
+ u + 1)
6
)(u
18
+ 5u
17
+ ··· + 9u + 1)(u
46
+ 14u
45
+ ··· + 143u + 9)
31
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
10
c
12
((y
2
+ y + 1)
6
)(y
18
+ 21y
17
+ ··· + 25y + 1)
· (y
46
+ 38y
45
+ ··· − 1657y + 81)
c
2
, c
6
, c
7
c
11
((y
2
+ y + 1)
6
)(y
18
+ 5y
17
+ ··· + 9y + 1)(y
46
+ 14y
45
+ ··· + 143y + 9)
c
3
, c
4
, c
8
c
9
y
4
(y + 2)
8
(y
18
+ 21y
17
+ ··· + 64y + 16)
· (y
23
+ 30y
22
+ ··· − 16y − 4)
2
32
