12a
1210
(K12a
1210
)
A knot diagram
1
Linearized knot diagam
5 6 7 8 10 3 11 12 1 2 4 9
Solving Sequence
2,6
3 7
4,10
11 8 5 1 9 12
c
2
c
6
c
3
c
10
c
7
c
5
c
1
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h9u
11
+ 16u
10
− 55u
9
− 83u
8
+ 129u
7
+ 99u
6
− 194u
5
+ 31u
4
+ 169u
3
− 50u
2
+ 5b + 11u + 23,
− 49u
11
− 81u
10
+ ··· + 15a − 123,
u
12
+ 3u
11
− 4u
10
− 17u
9
+ 3u
8
+ 30u
7
− 7u
6
− 25u
5
+ 22u
4
+ 19u
3
− 6u
2
+ 3u + 3i
I
u
2
= h−5352912u
25
− 50199792u
24
+ ··· + 3763339b − 53120096,
208439509u
25
+ 1342309427u
24
+ ··· + 18816695a + 581471885, u
26
+ 8u
25
+ ··· + 15u + 5i
I
u
3
= hu
4
− 2u
2
+ b, −u
2
+ a + 1, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
I
u
4
= h−u
2
+ b + u + 1, u
4
− 2u
2
+ a + 1, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
I
u
5
= hu
4
− u
2
+ b − u − 1, u
4
− 2u
3
− u
2
+ a + 2u, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
I
u
6
= h8u
25
a − 29u
25
+ ··· + 24a + 58, 31u
25
a − 5u
25
+ ··· − 138a + 42, u
26
− 2u
25
+ ··· − 6u + 2i
I
u
7
= hb − u, u
2
+ a − 2u, u
3
− 2u
2
+ u − 1i
I
u
8
= h−2u
2
+ b − u + 7, 3u
2
+ 5a + 2u − 7, u
3
− u
2
− 4u + 5i
I
u
9
= hb
2
+ bu + u, a + u − 1, u
2
− u − 1i
I
u
10
= hb − 1, a
4
− 2a
3
− a
2
+ 2a − 1, u + 1i
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).
1
I
u
11
= h−au + b − 1, 2a
2
+ au − u − 1, u
2
− 2i
I
u
12
= hb + 1, a
2
+ a − 1, u + 1i
I
v
1
= ha, b + 1, v −1i
I
v
2
= ha, b + v −2, v
2
− 3v + 1i
* 14 irreducible components of dim
C
= 0, with total 128 representations.
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= h9u
11
+ 16u
10
+ · · · + 5b + 23, −49u
11
− 81u
10
+ · · · + 15a −
123, u
12
+ 3u
11
+ · · · + 3u + 3i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
10
=
49
15
u
11
+
27
5
u
10
+ ··· −
3
5
u +
41
5
−
9
5
u
11
−
16
5
u
10
+ ··· −
11
5
u −
23
5
a
11
=
76
15
u
11
+
43
5
u
10
+ ··· +
8
5
u +
64
5
−
9
5
u
11
−
16
5
u
10
+ ··· −
11
5
u −
23
5
a
8
=
47
15
u
11
+
26
5
u
10
+ ··· +
11
5
u +
33
5
−
8
5
u
11
−
12
5
u
10
+ ··· +
3
5
u −
16
5
a
5
=
−2.26667u
11
− 3.40000u
10
+ ··· − 1.40000u − 4.20000
9
5
u
11
+
16
5
u
10
+ ··· +
11
5
u +
23
5
a
1
=
43
15
u
11
+
24
5
u
10
+ ··· +
4
5
u +
37
5
8
5
u
11
+
12
5
u
10
+ ··· +
2
5
u +
16
5
a
9
=
−
8
15
u
11
−
4
5
u
10
+ ··· −
9
5
u −
2
5
−4.20000u
11
− 6.80000u
10
+ ··· − 3.80000u − 9.40000
a
12
=
31
15
u
11
+
18
5
u
10
+ ··· −
2
5
u +
29
5
−4.20000u
11
− 6.80000u
10
+ ··· − 2.80000u − 9.40000
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
54
5
u
11
−
86
5
u
10
+68u
9
+
438
5
u
8
−
814
5
u
7
−
474
5
u
6
+
1184
5
u
5
−
296
5
u
4
−
964
5
u
3
+72u
2
−
96
5
u−
108
5
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
12
− u
11
+ ··· + 3u − 1
c
2
, c
3
, c
6
c
8
, c
9
, c
12
u
12
− 3u
11
+ ··· − 3u + 3
c
5
, c
11
u
12
+ 6u
11
+ ··· − 6u − 4
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
12
− 5y
11
+ ··· − 17y + 1
c
2
, c
3
, c
6
c
8
, c
9
, c
12
y
12
− 17y
11
+ ··· − 45y + 9
c
5
, c
11
y
12
− 6y
11
+ ··· − 92y + 16
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.680890 + 0.727135I
a = 1.248510 − 0.220272I
b = 0.971458 − 0.885290I
0.23394 + 9.33805I 5.53743 − 10.26363I
u = 0.680890 − 0.727135I
a = 1.248510 + 0.220272I
b = 0.971458 + 0.885290I
0.23394 − 9.33805I 5.53743 + 10.26363I
u = −1.324330 + 0.041686I
a = −0.211663 − 1.090800I
b = 0.378676 + 0.744569I
7.08595 − 1.62424I 11.35275 + 4.35698I
u = −1.324330 − 0.041686I
a = −0.211663 + 1.090800I
b = 0.378676 − 0.744569I
7.08595 + 1.62424I 11.35275 − 4.35698I
u = 0.290084 + 0.470154I
a = −0.244022 − 1.158860I
b = −0.759615 − 0.242701I
−1.81796 − 0.64242I −1.71526 + 0.28169I
u = 0.290084 − 0.470154I
a = −0.244022 + 1.158860I
b = −0.759615 + 0.242701I
−1.81796 + 0.64242I −1.71526 − 0.28169I
u = 1.47793
a = 1.25559
b = 1.72722
9.20200 9.69630
u = −0.440388
a = 1.38391
b = 0.273625
0.916684 11.0470
u = −1.60946 + 0.28464I
a = −0.987579 + 0.304012I
b = −1.21535 − 1.29571I
15.3678 − 17.2207I 11.19497 + 7.94421I
u = −1.60946 − 0.28464I
a = −0.987579 − 0.304012I
b = −1.21535 + 1.29571I
15.3678 + 17.2207I 11.19497 − 7.94421I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.74636
a = −0.648286
b = −0.819063
16.8884 17.0050
u = −1.85826
a = 0.398303
b = 1.06787
15.1451 −2.48750
7
II.
I
u
2
= h−5.35 × 10
6
u
25
− 5.02 × 10
7
u
24
+ · · · + 3.76 × 10
6
b − 5.31 × 10
7
, 2.08 ×
10
8
u
25
+1.34×10
9
u
24
+· · ·+1.88×10
7
a+5.81×10
8
, u
26
+8u
25
+· · ·+15u+5i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
10
=
−11.0774u
25
− 71.3361u
24
+ ··· − 92.5092u − 30.9019
1.42238u
25
+ 13.3392u
24
+ ··· + 24.8637u + 14.1152
a
11
=
−12.4998u
25
− 84.6753u
24
+ ··· − 117.373u − 45.0171
1.42238u
25
+ 13.3392u
24
+ ··· + 24.8637u + 14.1152
a
8
=
−2.00003u
25
− 9.31115u
24
+ ··· − 10.2443u + 5.69486
8.26240u
25
+ 51.3885u
24
+ ··· + 55.6414u + 23.4455
a
5
=
−7.53188u
25
− 48.5688u
24
+ ··· − 76.4824u − 17.3150
8.02156u
25
+ 54.0428u
24
+ ··· + 65.7952u + 31.3118
a
1
=
0.393800u
25
− 0.399903u
24
+ ··· + 26.8406u − 14.1831
−0.235718u
25
+ 0.476383u
24
+ ··· + 11.1399u + 3.39516
a
9
=
−8.23887u
25
− 55.1220u
24
+ ··· − 38.3819u − 40.4693
2.26480u
25
+ 17.3975u
24
+ ··· + 31.5190u + 12.4612
a
12
=
10.2768u
25
+ 63.5874u
24
+ ··· + 56.8805u + 31.5716
−8.33941u
25
− 53.4256u
24
+ ··· − 60.9941u − 23.6603
(ii) Obstruction class = −1
(iii) Cusp Shapes =
57166208
3763339
u
25
+
329816967
3763339
u
24
+ ··· +
279336200
3763339
u +
103669271
3763339
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
26
− 3u
25
+ ··· + 10u − 1
c
2
, c
3
, c
6
c
8
, c
9
, c
12
u
26
− 8u
25
+ ··· − 15u + 5
c
5
, c
11
(u
13
− 3u
12
+ ··· − 4u
2
+ 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
26
− 9y
25
+ ··· − 58y + 1
c
2
, c
3
, c
6
c
8
, c
9
, c
12
y
26
− 28y
25
+ ··· − 435y + 25
c
5
, c
11
(y
13
− 7y
12
+ ··· + 8y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.343289 + 0.874120I
a = 0.330309 + 0.915080I
b = 0.567628 + 0.481289I
−0.79020 − 4.12060I 3.35923 + 9.55417I
u = 0.343289 − 0.874120I
a = 0.330309 − 0.915080I
b = 0.567628 − 0.481289I
−0.79020 + 4.12060I 3.35923 − 9.55417I
u = 0.911007 + 0.034245I
a = 0.598014 − 0.185260I
b = 1.36067 − 0.53532I
5.38135 − 0.78993I 18.1611 + 8.2316I
u = 0.911007 − 0.034245I
a = 0.598014 + 0.185260I
b = 1.36067 + 0.53532I
5.38135 + 0.78993I 18.1611 − 8.2316I
u = −1.09289
a = −1.11726
b = 0.126239
6.54220 13.9260
u = 0.708346 + 0.858953I
a = −1.260640 + 0.418277I
b = −0.926363 + 0.940596I
7.7698 + 12.9581I 8.72824 − 8.95256I
u = 0.708346 − 0.858953I
a = −1.260640 − 0.418277I
b = −0.926363 − 0.940596I
7.7698 − 12.9581I 8.72824 + 8.95256I
u = 0.654603 + 0.506111I
a = −1.102020 − 0.068931I
b = −1.023120 + 0.862320I
−0.79020 + 4.12060I 3.35923 − 9.55417I
u = 0.654603 − 0.506111I
a = −1.102020 + 0.068931I
b = −1.023120 − 0.862320I
−0.79020 − 4.12060I 3.35923 + 9.55417I
u = 0.458169 + 1.136120I
a = −0.218594 − 0.876180I
b = −0.429207 − 0.618806I
6.87671 − 6.64700I 8.83563 + 10.57231I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.458169 − 1.136120I
a = −0.218594 + 0.876180I
b = −0.429207 + 0.618806I
6.87671 + 6.64700I 8.83563 − 10.57231I
u = −1.342220 + 0.045442I
a = 0.344656 − 0.623993I
b = −0.119008 + 0.591119I
2.78910 + 0.30737I 2.33273 − 1.31692I
u = −1.342220 − 0.045442I
a = 0.344656 + 0.623993I
b = −0.119008 − 0.591119I
2.78910 − 0.30737I 2.33273 + 1.31692I
u = 1.39644
a = 0.874395
b = 1.24703
6.54220 13.9260
u = 1.42342
a = −1.12461
b = −1.58372
3.37362 1.93880
u = −1.57195 + 0.27829I
a = −0.356146 + 0.031287I
b = −0.240475 − 0.531059I
5.38135 − 0.78993I 18.1611 + 8.2316I
u = −1.57195 − 0.27829I
a = −0.356146 − 0.031287I
b = −0.240475 + 0.531059I
5.38135 + 0.78993I 18.1611 − 8.2316I
u = −1.60202 + 0.16401I
a = −0.594151 + 0.344778I
b = −1.24453 − 1.41124I
6.87671 − 6.64700I 8.83563 + 10.57231I
u = −1.60202 − 0.16401I
a = −0.594151 − 0.344778I
b = −1.24453 + 1.41124I
6.87671 + 6.64700I 8.83563 − 10.57231I
u = −1.59466 + 0.23960I
a = 0.840412 − 0.366964I
b = 1.19152 + 1.30819I
7.7698 − 12.9581I 8.72824 + 8.95256I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.59466 − 0.23960I
a = 0.840412 + 0.366964I
b = 1.19152 − 1.30819I
7.7698 + 12.9581I 8.72824 − 8.95256I
u = 0.077131 + 0.343141I
a = 2.09606 + 1.73666I
b = 0.889556 − 0.403672I
2.78910 + 0.30737I 2.33273 − 1.31692I
u = 0.077131 − 0.343141I
a = 2.09606 − 1.73666I
b = 0.889556 + 0.403672I
2.78910 − 0.30737I 2.33273 + 1.31692I
u = −0.196019
a = 8.16649
b = 1.11179
3.37362 1.93880
u = −1.80717 + 0.12130I
a = 0.422586 + 0.028364I
b = 1.022660 + 0.520856I
15.1180 0
u = −1.80717 − 0.12130I
a = 0.422586 − 0.028364I
b = 1.022660 − 0.520856I
15.1180 0
13
III. I
u
3
= hu
4
− 2u
2
+ b, −u
2
+ a + 1, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
10
=
u
2
− 1
−u
4
+ 2u
2
a
11
=
u
4
− u
2
− 1
−u
4
+ 2u
2
a
8
=
−1
0
a
5
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
1
=
−u
u
3
− u
a
9
=
−1
u
2
a
12
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
3
+ 16u + 12
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
2
, c
3
, c
8
c
9
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
5
, c
11
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
6
, c
12
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
2
, c
3
, c
6
c
8
, c
9
, c
12
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
5
, c
11
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = 0.482881
b = 0.766826
4.80216 6.96230
u = −0.309916 + 0.549911I
a = −1.206350 − 0.340852I
b = −0.339110 − 0.822375I
0.65820 − 3.06116I 5.03023 + 8.86130I
u = −0.309916 − 0.549911I
a = −1.206350 + 0.340852I
b = −0.339110 + 0.822375I
0.65820 + 3.06116I 5.03023 − 8.86130I
u = 1.41878 + 0.21917I
a = 0.964913 + 0.621896I
b = 0.455697 − 1.200150I
11.7451 + 8.8017I 13.4886 − 6.9972I
u = 1.41878 − 0.21917I
a = 0.964913 − 0.621896I
b = 0.455697 + 1.200150I
11.7451 − 8.8017I 13.4886 + 6.9972I
17
IV. I
u
4
= h−u
2
+ b + u + 1, u
4
− 2u
2
+ a + 1, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
10
=
−u
4
+ 2u
2
− 1
u
2
− u − 1
a
11
=
−u
4
+ u
2
+ u
u
2
− u − 1
a
8
=
−u
3
+ u
−1
a
5
=
−u
4
+ u
2
+ u + 2
−u
2
+ u + 1
a
1
=
u
3
+ u
2
− 2u − 1
−u
4
+ 2u
3
+ u
2
− 2u − 1
a
9
=
u
3
− u − 1
u
4
− u
3
− u
a
12
=
−u
4
+ u
3
+ 2u
2
− u − 1
−u
4
+ 3u
2
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
3
+ 16u + 6
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
5
+ u
4
− u
3
− 4u
2
− 3u − 1
c
2
, c
3
, c
6
c
8
, c
9
, c
12
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
4
, c
7
u
5
− 2u
4
+ 3u
3
+ u
2
− 3u + 1
c
5
u
5
+ u
4
+ 3u
3
+ 6u
2
+ 5u + 1
c
11
u
5
+ 6u
4
+ 15u
3
+ 21u
2
+ 17u + 7
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
5
− 3y
4
+ 3y
3
− 8y
2
+ y −1
c
2
, c
3
, c
6
c
8
, c
9
, c
12
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
4
, c
7
y
5
+ 2y
4
+ 7y
3
− 15y
2
+ 7y −1
c
5
y
5
+ 5y
4
+ 7y
3
− 8y
2
+ 13y −1
c
11
y
5
− 6y
4
+ 7y
3
− 15y
2
− 5y −49
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = −0.233174
b = 1.70062
3.15723 0.962290
u = −0.309916 + 0.549911I
a = −1.33911 − 0.82238I
b = −0.896438 − 0.890762I
−0.98673 − 3.06116I −0.96977 + 8.86130I
u = −0.309916 − 0.549911I
a = −1.33911 + 0.82238I
b = −0.896438 + 0.890762I
−0.98673 + 3.06116I −0.96977 − 8.86130I
u = 1.41878 + 0.21917I
a = −0.544303 − 1.200150I
b = −0.453870 + 0.402731I
10.10020 + 8.80167I 7.48863 − 6.99717I
u = 1.41878 − 0.21917I
a = −0.544303 + 1.200150I
b = −0.453870 − 0.402731I
10.10020 − 8.80167I 7.48863 + 6.99717I
21
V.
I
u
5
= hu
4
− u
2
+ b − u − 1, u
4
− 2u
3
− u
2
+ a + 2u, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
10
=
−u
4
+ 2u
3
+ u
2
− 2u
−u
4
+ u
2
+ u + 1
a
11
=
2u
3
− 3u − 1
−u
4
+ u
2
+ u + 1
a
8
=
−u
3
+ 3u − 1
−1
a
5
=
−2u
3
+ 2u
2
+ u − 1
u
4
− u
2
− u − 1
a
1
=
u
3
− u
2
− u − 1
u
4
+ u
3
− u
2
− u − 1
a
9
=
u
3
− 3u
u
4
+ u
3
− u
2
− u
a
12
=
−u
4
+ u
3
+ 2u
2
− u − 1
−u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
3
+ 16u + 6
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
5
− 2u
4
+ 3u
3
+ u
2
− 3u + 1
c
2
, c
3
, c
6
c
8
, c
9
, c
12
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
4
, c
7
u
5
+ u
4
− u
3
− 4u
2
− 3u − 1
c
5
u
5
+ 6u
4
+ 15u
3
+ 21u
2
+ 17u + 7
c
11
u
5
+ u
4
+ 3u
3
+ 6u
2
+ 5u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
5
+ 2y
4
+ 7y
3
− 15y
2
+ 7y −1
c
2
, c
3
, c
6
c
8
, c
9
, c
12
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
4
, c
7
y
5
− 3y
4
+ 3y
3
− 8y
2
+ y −1
c
5
y
5
− 6y
4
+ 7y
3
− 15y
2
− 5y −49
c
11
y
5
+ 5y
4
+ 7y
3
− 8y
2
+ 13y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = −1.89210
b = −0.933791
3.15723 0.962290
u = −0.309916 + 0.549911I
a = 0.98986 − 1.59703I
b = 0.557328 + 0.068387I
−0.98673 − 3.06116I −0.96977 + 8.86130I
u = −0.309916 − 0.549911I
a = 0.98986 + 1.59703I
b = 0.557328 − 0.068387I
−0.98673 + 3.06116I −0.96977 − 8.86130I
u = 1.41878 + 0.21917I
a = 0.956194 + 0.365575I
b = 0.90957 − 1.60288I
10.10020 + 8.80167I 7.48863 − 6.99717I
u = 1.41878 − 0.21917I
a = 0.956194 − 0.365575I
b = 0.90957 + 1.60288I
10.10020 − 8.80167I 7.48863 + 6.99717I
25
VI. I
u
6
= h8u
25
a − 29u
25
+ · · · + 24a + 58, 31u
25
a − 5u
25
+ · · · − 138a +
42, u
26
− 2u
25
+ · · · − 6u + 2i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
10
=
a
−2u
25
a +
29
4
u
25
+ ··· − 6a −
29
2
a
11
=
2u
25
a −
29
4
u
25
+ ··· + 7a +
29
2
−2u
25
a +
29
4
u
25
+ ··· − 6a −
29
2
a
8
=
29
4
u
25
a −
11
2
u
25
+ ··· −
29
2
a − 15
−1
a
5
=
19
4
u
25
a −
3
4
u
25
+ ··· −
31
2
a +
5
2
−
13
4
u
25
a + 3u
25
+ ··· +
3
2
a + 11
a
1
=
4u
25
a −
11
2
u
25
+ ··· + 10a − 15
−
9
4
u
25
a +
9
4
u
25
+ ··· −
1
2
a +
9
2
a
9
=
−
1
2
u
25
a +
13
4
u
25
+ ··· − 6a +
19
2
−
3
4
u
25
a +
3
2
u
25
+ ··· −
9
2
a + 5
a
12
=
2u
25
a −
25
4
u
25
+ ··· + 7a +
11
2
−2u
25
a +
13
2
u
25
+ ··· − 6a − 10
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
63
4
u
25
+
89
4
u
24
+ ··· − 44u +
169
2
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
52
+ 11u
50
+ ··· + 733u + 337
c
2
, c
3
, c
6
c
8
, c
9
, c
12
(u
26
+ 2u
25
+ ··· + 6u + 2)
2
c
5
, c
11
(u
26
− u
25
+ ··· + 35u + 49)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
52
+ 22y
51
+ ··· + 1455729y + 113569
c
2
, c
3
, c
6
c
8
, c
9
, c
12
(y
26
− 28y
25
+ ··· − 100y + 4)
2
c
5
, c
11
(y
26
− 15y
25
+ ··· − 35721y + 2401)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.553208 + 0.775217I
a = 1.088170 + 0.312005I
b = 0.524604 + 0.662614I
1.77293 − 2.59129I 14.3131 + 5.4801I
u = −0.553208 + 0.775217I
a = −0.417434 − 0.520810I
b = −0.211040 − 0.742494I
1.77293 − 2.59129I 14.3131 + 5.4801I
u = −0.553208 − 0.775217I
a = 1.088170 − 0.312005I
b = 0.524604 − 0.662614I
1.77293 + 2.59129I 14.3131 − 5.4801I
u = −0.553208 − 0.775217I
a = −0.417434 + 0.520810I
b = −0.211040 + 0.742494I
1.77293 + 2.59129I 14.3131 − 5.4801I
u = −0.603297 + 0.868786I
a = 0.128987 + 0.870481I
b = −0.008992 + 0.944934I
8.28659 − 2.89485I 12.44020 + 3.54073I
u = −0.603297 + 0.868786I
a = −1.337050 − 0.449840I
b = −0.616963 − 0.787628I
8.28659 − 2.89485I 12.44020 + 3.54073I
u = −0.603297 − 0.868786I
a = 0.128987 − 0.870481I
b = −0.008992 − 0.944934I
8.28659 + 2.89485I 12.44020 − 3.54073I
u = −0.603297 − 0.868786I
a = −1.337050 + 0.449840I
b = −0.616963 + 0.787628I
8.28659 + 2.89485I 12.44020 − 3.54073I
u = −0.943425 + 0.499174I
a = −0.694495 − 0.686286I
b = 0.366066 − 0.740622I
6.88770 + 1.05584I 11.25609 − 1.96387I
u = −0.943425 + 0.499174I
a = −1.217920 + 0.300873I
b = −0.872153 + 0.173136I
6.88770 + 1.05584I 11.25609 − 1.96387I
29
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.943425 − 0.499174I
a = −0.694495 + 0.686286I
b = 0.366066 + 0.740622I
6.88770 − 1.05584I 11.25609 + 1.96387I
u = −0.943425 − 0.499174I
a = −1.217920 − 0.300873I
b = −0.872153 − 0.173136I
6.88770 − 1.05584I 11.25609 + 1.96387I
u = −0.245040 + 0.733784I
a = 1.15177 + 1.09789I
b = 0.733903 + 1.126320I
4.78648 − 5.46357I 4.53204 + 6.67901I
u = −0.245040 + 0.733784I
a = −1.77194 + 0.87563I
b = −0.773003 − 0.171756I
4.78648 − 5.46357I 4.53204 + 6.67901I
u = −0.245040 − 0.733784I
a = 1.15177 − 1.09789I
b = 0.733903 − 1.126320I
4.78648 + 5.46357I 4.53204 − 6.67901I
u = −0.245040 − 0.733784I
a = −1.77194 − 0.87563I
b = −0.773003 + 0.171756I
4.78648 + 5.46357I 4.53204 − 6.67901I
u = −0.692554
a = 1.32857
b = −0.584521
0.329189 14.3490
u = −0.692554
a = 1.57517
b = 1.09426
0.329189 14.3490
u = −0.547551
a = 1.68040
b = 1.23037
0.329189 14.3490
u = −0.547551
a = 1.99230
b = −0.501158
0.329189 14.3490
30
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45899 + 0.14778I
a = −0.037244 + 1.042010I
b = 0.145904 − 0.472929I
4.78648 + 5.46357I 4.53204 − 6.67901I
u = 1.45899 + 0.14778I
a = −0.777632 − 0.316112I
b = −1.20223 + 1.53623I
4.78648 + 5.46357I 4.53204 − 6.67901I
u = 1.45899 − 0.14778I
a = −0.037244 − 1.042010I
b = 0.145904 + 0.472929I
4.78648 − 5.46357I 4.53204 + 6.67901I
u = 1.45899 − 0.14778I
a = −0.777632 + 0.316112I
b = −1.20223 − 1.53623I
4.78648 − 5.46357I 4.53204 + 6.67901I
u = 0.491328 + 0.130745I
a = −1.98866 − 0.35148I
b = −0.565063 − 1.196090I
8.64852 + 6.39232I 13.2062 − 6.3296I
u = 0.491328 + 0.130745I
a = 2.96644 + 0.81564I
b = 0.477569 − 0.943122I
8.64852 + 6.39232I 13.2062 − 6.3296I
u = 0.491328 − 0.130745I
a = −1.98866 + 0.35148I
b = −0.565063 + 1.196090I
8.64852 − 6.39232I 13.2062 + 6.3296I
u = 0.491328 − 0.130745I
a = 2.96644 − 0.81564I
b = 0.477569 + 0.943122I
8.64852 − 6.39232I 13.2062 + 6.3296I
u = 1.50128 + 0.07571I
a = 0.633748 − 0.625993I
b = 0.226697 + 0.451550I
6.88770 + 1.05584I 11.25609 − 1.96387I
u = 1.50128 + 0.07571I
a = 0.673013 + 0.166410I
b = 1.53145 − 1.12805I
6.88770 + 1.05584I 11.25609 − 1.96387I
31
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50128 − 0.07571I
a = 0.633748 + 0.625993I
b = 0.226697 − 0.451550I
6.88770 − 1.05584I 11.25609 + 1.96387I
u = 1.50128 − 0.07571I
a = 0.673013 − 0.166410I
b = 1.53145 + 1.12805I
6.88770 − 1.05584I 11.25609 + 1.96387I
u = −1.50898 + 0.02041I
a = −0.801385 + 0.579109I
b = −0.83666 − 1.26270I
8.28659 − 2.89485I 12.44020 + 3.54073I
u = −1.50898 + 0.02041I
a = 0.548938 + 0.281185I
b = 1.00115 − 1.65322I
8.28659 − 2.89485I 12.44020 + 3.54073I
u = −1.50898 − 0.02041I
a = −0.801385 − 0.579109I
b = −0.83666 + 1.26270I
8.28659 + 2.89485I 12.44020 − 3.54073I
u = −1.50898 − 0.02041I
a = 0.548938 − 0.281185I
b = 1.00115 + 1.65322I
8.28659 + 2.89485I 12.44020 − 3.54073I
u = −1.53064 + 0.05712I
a = 1.125240 − 0.491051I
b = 1.04497 + 1.04117I
15.5113 − 7.1776I 13.07799 + 4.48831I
u = −1.53064 + 0.05712I
a = −0.603671 − 0.025101I
b = −1.29543 + 1.62004I
15.5113 − 7.1776I 13.07799 + 4.48831I
u = −1.53064 − 0.05712I
a = 1.125240 + 0.491051I
b = 1.04497 − 1.04117I
15.5113 + 7.1776I 13.07799 − 4.48831I
u = −1.53064 − 0.05712I
a = −0.603671 + 0.025101I
b = −1.29543 − 1.62004I
15.5113 + 7.1776I 13.07799 − 4.48831I
32
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54568 + 0.26203I
a = 0.933615 + 0.351925I
b = 0.897541 − 1.028160I
8.64852 + 6.39232I 13.2062 − 6.3296I
u = 1.54568 + 0.26203I
a = −0.631712 − 0.172853I
b = −0.482731 + 1.227480I
8.64852 + 6.39232I 13.2062 − 6.3296I
u = 1.54568 − 0.26203I
a = 0.933615 − 0.351925I
b = 0.897541 + 1.028160I
8.64852 − 6.39232I 13.2062 + 6.3296I
u = 1.54568 − 0.26203I
a = −0.631712 + 0.172853I
b = −0.482731 − 1.227480I
8.64852 − 6.39232I 13.2062 + 6.3296I
u = 0.416447 + 0.057781I
a = 1.50682 − 0.12386I
b = 0.392920 + 1.238970I
1.77293 + 2.59129I 14.3131 − 5.4801I
u = 0.416447 + 0.057781I
a = −2.20737 − 1.30490I
b = −0.334074 + 0.982377I
1.77293 + 2.59129I 14.3131 − 5.4801I
u = 0.416447 − 0.057781I
a = 1.50682 + 0.12386I
b = 0.392920 − 1.238970I
1.77293 − 2.59129I 14.3131 + 5.4801I
u = 0.416447 − 0.057781I
a = −2.20737 + 1.30490I
b = −0.334074 − 0.982377I
1.77293 − 2.59129I 14.3131 + 5.4801I
u = 1.59092 + 0.28889I
a = −1.121140 − 0.309256I
b = −1.08933 + 0.96858I
15.5113 + 7.1776I 13.07799 − 4.48831I
u = 1.59092 + 0.28889I
a = 0.562694 − 0.104657I
b = 0.32542 − 1.43702I
15.5113 + 7.1776I 13.07799 − 4.48831I
33
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59092 − 0.28889I
a = −1.121140 + 0.309256I
b = −1.08933 − 0.96858I
15.5113 − 7.1776I 13.07799 + 4.48831I
u = 1.59092 − 0.28889I
a = 0.562694 + 0.104657I
b = 0.32542 + 1.43702I
15.5113 − 7.1776I 13.07799 + 4.48831I
34
VII. I
u
7
= hb − u, u
2
+ a − 2u, u
3
− 2u
2
+ u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
−2u
2
+ 2u − 1
a
4
=
−u
2
+ 1
u
2
− u + 2
a
10
=
−u
2
+ 2u
u
a
11
=
−u
2
+ u
u
a
8
=
u
2
+ 1
−3u
2
+ 2u − 1
a
5
=
−u
2
+ u + 1
−u
2
+ 2u
a
1
=
2u
2
− 4u + 2
u
2
− 3u + 2
a
9
=
u
2
− 4u + 2
2u
2
− 4u + 3
a
12
=
−2u
2
+ 3u − 2
3u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
2
+ 3u + 12
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
3
− 2u
2
+ 3u − 1
c
2
, c
3
u
3
− 2u
2
+ u − 1
c
5
, c
11
u
3
− u
2
+ 1
c
6
, c
7
, c
10
u
3
+ 2u
2
+ u + 1
c
8
, c
9
u
3
− u
2
− 4u + 5
c
12
u
3
+ u
2
− 4u − 5
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
3
+ 2y
2
+ 5y −1
c
2
, c
3
, c
6
c
7
, c
10
y
3
− 2y
2
− 3y −1
c
5
, c
11
y
3
− y
2
+ 2y −1
c
8
, c
9
, c
12
y
3
− 9y
2
+ 26y −25
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.122561 + 0.744862I
a = 0.78492 + 1.30714I
b = 0.122561 + 0.744862I
7.11122 − 5.65624I 9.12890 + 3.33008I
u = 0.122561 − 0.744862I
a = 0.78492 − 1.30714I
b = 0.122561 − 0.744862I
7.11122 + 5.65624I 9.12890 − 3.33008I
u = 1.75488
a = 0.430160
b = 1.75488
15.3864 35.7420
38
VIII. I
u
8
= h−2u
2
+ b − u + 7, 3u
2
+ 5a + 2u − 7, u
3
− u
2
− 4u + 5i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
−u
2
− 3u + 5
a
4
=
−u
2
+ 1
3u
2
− u − 5
a
10
=
−
3
5
u
2
−
2
5
u +
7
5
2u
2
+ u − 7
a
11
=
−
13
5
u
2
−
7
5
u +
42
5
2u
2
+ u − 7
a
8
=
−
11
5
u
2
−
4
5
u +
29
5
2u
2
− u − 4
a
5
=
−
6
5
u
2
−
4
5
u +
19
5
u
2
+ u − 4
a
1
=
1
5
u
2
−
1
5
u +
1
5
u − 1
a
9
=
−
4
5
u
2
−
6
5
u +
16
5
u
2
+ 2u − 6
a
12
=
−
3
5
u
2
+
3
5
u +
7
5
−2u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
2
− 9u + 30
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
3
+ 2u
2
+ u + 1
c
2
, c
3
u
3
− u
2
− 4u + 5
c
5
, c
11
u
3
− u
2
+ 1
c
6
u
3
+ u
2
− 4u − 5
c
7
, c
10
u
3
− 2u
2
+ 3u − 1
c
8
, c
9
u
3
− 2u
2
+ u − 1
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
c
9
, c
12
y
3
− 2y
2
− 3y −1
c
2
, c
3
, c
6
y
3
− 9y
2
+ 26y −25
c
5
, c
11
y
3
− y
2
+ 2y −1
c
7
, c
10
y
3
+ 2y
2
+ 5y −1
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53980 + 0.18258I
a = −0.618504 − 0.410401I
b = −0.78492 + 1.30714I
7.11122 + 5.65624I 9.12890 − 3.33008I
u = 1.53980 − 0.18258I
a = −0.618504 + 0.410401I
b = −0.78492 − 1.30714I
7.11122 − 5.65624I 9.12890 + 3.33008I
u = −2.07960
a = −0.362993
b = −0.430160
15.3864 35.7420
42
IX. I
u
9
= hb
2
+ bu + u, a + u − 1, u
2
− u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u − 1
a
7
=
u
−u − 1
a
4
=
−u
u
a
10
=
−u + 1
b
a
11
=
−b − u + 1
b
a
8
=
bu − b + 1
−1
a
5
=
−u + 1
b + u
a
1
=
bu − b + 2
−bu − 1
a
9
=
b + u + 1
−bu − u
a
12
=
−b − 2u + 1
b + u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 14
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
4
+ u
3
− 2u − 1
c
2
, c
3
, c
6
c
8
, c
9
, c
12
(u
2
+ u − 1)
2
c
5
, c
11
(u − 1)
4
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
4
− y
3
+ 2y
2
− 4y + 1
c
2
, c
3
, c
6
c
8
, c
9
, c
12
(y
2
− 3y + 1)
2
c
5
, c
11
(y −1)
4
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 1.61803
b = 1.15372
0.328987 14.0000
u = −0.618034
a = 1.61803
b = −0.535687
0.328987 14.0000
u = 1.61803
a = −0.618034
b = −0.809017 + 0.981593I
16.1204 14.0000
u = 1.61803
a = −0.618034
b = −0.809017 − 0.981593I
16.1204 14.0000
46
X. I
u
10
= hb − 1, a
4
− 2a
3
− a
2
+ 2a − 1, u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
−1
a
3
=
1
−1
a
7
=
−1
0
a
4
=
0
−1
a
10
=
a
1
a
11
=
a − 1
1
a
8
=
−a
−1
a
5
=
a
2
a − 1
a
1
=
−a
3
+ a
2
+ 1
−a
2
+ 2a − 1
a
9
=
−a
3
+ 2a
2
− a − 1
a
3
− 3a
2
+ a + 1
a
12
=
a − 1
−a + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8
47
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
4
+ 2u
3
− u
2
− 2u − 1
c
2
, c
3
, c
7
c
10
(u + 1)
4
c
5
, c
11
u
4
− 2u
3
− u
2
+ 2u − 1
c
6
(u − 1)
4
c
8
, c
9
, c
12
(u
2
− 2)
2
48
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
11
y
4
− 6y
3
+ 7y
2
− 2y + 1
c
2
, c
3
, c
6
c
7
, c
10
(y −1)
4
c
8
, c
9
, c
12
(y −2)
4
49
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.13224
b = 1.00000
4.93480 8.00000
u = −1.00000
a = 0.500000 + 0.405233I
b = 1.00000
4.93480 8.00000
u = −1.00000
a = 0.500000 − 0.405233I
b = 1.00000
4.93480 8.00000
u = −1.00000
a = 2.13224
b = 1.00000
4.93480 8.00000
50
XI. I
u
11
= h−au + b − 1, 2a
2
+ au − u − 1, u
2
− 2i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−2
a
7
=
u
−u
a
4
=
−1
0
a
10
=
a
au + 1
a
11
=
−au + a − 1
au + 1
a
8
=
−a +
1
2
u
1
a
5
=
a −
1
2
u − 1
−1
a
1
=
a −
1
2
u
−1
a
9
=
1
2
u
au + 2
a
12
=
a
au + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8
51
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
8
c
9
(u + 1)
4
c
2
, c
3
, c
6
(u
2
− 2)
2
c
5
, c
11
u
4
− 2u
3
− u
2
+ 2u − 1
c
7
, c
10
u
4
+ 2u
3
− u
2
− 2u − 1
c
12
(u − 1)
4
52
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
c
9
, c
12
(y −1)
4
c
2
, c
3
, c
6
(y −2)
4
c
5
, c
7
, c
10
c
11
y
4
− 6y
3
+ 7y
2
− 2y + 1
53
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = 0.800616
b = 2.13224
4.93480 8.00000
u = 1.41421
a = −1.50772
b = −1.13224
4.93480 8.00000
u = −1.41421
a = 0.353553 + 0.286543I
b = 0.500000 − 0.405233I
4.93480 8.00000
u = −1.41421
a = 0.353553 − 0.286543I
b = 0.500000 + 0.405233I
4.93480 8.00000
54
XII. I
u
12
= hb + 1, a
2
+ a − 1, u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
−1
a
3
=
1
−1
a
7
=
−1
0
a
4
=
0
−1
a
10
=
a
−1
a
11
=
a + 1
−1
a
8
=
a
−1
a
5
=
−a + 1
−a − 1
a
1
=
a + 1
−a − 2
a
9
=
a
−1
a
12
=
a + 1
−a − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −10
55
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
11
u
2
+ u − 1
c
2
, c
3
(u + 1)
2
c
6
, c
7
, c
10
(u − 1)
2
c
8
, c
9
, c
12
u
2
56
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
11
y
2
− 3y + 1
c
2
, c
3
, c
6
c
7
, c
10
(y −1)
2
c
8
, c
9
, c
12
y
2
57
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.618034
b = −1.00000
0 −10.0000
u = −1.00000
a = −1.61803
b = −1.00000
0 −10.0000
58
XIII. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
1
0
a
3
=
1
0
a
7
=
1
0
a
4
=
1
0
a
10
=
0
−1
a
11
=
1
−1
a
8
=
0
1
a
5
=
1
1
a
1
=
0
−1
a
9
=
0
−1
a
12
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
59
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
7
, c
10
, c
11
u + 1
c
2
, c
3
, c
6
c
8
, c
9
, c
12
u
60
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
7
, c
10
, c
11
y −1
c
2
, c
3
, c
6
c
8
, c
9
, c
12
y
61
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
−1.64493 −6.00000
62
XIV. I
v
2
= ha, b + v − 2, v
2
− 3v + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
v
0
a
3
=
1
0
a
7
=
v
0
a
4
=
1
0
a
10
=
0
−v + 2
a
11
=
v − 2
−v + 2
a
8
=
v − 1
1
a
5
=
v
1
a
1
=
−v + 1
−1
a
9
=
v − 1
−v + 3
a
12
=
0
−v + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −10
63
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
(u − 1)
2
c
2
, c
3
, c
6
u
2
c
5
, c
7
, c
10
c
11
u
2
+ u − 1
c
8
, c
9
(u + 1)
2
64
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
c
9
, c
12
(y − 1)
2
c
2
, c
3
, c
6
y
2
c
5
, c
7
, c
10
c
11
y
2
− 3y + 1
65
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.381966
a = 0
b = 1.61803
0 −10.0000
v = 2.61803
a = 0
b = −0.618034
0 −10.0000
66
XV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
((u − 1)
2
)(u + 1)
5
(u
2
+ u − 1)(u
3
− 2u
2
+ 3u − 1)(u
3
+ 2u
2
+ u + 1)
· (u
4
+ u
3
− 2u − 1)(u
4
+ 2u
3
− u
2
− 2u − 1)(u
5
− 2u
4
+ ··· − 3u + 1)
· (u
5
+ u
4
− u
3
− 4u
2
− 3u − 1)(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
· (u
12
− u
11
+ ··· + 3u − 1)(u
26
− 3u
25
+ ··· + 10u − 1)
· (u
52
+ 11u
50
+ ··· + 733u + 337)
c
2
, c
3
, c
8
c
9
u
3
(u + 1)
6
(u
2
− 2)
2
(u
2
+ u − 1)
2
(u
3
− 2u
2
+ u − 1)(u
3
− u
2
− 4u + 5)
· (u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
· (u
12
− 3u
11
+ ··· − 3u + 3)(u
26
− 8u
25
+ ··· − 15u + 5)
· (u
26
+ 2u
25
+ ··· + 6u + 2)
2
c
5
, c
11
((u − 1)
4
)(u + 1)(u
2
+ u − 1)
2
(u
3
− u
2
+ 1)
2
(u
4
− 2u
3
+ ··· + 2u − 1)
2
· (u
5
+ u
4
+ 3u
3
+ 6u
2
+ 5u + 1)(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
· (u
5
+ 6u
4
+ 15u
3
+ 21u
2
+ 17u + 7)(u
12
+ 6u
11
+ ··· − 6u − 4)
· ((u
13
− 3u
12
+ ··· − 4u
2
+ 1)
2
)(u
26
− u
25
+ ··· + 35u + 49)
2
c
6
, c
12
u
3
(u − 1)
6
(u
2
− 2)
2
(u
2
+ u − 1)
2
(u
3
+ u
2
− 4u − 5)(u
3
+ 2u
2
+ u + 1)
· ((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
3
)(u
12
− 3u
11
+ ··· − 3u + 3)
· (u
26
− 8u
25
+ ··· − 15u + 5)(u
26
+ 2u
25
+ ··· + 6u + 2)
2
67
XVI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(y − 1)
7
(y
2
− 3y + 1)(y
3
− 2y
2
− 3y − 1)(y
3
+ 2y
2
+ 5y − 1)
· (y
4
− 6y
3
+ 7y
2
− 2y + 1)(y
4
− y
3
+ 2y
2
− 4y + 1)
· (y
5
− 3y
4
+ 3y
3
− 8y
2
+ y − 1)(y
5
+ 2y
4
+ 7y
3
− 15y
2
+ 7y − 1)
· (y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)(y
12
− 5y
11
+ ··· − 17y + 1)
· (y
26
− 9y
25
+ ··· − 58y + 1)(y
52
+ 22y
51
+ ··· + 1455729y + 113569)
c
2
, c
3
, c
6
c
8
, c
9
, c
12
y
3
(y − 2)
4
(y − 1)
6
(y
2
− 3y + 1)
2
(y
3
− 9y
2
+ 26y − 25)
· (y
3
− 2y
2
− 3y − 1)(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
3
· (y
12
− 17y
11
+ ··· − 45y + 9)(y
26
− 28y
25
+ ··· − 435y + 25)
· (y
26
− 28y
25
+ ··· − 100y + 4)
2
c
5
, c
11
(y − 1)
5
(y
2
− 3y + 1)
2
(y
3
− y
2
+ 2y − 1)
2
· (y
4
− 6y
3
+ 7y
2
− 2y + 1)
2
(y
5
− 6y
4
+ 7y
3
− 15y
2
− 5y − 49)
· (y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)(y
5
+ 5y
4
+ 7y
3
− 8y
2
+ 13y − 1)
· (y
12
− 6y
11
+ ··· − 92y + 16)(y
13
− 7y
12
+ ··· + 8y − 1)
2
· (y
26
− 15y
25
+ ··· − 35721y + 2401)
2
68
