12a
0554
(K12a
0554
)
A knot diagram
1
Linearized knot diagam
3 7 9 8 10 12 2 4 11 5 1 6
Solving Sequence
3,9 4,11 7,10
2 1 12 6 8 5
c
3
c
9
c
2
c
1
c
11
c
6
c
8
c
4
c
5
, c
7
, c
10
, c
12
Ideals for irreducible components
2
of X
par
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
1
= h−u
10
+ u
9
− 4u
8
+ 4u
7
− 4u
6
+ 6u
5
+ 5u
3
− 3u
2
+ 2d + 2u − 2,
− u
11
+ u
10
− 4u
9
+ 4u
8
− 5u
7
+ 7u
6
− u
5
+ 7u
4
− u
3
+ u
2
+ 4c,
− u
9
+ u
8
− 4u
7
+ 3u
6
− 5u
5
+ 3u
4
− 2u
3
+ 3u
2
+ 2b − 2u + 2,
− u
11
− u
10
− 2u
9
− 6u
8
+ 3u
7
− 9u
6
+ 9u
5
− u
4
+ 3u
3
− 3u
2
+ 4a − 4,
u
12
− u
11
+ 6u
10
− 6u
9
+ 13u
8
− 13u
7
+ 11u
6
− 13u
5
+ 5u
4
− 7u
3
+ 8u
2
− 4u + 4i
I
u
2
= hu
4
+ 2u
2
+ d, −u
9
+ 2u
8
− 6u
7
+ 10u
6
− 13u
5
+ 18u
4
− 11u
3
+ 11u
2
+ 2c − u − 1,
− u
9
− 6u
7
+ 2u
6
− 13u
5
+ 8u
4
− 11u
3
+ 9u
2
+ 2b − u + 1, −u
6
− 3u
4
− 2u
2
+ a + 1,
u
10
− u
9
+ 6u
8
− 6u
7
+ 13u
6
− 13u
5
+ 11u
4
− 10u
3
+ 2u
2
+ 1i
I
u
3
= hu
4
+ 2u
2
+ d, −u
9
+ 2u
8
− 6u
7
+ 10u
6
− 13u
5
+ 18u
4
− 11u
3
+ 11u
2
+ 2c − u − 1,
u
9
+ 6u
7
− 2u
6
+ 13u
5
− 8u
4
+ 11u
3
− 9u
2
+ 2b + 3u − 1,
3u
9
− 4u
8
+ 20u
7
− 22u
6
+ 49u
5
− 46u
4
+ 49u
3
− 37u
2
+ 2a + 11u − 3,
u
10
− u
9
+ 6u
8
− 6u
7
+ 13u
6
− 13u
5
+ 11u
4
− 10u
3
+ 2u
2
+ 1i
I
u
4
= h−u
9
− 4u
7
− 3u
5
− 2u
4
+ 7u
3
− 5u
2
+ 2d + 9u − 1,
− 3u
9
+ 2u
8
− 18u
7
+ 14u
6
− 39u
5
+ 34u
4
− 33u
3
+ 29u
2
+ 2c − 5u + 1,
− u
9
− 6u
7
+ 2u
6
− 13u
5
+ 8u
4
− 11u
3
+ 9u
2
+ 2b − u + 1, −u
6
− 3u
4
− 2u
2
+ a + 1,
u
10
− u
9
+ 6u
8
− 6u
7
+ 13u
6
− 13u
5
+ 11u
4
− 10u
3
+ 2u
2
+ 1i
I
u
5
= h−u
3
+ d − u, c − u, −u
5
− 2u
3
− u
2
+ b − 1, −u
7
+ 2u
6
− u
5
+ 2u
4
+ 2u
3
+ 2a − u + 1,
u
8
+ 3u
6
+ 2u
5
+ 2u
4
+ 4u
3
+ u
2
+ u + 2i
I
u
6
= hu
6
+ u
5
+ u
4
+ 3u
3
+ d + u + 1, −u
7
− u
5
− 2u
4
+ 2u
3
− 2u
2
+ 2c + u + 1, b − u, a,
u
8
+ 3u
6
+ 2u
5
+ 2u
4
+ 4u
3
+ u
2
+ u + 2i
I
u
7
= hu
6
+ u
5
+ u
4
+ 3u
3
+ d + u + 1, −u
7
− u
5
− 2u
4
+ 2u
3
− 2u
2
+ 2c + u + 1, −u
5
− 2u
3
− u
2
+ b − 1,
− u
7
+ 2u
6
− u
5
+ 2u
4
+ 2u
3
+ 2a − u + 1, u
8
+ 3u
6
+ 2u
5
+ 2u
4
+ 4u
3
+ u
2
+ u + 2i
I
u
8
= h−u
3
+ d − u, c − u, b − u, a, u
4
+ u
2
+ u + 1i
I
u
9
= hu
2
+ d + u + 1, c − u, −u
2
a − u
2
+ 2b − a − 2, 2u
2
a + a
2
+ 4u
2
+ 2a + 3u + 5, u
3
+ u
2
+ 2u + 1i
I
u
10
= hu
2
c + 2cu − u
2
+ d + c − u − 2, −2u
2
c + c
2
− cu + 3u
2
− 4c + u + 5, b − u, a, u
3
+ u
2
+ 2u + 1i
2
I
u
11
= h−u
2
a − au + 2d − u − 3, −u
2
a − 3u
2
+ 2c − a − 2u − 6, −u
2
a − u
2
+ 2b − a − 2,
2u
2
a + a
2
+ 4u
2
+ 2a + 3u + 5, u
3
+ u
2
+ 2u + 1i
I
u
12
= h−u
3
+ d − u, c − u, b − u, a, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
I
u
13
= h−u
3
+ d − u, c − u, −u
5
− 2u
3
+ u
2
+ b − u + 1, u
5
− u
4
− 2u
2
+ a, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
I
u
14
= h2u
5
− u
4
+ 2u
3
− 2u
2
+ d + 2u, u
4
+ u
2
+ c + 1, b − u, a, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
I
u
15
= hd + 1, c − u, b, a − u, u
2
+ 1i
I
u
16
= hd + 1, c − u, b − u, a − 1, u
2
+ 1i
I
u
17
= hd − u, c, b − u, a − 1, u
2
+ 1i
I
u
18
= hda + u + 1, c − u, b − u, u
2
+ 1i
I
v
1
= ha, d + v, c + a + 1, b − v, v
2
+ 1i
* 18 irreducible components of dim
C
= 0, with total 114 representations.
* 1 irreducible components of dim
C
= 1
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
3
I. I
u
1
= h−u
10
+ u
9
+ · · · + 2d − 2, −u
11
+ u
10
+ · · · + u
2
+ 4c, −u
9
+ u
8
+
· · · + 2b + 2, −u
11
− u
10
+ · · · + 4a − 4, u
12
− u
11
+ · · · − 4u + 4i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
11
=
1
4
u
11
−
1
4
u
10
+ ··· +
1
4
u
3
−
1
4
u
2
1
2
u
10
−
1
2
u
9
+ ··· − u + 1
a
7
=
1
4
u
11
+
1
4
u
10
+ ··· +
3
4
u
2
+ 1
1
2
u
9
−
1
2
u
8
+ ··· + u − 1
a
10
=
−
1
4
u
11
+
1
4
u
10
+ ··· − u + 1
−
1
2
u
9
−
5
2
u
7
+ ··· + u + 1
a
2
=
−
1
4
u
11
+
3
4
u
10
+ ··· −
3
2
u + 1
−
1
2
u
10
+
1
2
u
9
+ ··· + u − 1
a
1
=
−
1
4
u
11
+
1
4
u
10
+ ··· −
3
4
u
2
−
1
2
u
−
1
2
u
10
+
1
2
u
9
+ ··· + u − 1
a
12
=
1
2
u
11
−
1
2
u
10
+ ··· +
1
2
u − 1
1
2
u
10
+ 2u
8
+ ··· +
1
2
u
2
− u
a
6
=
1
4
u
11
+
1
4
u
10
+ ··· −
1
2
u + 1
−
1
2
u
10
+
1
2
u
9
+ ··· + u − 1
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
11
+ u
10
+ 6u
9
+ 2u
8
+ 13u
7
−u
6
+ 5u
5
−5u
4
−11u
3
−u
2
+ 2u + 2
4
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
u
12
+ 5u
11
+ ··· + 6u + 1
c
2
, c
5
, c
6
c
7
, c
10
, c
12
u
12
+ u
11
+ 3u
10
+ 3u
9
+ 7u
8
+ 7u
7
+ 8u
6
+ 7u
5
+ 9u
4
+ 6u
3
+ 3u
2
+ 1
c
3
, c
4
, c
8
u
12
+ u
11
+ ··· + 4u + 4
5
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
y
12
+ 9y
11
+ ··· + 18y + 1
c
2
, c
5
, c
6
c
7
, c
10
, c
12
y
12
+ 5y
11
+ ··· + 6y + 1
c
3
, c
4
, c
8
y
12
+ 11y
11
+ ··· + 48y + 16
6
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.930547 + 0.179955I
a = 0.670259 + 1.162990I
b = −0.563501 + 1.188620I
c = −1.40294 − 1.16824I
d = −1.51082 − 1.44889I
−5.48513 − 12.85560I −4.74505 + 9.29863I
u = 0.930547 − 0.179955I
a = 0.670259 − 1.162990I
b = −0.563501 − 1.188620I
c = −1.40294 + 1.16824I
d = −1.51082 + 1.44889I
−5.48513 + 12.85560I −4.74505 − 9.29863I
u = −0.686814 + 0.551480I
a = −0.796508 + 0.745631I
b = 0.603454 + 0.816648I
c = 0.968608 − 0.657314I
d = −0.163512 − 0.755585I
0.72149 + 5.92893I 1.32923 − 9.67861I
u = −0.686814 − 0.551480I
a = −0.796508 − 0.745631I
b = 0.603454 − 0.816648I
c = 0.968608 + 0.657314I
d = −0.163512 + 0.755585I
0.72149 − 5.92893I 1.32923 + 9.67861I
u = 0.185101 + 0.743746I
a = 0.370768 + 0.449966I
b = −0.222861 + 0.420471I
c = −0.277347 + 0.101905I
d = 0.209277 + 0.422629I
0.425064 − 1.127160I 4.87896 + 6.40596I
u = 0.185101 − 0.743746I
a = 0.370768 − 0.449966I
b = −0.222861 − 0.420471I
c = −0.277347 − 0.101905I
d = 0.209277 − 0.422629I
0.425064 + 1.127160I 4.87896 − 6.40596I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.18488 + 1.42300I
a = −1.041110 + 0.719276I
b = 0.842304 − 0.448362I
c = −0.567633 − 0.283558I
d = −0.62794 + 1.29888I
7.14373 + 1.01626I 7.50962 + 1.51234I
u = −0.18488 − 1.42300I
a = −1.041110 − 0.719276I
b = 0.842304 + 0.448362I
c = −0.567633 + 0.283558I
d = −0.62794 − 1.29888I
7.14373 − 1.01626I 7.50962 − 1.51234I
u = 0.40234 + 1.40049I
a = −1.76208 − 0.32910I
b = 0.593901 − 1.231770I
c = −1.185730 + 0.490884I
d = −1.36730 − 2.05780I
−0.4877 − 17.6327I −1.23582 + 10.46043I
u = 0.40234 − 1.40049I
a = −1.76208 + 0.32910I
b = 0.593901 + 1.231770I
c = −1.185730 − 0.490884I
d = −1.36730 + 2.05780I
−0.4877 + 17.6327I −1.23582 − 10.46043I
u = −0.14629 + 1.48775I
a = 1.55868 + 0.32070I
b = −0.753298 − 0.941385I
c = 0.965047 + 0.119356I
d = 0.460302 − 0.241641I
7.55213 + 8.70787I 4.26306 − 7.95599I
u = −0.14629 − 1.48775I
a = 1.55868 − 0.32070I
b = −0.753298 + 0.941385I
c = 0.965047 − 0.119356I
d = 0.460302 + 0.241641I
7.55213 − 8.70787I 4.26306 + 7.95599I
8
II. I
u
2
= hu
4
+ 2u
2
+ d, −u
9
+ 2u
8
+ · · · + 2c − 1, −u
9
− 6u
7
+ · · · + 2b +
1, −u
6
− 3u
4
− 2u
2
+ a + 1, u
10
− u
9
+ · · · + 2u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
11
=
1
2
u
9
− u
8
+ ··· +
1
2
u +
1
2
−u
4
− 2u
2
a
7
=
u
6
+ 3u
4
+ 2u
2
− 1
1
2
u
9
+ 3u
7
+ ··· +
1
2
u −
1
2
a
10
=
−
1
2
u
9
− 3u
7
+ ··· +
1
2
u +
3
2
−
1
2
u
9
− 3u
7
+ ··· +
3
2
u +
1
2
a
2
=
1
2
u
9
+ 2u
7
+ ··· −
5
2
u +
1
2
−
1
2
u
9
− 2u
7
+ ··· +
1
2
u −
1
2
a
1
=
−u
3
− 2u
−
1
2
u
9
− 2u
7
+ ··· +
1
2
u −
1
2
a
12
=
−u
8
− 5u
6
+ u
5
− 8u
4
+ 4u
3
− 3u
2
+ 4u + 1
1
a
6
=
1
2
u
9
+ 2u
7
+ ··· −
5
2
u +
1
2
−u
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
8
− 2u
7
+ 20u
6
− 10u
5
+ 32u
4
− 20u
3
+ 12u
2
− 14u − 4
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
10
+ 4u
9
+ 10u
8
+ 14u
7
+ 15u
6
+ 10u
5
+ 7u
4
+ 5u
3
+ 11u
2
+ 11u + 4
c
2
, c
5
, c
7
c
10
u
10
− 2u
9
+ 4u
8
− 4u
7
+ 5u
6
− 6u
5
+ 7u
4
− 7u
3
+ 5u
2
− 3u + 2
c
3
, c
4
, c
8
u
10
+ u
9
+ 6u
8
+ 6u
7
+ 13u
6
+ 13u
5
+ 11u
4
+ 10u
3
+ 2u
2
+ 1
c
6
, c
12
u
10
+ u
9
+ 3u
8
+ 3u
7
+ 4u
6
+ 4u
5
+ 3u
4
+ 5u
3
+ 4u
2
+ 4u + 4
c
11
u
10
+ 5u
9
+ 11u
8
+ 13u
7
+ 8u
6
+ 2u
5
+ u
4
− u
3
+ 16u + 16
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
10
+ 4y
9
+ ··· − 33y + 16
c
2
, c
5
, c
7
c
10
y
10
+ 4y
9
+ 10y
8
+ 14y
7
+ 15y
6
+ 10y
5
+ 7y
4
+ 5y
3
+ 11y
2
+ 11y + 4
c
3
, c
4
, c
8
y
10
+ 11y
9
+ ··· + 4y + 1
c
6
, c
12
y
10
+ 5y
9
+ 11y
8
+ 13y
7
+ 8y
6
+ 2y
5
+ y
4
− y
3
+ 16y + 16
c
11
y
10
− 3y
9
+ ··· − 256y + 256
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.748770 + 0.138462I
a = 0.92253 + 1.26185I
b = −0.439859 + 1.118370I
c = −1.60028 − 1.01804I
d = −1.33318 − 0.63926I
−7.31978 − 3.81695I −7.33347 + 4.73761I
u = 0.748770 − 0.138462I
a = 0.92253 − 1.26185I
b = −0.439859 − 1.118370I
c = −1.60028 + 1.01804I
d = −1.33318 + 0.63926I
−7.31978 + 3.81695I −7.33347 − 4.73761I
u = 0.28433 + 1.41260I
a = 0.919982 + 0.694170I
b = −0.910142 − 0.314063I
c = 0.488875 − 0.418182I
d = 0.80878 + 1.46934I
5.18879 − 6.45670I 5.02275 + 3.64794I
u = 0.28433 − 1.41260I
a = 0.919982 − 0.694170I
b = −0.910142 + 0.314063I
c = 0.488875 + 0.418182I
d = 0.80878 − 1.46934I
5.18879 + 6.45670I 5.02275 − 3.64794I
u = −0.35489 + 1.40814I
a = 1.79571 − 0.20376I
b = −0.609606 − 1.180280I
c = 1.132790 + 0.439888I
d = 1.26468 − 1.71290I
2.57186 + 12.00600I 1.91374 − 7.39232I
u = −0.35489 − 1.40814I
a = 1.79571 + 0.20376I
b = −0.609606 + 1.180280I
c = 1.132790 − 0.439888I
d = 1.26468 + 1.71290I
2.57186 − 12.00600I 1.91374 + 7.39232I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.05139 + 1.48296I
a = −1.43312 + 0.49863I
b = 0.782018 − 0.812236I
c = −0.856742 + 0.002799I
d = −0.408434 + 0.364710I
8.34709 − 2.88363I 6.09026 + 2.85464I
u = 0.05139 − 1.48296I
a = −1.43312 − 0.49863I
b = 0.782018 + 0.812236I
c = −0.856742 − 0.002799I
d = −0.408434 − 0.364710I
8.34709 + 2.88363I 6.09026 − 2.85464I
u = −0.229588 + 0.355227I
a = −1.205100 − 0.252617I
b = 0.177588 + 0.796469I
c = 1.33535 + 0.83396I
d = 0.168159 + 0.302254I
−3.85316 + 1.05773I −3.69328 − 6.23330I
u = −0.229588 − 0.355227I
a = −1.205100 + 0.252617I
b = 0.177588 − 0.796469I
c = 1.33535 − 0.83396I
d = 0.168159 − 0.302254I
−3.85316 − 1.05773I −3.69328 + 6.23330I
13
III. I
u
3
= hu
4
+ 2u
2
+ d, −u
9
+ 2u
8
+ · · · + 2c − 1, u
9
+ 6u
7
+ · · · + 2b −
1, 3u
9
− 4u
8
+ · · · + 2a − 3, u
10
− u
9
+ · · · + 2u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
11
=
1
2
u
9
− u
8
+ ··· +
1
2
u +
1
2
−u
4
− 2u
2
a
7
=
−
3
2
u
9
+ 2u
8
+ ··· −
11
2
u +
3
2
−
1
2
u
9
− 3u
7
+ ··· −
3
2
u +
1
2
a
10
=
−
1
2
u
9
− 3u
7
+ ··· +
1
2
u +
3
2
−
1
2
u
9
− 3u
7
+ ··· +
3
2
u +
1
2
a
2
=
−u
9
+ u
8
− 5u
7
+ 5u
6
− 9u
5
+ 8u
4
− 5u
3
+ 2u
2
+ 2u − 3
1
2
u
9
+ 2u
7
+ ··· −
1
2
u −
3
2
a
1
=
−
1
2
u
9
+ u
8
+ ··· +
3
2
u −
9
2
1
2
u
9
+ 2u
7
+ ··· −
1
2
u −
3
2
a
12
=
u
9
− u
8
+ 6u
7
− 5u
6
+ 12u
5
− 8u
4
+ 7u
3
− 2u
2
− 3u + 3
1
a
6
=
1
2
u
9
+ 2u
7
+ ··· −
5
2
u +
1
2
−u
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
8
− 2u
7
+ 20u
6
− 10u
5
+ 32u
4
− 20u
3
+ 12u
2
− 14u − 4
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ 5u
9
+ 11u
8
+ 13u
7
+ 8u
6
+ 2u
5
+ u
4
− u
3
+ 16u + 16
c
2
, c
7
u
10
+ u
9
+ 3u
8
+ 3u
7
+ 4u
6
+ 4u
5
+ 3u
4
+ 5u
3
+ 4u
2
+ 4u + 4
c
3
, c
4
, c
8
u
10
+ u
9
+ 6u
8
+ 6u
7
+ 13u
6
+ 13u
5
+ 11u
4
+ 10u
3
+ 2u
2
+ 1
c
5
, c
6
, c
10
c
12
u
10
− 2u
9
+ 4u
8
− 4u
7
+ 5u
6
− 6u
5
+ 7u
4
− 7u
3
+ 5u
2
− 3u + 2
c
9
, c
11
u
10
+ 4u
9
+ 10u
8
+ 14u
7
+ 15u
6
+ 10u
5
+ 7u
4
+ 5u
3
+ 11u
2
+ 11u + 4
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
− 3y
9
+ ··· − 256y + 256
c
2
, c
7
y
10
+ 5y
9
+ 11y
8
+ 13y
7
+ 8y
6
+ 2y
5
+ y
4
− y
3
+ 16y + 16
c
3
, c
4
, c
8
y
10
+ 11y
9
+ ··· + 4y + 1
c
5
, c
6
, c
10
c
12
y
10
+ 4y
9
+ 10y
8
+ 14y
7
+ 15y
6
+ 10y
5
+ 7y
4
+ 5y
3
+ 11y
2
+ 11y + 4
c
9
, c
11
y
10
+ 4y
9
+ ··· − 33y + 16
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.748770 + 0.138462I
a = 0.68224 − 1.78754I
b = −0.308911 − 1.256830I
c = −1.60028 − 1.01804I
d = −1.33318 − 0.63926I
−7.31978 − 3.81695I −7.33347 + 4.73761I
u = 0.748770 − 0.138462I
a = 0.68224 + 1.78754I
b = −0.308911 + 1.256830I
c = −1.60028 + 1.01804I
d = −1.33318 + 0.63926I
−7.31978 + 3.81695I −7.33347 − 4.73761I
u = 0.28433 + 1.41260I
a = −1.82670 − 0.00276I
b = 0.625816 − 1.098530I
c = 0.488875 − 0.418182I
d = 0.80878 + 1.46934I
5.18879 − 6.45670I 5.02275 + 3.64794I
u = 0.28433 − 1.41260I
a = −1.82670 + 0.00276I
b = 0.625816 + 1.098530I
c = 0.488875 + 0.418182I
d = 0.80878 − 1.46934I
5.18879 + 6.45670I 5.02275 − 3.64794I
u = −0.35489 + 1.40814I
a = −0.859188 + 0.669926I
b = 0.964500 − 0.227856I
c = 1.132790 + 0.439888I
d = 1.26468 − 1.71290I
2.57186 + 12.00600I 1.91374 − 7.39232I
u = −0.35489 − 1.40814I
a = −0.859188 − 0.669926I
b = 0.964500 + 0.227856I
c = 1.132790 − 0.439888I
d = 1.26468 + 1.71290I
2.57186 − 12.00600I 1.91374 + 7.39232I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.05139 + 1.48296I
a = 1.253620 + 0.604304I
b = −0.833404 − 0.670721I
c = −0.856742 + 0.002799I
d = −0.408434 + 0.364710I
8.34709 − 2.88363I 6.09026 + 2.85464I
u = 0.05139 − 1.48296I
a = 1.253620 − 0.604304I
b = −0.833404 + 0.670721I
c = −0.856742 − 0.002799I
d = −0.408434 − 0.364710I
8.34709 + 2.88363I 6.09026 − 2.85464I
u = −0.229588 + 0.355227I
a = −0.74997 − 4.37781I
b = 0.051999 − 1.151700I
c = 1.33535 + 0.83396I
d = 0.168159 + 0.302254I
−3.85316 + 1.05773I −3.69328 − 6.23330I
u = −0.229588 − 0.355227I
a = −0.74997 + 4.37781I
b = 0.051999 + 1.151700I
c = 1.33535 − 0.83396I
d = 0.168159 − 0.302254I
−3.85316 − 1.05773I −3.69328 + 6.23330I
18
IV. I
u
4
= h−u
9
− 4u
7
+ · · · + 2d − 1, −3u
9
+ 2u
8
+ · · · + 2c + 1, −u
9
− 6u
7
+
· · · + 2b + 1, −u
6
− 3u
4
− 2u
2
+ a + 1, u
10
− u
9
+ · · · + 2u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
11
=
3
2
u
9
− u
8
+ ··· +
5
2
u −
1
2
1
2
u
9
+ 2u
7
+ ··· −
9
2
u +
1
2
a
7
=
u
6
+ 3u
4
+ 2u
2
− 1
1
2
u
9
+ 3u
7
+ ··· +
1
2
u −
1
2
a
10
=
5
2
u
9
− 2u
8
+ ··· +
7
2
u −
3
2
u
9
+ 5u
7
+ 8u
5
+ u
3
− 6u
a
2
=
1
2
u
9
+ 2u
7
+ ··· −
5
2
u +
1
2
−
1
2
u
9
− 2u
7
+ ··· +
1
2
u −
1
2
a
1
=
−u
3
− 2u
−
1
2
u
9
− 2u
7
+ ··· +
1
2
u −
1
2
a
12
=
2u
9
− u
8
+ 12u
7
− 7u
6
+ 26u
5
− 18u
4
+ 22u
3
− 17u
2
+ 3u − 1
u
9
+ 5u
7
+ 8u
5
+ u
3
+ u
2
− 6u
a
6
=
−
1
2
u
9
− 2u
7
+ ··· +
5
2
u −
7
2
1
2
u
9
− u
8
+ ··· +
3
2
u +
3
2
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
8
− 2u
7
+ 20u
6
− 10u
5
+ 32u
4
− 20u
3
+ 12u
2
− 14u − 4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
10
+ 4u
9
+ 10u
8
+ 14u
7
+ 15u
6
+ 10u
5
+ 7u
4
+ 5u
3
+ 11u
2
+ 11u + 4
c
2
, c
6
, c
7
c
12
u
10
− 2u
9
+ 4u
8
− 4u
7
+ 5u
6
− 6u
5
+ 7u
4
− 7u
3
+ 5u
2
− 3u + 2
c
3
, c
4
, c
8
u
10
+ u
9
+ 6u
8
+ 6u
7
+ 13u
6
+ 13u
5
+ 11u
4
+ 10u
3
+ 2u
2
+ 1
c
5
, c
10
u
10
+ u
9
+ 3u
8
+ 3u
7
+ 4u
6
+ 4u
5
+ 3u
4
+ 5u
3
+ 4u
2
+ 4u + 4
c
9
u
10
+ 5u
9
+ 11u
8
+ 13u
7
+ 8u
6
+ 2u
5
+ u
4
− u
3
+ 16u + 16
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
10
+ 4y
9
+ ··· − 33y + 16
c
2
, c
6
, c
7
c
12
y
10
+ 4y
9
+ 10y
8
+ 14y
7
+ 15y
6
+ 10y
5
+ 7y
4
+ 5y
3
+ 11y
2
+ 11y + 4
c
3
, c
4
, c
8
y
10
+ 11y
9
+ ··· + 4y + 1
c
5
, c
10
y
10
+ 5y
9
+ 11y
8
+ 13y
7
+ 8y
6
+ 2y
5
+ y
4
− y
3
+ 16y + 16
c
9
y
10
− 3y
9
+ ··· − 256y + 256
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.748770 + 0.138462I
a = 0.92253 + 1.26185I
b = −0.439859 + 1.118370I
c = −1.73122 + 1.35717I
d = −2.26783 − 0.05446I
−7.31978 − 3.81695I −7.33347 + 4.73761I
u = 0.748770 − 0.138462I
a = 0.92253 − 1.26185I
b = −0.439859 − 1.118370I
c = −1.73122 − 1.35717I
d = −2.26783 + 0.05446I
−7.31978 + 3.81695I −7.33347 − 4.73761I
u = 0.28433 + 1.41260I
a = 0.919982 + 0.694170I
b = −0.910142 − 0.314063I
c = −1.047080 + 0.366289I
d = −1.16328 − 1.17886I
5.18879 − 6.45670I 5.02275 + 3.64794I
u = 0.28433 − 1.41260I
a = 0.919982 − 0.694170I
b = −0.910142 + 0.314063I
c = −1.047080 − 0.366289I
d = −1.16328 + 1.17886I
5.18879 + 6.45670I 5.02275 − 3.64794I
u = −0.35489 + 1.40814I
a = 1.79571 − 0.20376I
b = −0.609606 − 1.180280I
c = −0.441314 − 0.512537I
d = −0.99330 + 1.55020I
2.57186 + 12.00600I 1.91374 − 7.39232I
u = −0.35489 − 1.40814I
a = 1.79571 + 0.20376I
b = −0.609606 + 1.180280I
c = −0.441314 + 0.512537I
d = −0.99330 − 1.55020I
2.57186 − 12.00600I 1.91374 + 7.39232I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.05139 + 1.48296I
a = −1.43312 + 0.49863I
b = 0.782018 − 0.812236I
c = 0.758680 − 0.138716I
d = 0.366987 + 0.885907I
8.34709 − 2.88363I 6.09026 + 2.85464I
u = 0.05139 − 1.48296I
a = −1.43312 − 0.49863I
b = 0.782018 + 0.812236I
c = 0.758680 + 0.138716I
d = 0.366987 − 0.885907I
8.34709 + 2.88363I 6.09026 − 2.85464I
u = −0.229588 + 0.355227I
a = −1.205100 − 0.252617I
b = 0.177588 + 0.796469I
c = 1.46094 + 2.78212I
d = 1.05742 − 2.03840I
−3.85316 + 1.05773I −3.69328 − 6.23330I
u = −0.229588 − 0.355227I
a = −1.205100 + 0.252617I
b = 0.177588 − 0.796469I
c = 1.46094 − 2.78212I
d = 1.05742 + 2.03840I
−3.85316 − 1.05773I −3.69328 + 6.23330I
23
V. I
u
5
= h−u
3
+ d − u, c − u, −u
5
− 2u
3
− u
2
+ b − 1, −u
7
+ 2u
6
+ · · · +
2a + 1, u
8
+ 3u
6
+ · · · + u + 2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
11
=
u
u
3
+ u
a
7
=
1
2
u
7
− u
6
+ ··· +
1
2
u −
1
2
u
5
+ 2u
3
+ u
2
+ 1
a
10
=
−u
3
−u
5
− u
3
+ u
a
2
=
1
2
u
7
+ u
6
+ ··· +
3
2
u +
1
2
−u
6
− 2u
4
− u
3
− u
2
− u − 1
a
1
=
1
2
u
7
+
1
2
u
5
− u
2
+
1
2
u −
1
2
−u
6
− 2u
4
− u
3
− u
2
− u − 1
a
12
=
−
1
2
u
7
+ u
6
+ ··· +
3
2
u −
1
2
u
6
− u
5
+ 2u
4
+ 2u − 1
a
6
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
6
− 4u
5
+ 8u
4
+ 8u + 2
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
2
c
2
, c
6
, c
7
c
12
(u
4
+ u
2
− u + 1)
2
c
3
, c
4
, c
5
c
8
, c
10
u
8
+ 3u
6
− 2u
5
+ 2u
4
− 4u
3
+ u
2
− u + 2
c
9
u
8
+ 6u
7
+ 13u
6
+ 10u
5
− 2u
4
− 4u
3
+ u
2
+ 3u + 4
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
2
c
2
, c
6
, c
7
c
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
2
c
3
, c
4
, c
5
c
8
, c
10
y
8
+ 6y
7
+ 13y
6
+ 10y
5
− 2y
4
− 4y
3
+ y
2
+ 3y + 4
c
9
y
8
− 10y
7
+ 45y
6
− 102y
5
+ 82y
4
+ 24y
3
+ 9y
2
− y + 16
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.856926 + 0.228629I
a = −0.766503 + 1.117310I
b = 0.547424 + 1.120870I
c = −0.856926 + 0.228629I
d = −1.35181 + 0.72034I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = −0.856926 − 0.228629I
a = −0.766503 − 1.117310I
b = 0.547424 − 1.120870I
c = −0.856926 − 0.228629I
d = −1.35181 − 0.72034I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = 0.511330 + 0.719091I
a = 0.699144 + 0.608069I
b = −0.547424 + 0.585652I
c = 0.511330 + 0.719091I
d = −0.148192 + 0.911292I
0.98010 − 1.39709I 3.77019 + 3.86736I
u = 0.511330 − 0.719091I
a = 0.699144 − 0.608069I
b = −0.547424 − 0.585652I
c = 0.511330 − 0.719091I
d = −0.148192 − 0.911292I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.036094 + 1.304740I
a = 1.33473 + 1.08141I
b = −0.547424 − 0.585652I
c = 0.036094 + 1.304740I
d = −0.148192 − 0.911292I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.036094 − 1.304740I
a = 1.33473 − 1.08141I
b = −0.547424 + 0.585652I
c = 0.036094 − 1.304740I
d = −0.148192 + 0.911292I
0.98010 − 1.39709I 3.77019 + 3.86736I
27
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.309502 + 1.349500I
a = −2.01737 − 0.12267I
b = 0.547424 − 1.120870I
c = 0.309502 + 1.349500I
d = −1.35181 − 0.72034I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = 0.309502 − 1.349500I
a = −2.01737 + 0.12267I
b = 0.547424 + 1.120870I
c = 0.309502 − 1.349500I
d = −1.35181 + 0.72034I
−2.62503 + 7.64338I −1.77019 − 6.51087I
28
VI.
I
u
6
= hu
6
+u
5
+· · ·+d+1, −u
7
−u
5
+· · ·+2c+1, b−u, a, u
8
+3u
6
+· · ·+u+2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
11
=
1
2
u
7
+
1
2
u
5
+ ··· −
1
2
u −
1
2
−u
6
− u
5
− u
4
− 3u
3
− u − 1
a
7
=
0
u
a
10
=
−
1
2
u
7
−
5
2
u
5
+ ··· −
1
2
u −
3
2
−u
7
− 3u
5
− 2u
3
− u
2
+ u − 1
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
1
2
u
7
+
3
2
u
5
+ u
3
−
1
2
u +
1
2
1
a
6
=
−
1
2
u
7
−
1
2
u
5
+ ··· +
1
2
u +
1
2
u
5
+ 2u
3
+ u
2
+ u + 1
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
6
− 4u
5
+ 8u
4
+ 8u + 2
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ 6u
7
+ 13u
6
+ 10u
5
− 2u
4
− 4u
3
+ u
2
+ 3u + 4
c
2
, c
3
, c
4
c
7
, c
8
u
8
+ 3u
6
− 2u
5
+ 2u
4
− 4u
3
+ u
2
− u + 2
c
5
, c
6
, c
10
c
12
(u
4
+ u
2
− u + 1)
2
c
9
, c
11
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 10y
7
+ 45y
6
− 102y
5
+ 82y
4
+ 24y
3
+ 9y
2
− y + 16
c
2
, c
3
, c
4
c
7
, c
8
y
8
+ 6y
7
+ 13y
6
+ 10y
5
− 2y
4
− 4y
3
+ y
2
+ 3y + 4
c
5
, c
6
, c
10
c
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
2
c
9
, c
11
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.856926 + 0.228629I
a = 0
b = −0.856926 + 0.228629I
c = 1.39892 − 1.05885I
d = 1.17165 − 1.21187I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = −0.856926 − 0.228629I
a = 0
b = −0.856926 − 0.228629I
c = 1.39892 + 1.05885I
d = 1.17165 + 1.21187I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = 0.511330 + 0.719091I
a = 0
b = 0.511330 + 0.719091I
c = −0.620678 − 0.381115I
d = 0.517398 − 0.132058I
0.98010 − 1.39709I 3.77019 + 3.86736I
u = 0.511330 − 0.719091I
a = 0
b = 0.511330 − 0.719091I
c = −0.620678 + 0.381115I
d = 0.517398 + 0.132058I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.036094 + 1.304740I
a = 0
b = 0.036094 + 1.304740I
c = 0.490144 + 0.046758I
d = 0.98671 + 1.09479I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.036094 − 1.304740I
a = 0
b = 0.036094 − 1.304740I
c = 0.490144 − 0.046758I
d = 0.98671 − 1.09479I
0.98010 − 1.39709I 3.77019 + 3.86736I
32
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.309502 + 1.349500I
a = 0
b = 0.309502 + 1.349500I
c = −1.018380 + 0.475355I
d = −1.67576 − 1.31818I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = 0.309502 − 1.349500I
a = 0
b = 0.309502 − 1.349500I
c = −1.018380 − 0.475355I
d = −1.67576 + 1.31818I
−2.62503 + 7.64338I −1.77019 − 6.51087I
33
VII. I
u
7
= hu
6
+ u
5
+ · · · + d + 1, −u
7
− u
5
+ · · · + 2c + 1, −u
5
− 2u
3
− u
2
+
b − 1, −u
7
+ 2u
6
+ · · · + 2a + 1, u
8
+ 3u
6
+ · · · + u + 2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
11
=
1
2
u
7
+
1
2
u
5
+ ··· −
1
2
u −
1
2
−u
6
− u
5
− u
4
− 3u
3
− u − 1
a
7
=
1
2
u
7
− u
6
+ ··· +
1
2
u −
1
2
u
5
+ 2u
3
+ u
2
+ 1
a
10
=
−
1
2
u
7
−
5
2
u
5
+ ··· −
1
2
u −
3
2
−u
7
− 3u
5
− 2u
3
− u
2
+ u − 1
a
2
=
1
2
u
7
+ u
6
+ ··· +
3
2
u +
1
2
−u
6
− 2u
4
− u
3
− u
2
− u − 1
a
1
=
1
2
u
7
+
1
2
u
5
− u
2
+
1
2
u −
1
2
−u
6
− 2u
4
− u
3
− u
2
− u − 1
a
12
=
−
1
2
u
7
− u
6
+ ··· −
3
2
u −
1
2
1
a
6
=
−
1
2
u
7
−
1
2
u
5
+ ··· +
1
2
u +
1
2
u
5
+ 2u
3
+ u
2
+ u + 1
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
6
− 4u
5
+ 8u
4
+ 8u + 2
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
2
c
2
, c
5
, c
7
c
10
(u
4
+ u
2
− u + 1)
2
c
3
, c
4
, c
6
c
8
, c
12
u
8
+ 3u
6
− 2u
5
+ 2u
4
− 4u
3
+ u
2
− u + 2
c
11
u
8
+ 6u
7
+ 13u
6
+ 10u
5
− 2u
4
− 4u
3
+ u
2
+ 3u + 4
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
2
c
2
, c
5
, c
7
c
10
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
2
c
3
, c
4
, c
6
c
8
, c
12
y
8
+ 6y
7
+ 13y
6
+ 10y
5
− 2y
4
− 4y
3
+ y
2
+ 3y + 4
c
11
y
8
− 10y
7
+ 45y
6
− 102y
5
+ 82y
4
+ 24y
3
+ 9y
2
− y + 16
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.856926 + 0.228629I
a = −0.766503 + 1.117310I
b = 0.547424 + 1.120870I
c = 1.39892 − 1.05885I
d = 1.17165 − 1.21187I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = −0.856926 − 0.228629I
a = −0.766503 − 1.117310I
b = 0.547424 − 1.120870I
c = 1.39892 + 1.05885I
d = 1.17165 + 1.21187I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = 0.511330 + 0.719091I
a = 0.699144 + 0.608069I
b = −0.547424 + 0.585652I
c = −0.620678 − 0.381115I
d = 0.517398 − 0.132058I
0.98010 − 1.39709I 3.77019 + 3.86736I
u = 0.511330 − 0.719091I
a = 0.699144 − 0.608069I
b = −0.547424 − 0.585652I
c = −0.620678 + 0.381115I
d = 0.517398 + 0.132058I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.036094 + 1.304740I
a = 1.33473 + 1.08141I
b = −0.547424 − 0.585652I
c = 0.490144 + 0.046758I
d = 0.98671 + 1.09479I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.036094 − 1.304740I
a = 1.33473 − 1.08141I
b = −0.547424 + 0.585652I
c = 0.490144 − 0.046758I
d = 0.98671 − 1.09479I
0.98010 − 1.39709I 3.77019 + 3.86736I
37
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.309502 + 1.349500I
a = −2.01737 − 0.12267I
b = 0.547424 − 1.120870I
c = −1.018380 + 0.475355I
d = −1.67576 − 1.31818I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = 0.309502 − 1.349500I
a = −2.01737 + 0.12267I
b = 0.547424 + 1.120870I
c = −1.018380 − 0.475355I
d = −1.67576 + 1.31818I
−2.62503 + 7.64338I −1.77019 − 6.51087I
38
VIII. I
u
8
= h−u
3
+ d − u, c − u, b − u, a, u
4
+ u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
11
=
u
u
3
+ u
a
7
=
0
u
a
10
=
−u
3
u
2
+ 2u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
−1
u
3
− u
2
− 1
a
6
=
−u
−u
3
− u
2
− u − 1
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
2
− u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
− 4u
2
+ 2
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
u
4
+ u
2
− u + 1
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
y
4
+ 2y
3
+ 3y
2
+ y + 1
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 0.585652I
a = 0
b = −0.547424 + 0.585652I
c = −0.547424 + 0.585652I
d = −0.148192 + 0.911292I
0.98010 − 1.39709I 3.77019 + 3.86736I
u = −0.547424 − 0.585652I
a = 0
b = −0.547424 − 0.585652I
c = −0.547424 − 0.585652I
d = −0.148192 − 0.911292I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.547424 + 1.120870I
a = 0
b = 0.547424 + 1.120870I
c = 0.547424 + 1.120870I
d = −1.35181 + 0.72034I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = 0.547424 − 1.120870I
a = 0
b = 0.547424 − 1.120870I
c = 0.547424 − 1.120870I
d = −1.35181 − 0.72034I
−2.62503 − 7.64338I −1.77019 + 6.51087I
42
IX. I
u
9
= hu
2
+ d + u + 1, c − u, −u
2
a − u
2
+ 2b − a − 2, 2u
2
a + 4u
2
+ · · · +
2a + 5, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
11
=
u
−u
2
− u − 1
a
7
=
a
1
2
u
2
a +
1
2
u
2
+
1
2
a + 1
a
10
=
u
2
+ 2u + 1
−u
2
a
2
=
−
1
2
u
2
a − au − u
2
− a −
1
2
u − 2
1
2
u
2
a −
1
2
u
2
+ ··· +
1
2
a −
1
2
a
1
=
−
1
2
au −
3
2
u
2
+ ··· −
1
2
a −
5
2
1
2
u
2
a −
1
2
u
2
+ ··· +
1
2
a −
1
2
a
12
=
1
2
u
2
a + 3u
2
+ a +
5
2
u + 4
1
a
6
=
u + 2
−u
a
8
=
u
−u
2
− u − 1
a
5
=
u
2
+ 1
u
2
+ u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
− 4u − 6
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
2
, c
6
, c
7
c
12
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
3
, c
4
, c
5
c
8
, c
10
(u
3
− u
2
+ 2u − 1)
2
c
9
(u
3
+ 3u
2
+ 2u − 1)
2
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
6
, c
7
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
3
, c
4
, c
5
c
8
, c
10
(y
3
+ 3y
2
+ 2y −1)
2
c
9
(y
3
− 5y
2
+ 10y −1)
2
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.919774 + 0.855379I
b = 0.713912 − 0.305839I
c = −0.215080 + 1.307140I
d = 0.877439 − 0.744862I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.215080 + 1.307140I
a = 2.24449 + 0.26918I
b = −0.498832 − 1.001300I
c = −0.215080 + 1.307140I
d = 0.877439 − 0.744862I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.215080 − 1.307140I
a = −0.919774 − 0.855379I
b = 0.713912 + 0.305839I
c = −0.215080 − 1.307140I
d = 0.877439 + 0.744862I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.215080 − 1.307140I
a = 2.24449 − 0.26918I
b = −0.498832 + 1.001300I
c = −0.215080 − 1.307140I
d = 0.877439 + 0.744862I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.569840
a = −1.32472 + 1.68359I
b = 0.284920 + 1.115140I
c = −0.569840
d = −0.754878
−4.40332 −5.01950
u = −0.569840
a = −1.32472 − 1.68359I
b = 0.284920 − 1.115140I
c = −0.569840
d = −0.754878
−4.40332 −5.01950
46
X.
I
u
10
= hu
2
c−u
2
+· · ·+c−2, −2u
2
c+3u
2
+· · ·−4c+5, b−u, a, u
3
+u
2
+2u+1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
11
=
c
−u
2
c − 2cu + u
2
− c + u + 2
a
7
=
0
u
a
10
=
u
2
c − 2u
2
+ 2c − u − 3
−cu
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
u
2
c + cu − 2u
2
+ 2c − u − 3
1
a
6
=
−2u
2
+ c − u − 4
−u
2
+ c − 2
a
8
=
u
−u
2
− u − 1
a
5
=
u
2
+ 1
u
2
+ u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
− 4u − 6
47
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ 3u
2
+ 2u − 1)
2
c
2
, c
3
, c
4
c
7
, c
8
(u
3
− u
2
+ 2u − 1)
2
c
5
, c
6
, c
10
c
12
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
9
, c
11
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
48
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− 5y
2
+ 10y −1)
2
c
2
, c
3
, c
4
c
7
, c
8
(y
3
+ 3y
2
+ 2y −1)
2
c
5
, c
6
, c
10
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
9
, c
11
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
49
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0
b = −0.215080 + 1.307140I
c = 0.836473 + 0.439023I
d = 1.93730 − 0.49194I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.215080 + 1.307140I
a = 0
b = −0.215080 + 1.307140I
c = −0.376271 − 0.256441I
d = −0.81474 + 1.23680I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.215080 − 1.307140I
a = 0
b = −0.215080 − 1.307140I
c = 0.836473 − 0.439023I
d = 1.93730 + 0.49194I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.215080 − 1.307140I
a = 0
b = −0.215080 − 1.307140I
c = −0.376271 + 0.256441I
d = −0.81474 − 1.23680I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.569840
a = 0
b = −0.569840
c = 2.03980 + 1.11514I
d = 1.377440 − 0.206343I
−4.40332 −5.01950
u = −0.569840
a = 0
b = −0.569840
c = 2.03980 − 1.11514I
d = 1.377440 + 0.206343I
−4.40332 −5.01950
50
XI. I
u
11
= h−u
2
a − au + 2d − u − 3, −u
2
a − 3u
2
+ · · · − a − 6, −u
2
a − u
2
+
2b − a − 2, 2u
2
a + 4u
2
+ · · · + 2a + 5, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
11
=
1
2
u
2
a +
3
2
u
2
+
1
2
a + u + 3
1
2
u
2
a +
1
2
au +
1
2
u +
3
2
a
7
=
a
1
2
u
2
a +
1
2
u
2
+
1
2
a + 1
a
10
=
u
2
a +
3
2
u
2
+ ··· +
3
2
a +
7
2
1
2
u
2
a +
1
2
u
2
+ ··· +
1
2
a +
3
2
a
2
=
−
1
2
u
2
a − au − u
2
− a −
1
2
u − 2
1
2
u
2
a −
1
2
u
2
+ ··· +
1
2
a −
1
2
a
1
=
−
1
2
au −
3
2
u
2
+ ··· −
1
2
a −
5
2
1
2
u
2
a −
1
2
u
2
+ ··· +
1
2
a −
1
2
a
12
=
1
2
u
2
a + au + u
2
+ a +
1
2
u + 2
1
a
6
=
1
2
u
2
a −
1
2
u
2
+
1
2
a − 1
1
2
u
2
a +
1
2
u
2
+
1
2
a + u + 1
a
8
=
u
−u
2
− u − 1
a
5
=
u
2
+ 1
u
2
+ u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
− 4u − 6
51
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
2
, c
5
, c
7
c
10
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
3
, c
4
, c
6
c
8
, c
12
(u
3
− u
2
+ 2u − 1)
2
c
11
(u
3
+ 3u
2
+ 2u − 1)
2
52
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
5
, c
7
c
10
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
3
, c
4
, c
6
c
8
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
11
(y
3
− 5y
2
+ 10y −1)
2
53
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.919774 + 0.855379I
b = 0.713912 − 0.305839I
c = 0.836473 + 0.439023I
d = 1.93730 − 0.49194I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.215080 + 1.307140I
a = 2.24449 + 0.26918I
b = −0.498832 − 1.001300I
c = −0.376271 − 0.256441I
d = −0.81474 + 1.23680I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.215080 − 1.307140I
a = −0.919774 − 0.855379I
b = 0.713912 + 0.305839I
c = 0.836473 − 0.439023I
d = 1.93730 + 0.49194I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.215080 − 1.307140I
a = 2.24449 − 0.26918I
b = −0.498832 + 1.001300I
c = −0.376271 + 0.256441I
d = −0.81474 − 1.23680I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.569840
a = −1.32472 + 1.68359I
b = 0.284920 + 1.115140I
c = 2.03980 + 1.11514I
d = 1.377440 − 0.206343I
−4.40332 −5.01950
u = −0.569840
a = −1.32472 − 1.68359I
b = 0.284920 − 1.115140I
c = 2.03980 − 1.11514I
d = 1.377440 + 0.206343I
−4.40332 −5.01950
54
XII. I
u
12
= h−u
3
+ d − u, c − u, b − u, a, u
6
− u
5
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
11
=
u
u
3
+ u
a
7
=
0
u
a
10
=
−u
3
−u
5
− u
3
+ u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
−u
5
− 2u
3
− u + 1
1
a
6
=
u
4
+ u
2
+ 1
u
5
+ 2u
3
− u
2
+ 2u − 1
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u − 2
55
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
56
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
57
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = 0
b = −0.498832 + 1.001300I
c = −0.498832 + 1.001300I
d = 0.877439 + 0.744862I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.498832 − 1.001300I
a = 0
b = −0.498832 − 1.001300I
c = −0.498832 − 1.001300I
d = 0.877439 − 0.744862I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.284920 + 1.115140I
a = 0
b = 0.284920 + 1.115140I
c = 0.284920 + 1.115140I
d = −0.754878
−4.40332 −5.01951 + 0.I
u = 0.284920 − 1.115140I
a = 0
b = 0.284920 − 1.115140I
c = 0.284920 − 1.115140I
d = −0.754878
−4.40332 −5.01951 + 0.I
u = 0.713912 + 0.305839I
a = 0
b = 0.713912 + 0.305839I
c = 0.713912 + 0.305839I
d = 0.877439 + 0.744862I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.713912 − 0.305839I
a = 0
b = 0.713912 − 0.305839I
c = 0.713912 − 0.305839I
d = 0.877439 − 0.744862I
−0.26574 + 2.82812I 1.50976 − 2.97945I
58
XIII. I
u
13
=
h−u
3
+d−u, c−u, −u
5
−2u
3
+· · ·+b+1, u
5
−u
4
−2u
2
+a, u
6
−u
5
+· · ·−2u+1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
11
=
u
u
3
+ u
a
7
=
−u
5
+ u
4
+ 2u
2
u
5
+ 2u
3
− u
2
+ u − 1
a
10
=
−u
3
−u
5
− u
3
+ u
a
2
=
u
5
− 2u
4
+ 2u
3
− 2u
2
+ 3u − 2
−u
5
− u
3
− u
a
1
=
−2u
4
+ u
3
− 2u
2
+ 2u − 2
−u
5
− u
3
− u
a
12
=
−u
5
+ 2u
4
− 2u
3
+ 2u
2
− 3u + 2
1
a
6
=
u
4
+ u
2
+ 1
u
5
+ 2u
3
− u
2
+ 2u − 1
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u − 2
59
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
60
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
61
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
13
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = −0.643729 + 0.689603I
b = 0.713912 + 0.305839I
c = −0.498832 + 1.001300I
d = 0.877439 + 0.744862I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.498832 − 1.001300I
a = −0.643729 − 0.689603I
b = 0.713912 − 0.305839I
c = −0.498832 − 1.001300I
d = 0.877439 − 0.744862I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.284920 + 1.115140I
a = −3.29468 − 0.84179I
b = 0.284920 − 1.115140I
c = 0.284920 + 1.115140I
d = −0.754878
−4.40332 −5.01951 + 0.I
u = 0.284920 − 1.115140I
a = −3.29468 + 0.84179I
b = 0.284920 + 1.115140I
c = 0.284920 − 1.115140I
d = −0.754878
−4.40332 −5.01951 + 0.I
u = 0.713912 + 0.305839I
a = 0.938404 + 0.982703I
b = −0.498832 + 1.001300I
c = 0.713912 + 0.305839I
d = 0.877439 + 0.744862I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.713912 − 0.305839I
a = 0.938404 − 0.982703I
b = −0.498832 − 1.001300I
c = 0.713912 − 0.305839I
d = 0.877439 − 0.744862I
−0.26574 + 2.82812I 1.50976 − 2.97945I
62
XIV.
I
u
14
= h2u
5
− u
4
+ · · · + d + 2u, u
4
+ u
2
+ c + 1, b − u, a, u
6
− u
5
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
11
=
−u
4
− u
2
− 1
−2u
5
+ u
4
− 2u
3
+ 2u
2
− 2u
a
7
=
0
u
a
10
=
−2u
5
− 3u
3
+ u
2
− 2u + 1
−3u
5
+ 2u
4
− 3u
3
+ 3u
2
− 3u + 2
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
−1
−2u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u
a
6
=
−u
2u
4
− 2u
3
+ 2u
2
− 3u + 2
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u − 2
63
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
64
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
65
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
14
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = 0
b = −0.498832 + 1.001300I
c = 0.183526 − 0.507021I
d = −1.105040 + 0.381425I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.498832 − 1.001300I
a = 0
b = −0.498832 − 1.001300I
c = 0.183526 + 0.507021I
d = −1.105040 − 0.381425I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.284920 + 1.115140I
a = 0
b = 0.284920 + 1.115140I
c = −0.784920 + 0.841795I
d = −3.70216 − 1.47725I
−4.40332 −5.01951 + 0.I
u = 0.284920 − 1.115140I
a = 0
b = 0.284920 − 1.115140I
c = −0.784920 − 0.841795I
d = −3.70216 + 1.47725I
−4.40332 −5.01951 + 0.I
u = 0.713912 + 0.305839I
a = 0
b = 0.713912 + 0.305839I
c = −1.39861 − 0.80012I
d = −0.692808 − 0.761122I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.713912 − 0.305839I
a = 0
b = 0.713912 − 0.305839I
c = −1.39861 + 0.80012I
d = −0.692808 + 0.761122I
−0.26574 + 2.82812I 1.50976 − 2.97945I
66
XV. I
u
15
= hd + 1, c − u, b, a − u, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−1
a
11
=
u
−1
a
7
=
u
0
a
10
=
u
u − 1
a
2
=
1
0
a
1
=
1
0
a
12
=
u + 1
−1
a
6
=
1
u
a
8
=
u
0
a
5
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
67
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
2
c
3
, c
4
, c
5
c
6
, c
8
, c
10
c
12
u
2
+ 1
c
9
, c
11
(u − 1)
2
68
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
2
c
3
, c
4
, c
5
c
6
, c
8
, c
10
c
12
(y + 1)
2
c
9
, c
11
(y −1)
2
69
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
15
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.000000I
b = 0
c = 1.000000I
d = −1.00000
−1.64493 0
u = − 1.000000I
a = − 1.000000I
b = 0
c = − 1.000000I
d = −1.00000
−1.64493 0
70
XVI. I
u
16
= hd + 1, c − u, b − u, a − 1, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−1
a
11
=
u
−1
a
7
=
1
u
a
10
=
u
u − 1
a
2
=
u + 1
−1
a
1
=
u
−1
a
12
=
u
−1
a
6
=
1
u
a
8
=
u
0
a
5
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
71
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
(u − 1)
2
c
2
, c
3
, c
4
c
5
, c
7
, c
8
c
10
u
2
+ 1
c
6
, c
11
, c
12
u
2
72
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
(y −1)
2
c
2
, c
3
, c
4
c
5
, c
7
, c
8
c
10
(y + 1)
2
c
6
, c
11
, c
12
y
2
73
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
16
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.00000
b = 1.000000I
c = 1.000000I
d = −1.00000
−1.64493 0
u = − 1.000000I
a = 1.00000
b = − 1.000000I
c = − 1.000000I
d = −1.00000
−1.64493 0
74
XVII. I
u
17
= hd − u, c, b − u, a − 1, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−1
a
11
=
0
u
a
7
=
1
u
a
10
=
0
u
a
2
=
u + 1
−1
a
1
=
u
−1
a
12
=
u
u − 1
a
6
=
0
−1
a
8
=
u
0
a
5
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
75
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u − 1)
2
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
12
u
2
+ 1
c
5
, c
9
, c
10
u
2
76
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y −1)
2
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
12
(y + 1)
2
c
5
, c
9
, c
10
y
2
77
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
17
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.00000
b = 1.000000I
c = 0
d = 1.000000I
−1.64493 0
u = − 1.000000I
a = 1.00000
b = − 1.000000I
c = 0
d = − 1.000000I
−1.64493 0
78
XVIII. I
u
18
= hda + u + 1, c − u, b − u, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−1
a
11
=
u
d
a
7
=
a
u
a
10
=
u
d + u
a
2
=
au + 1
−1
a
1
=
au
−1
a
12
=
−au + u
d + 1
a
6
=
1
−du
a
8
=
u
0
a
5
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
79
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
18
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
c = ···
d = ···
−3.28987 −6.00000
80
XIX. I
v
1
= ha, d + v, c + a + 1, b − v, v
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
11
=
−1
−v
a
7
=
0
v
a
10
=
v −1
−v
a
2
=
1
−1
a
1
=
0
−1
a
12
=
−1
−v −1
a
6
=
−v
1
a
8
=
v
0
a
5
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
81
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
(u − 1)
2
c
2
, c
5
, c
6
c
7
, c
10
, c
12
u
2
+ 1
c
3
, c
4
, c
8
u
2
82
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
(y −1)
2
c
2
, c
5
, c
6
c
7
, c
10
, c
12
(y + 1)
2
c
3
, c
4
, c
8
y
2
83
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.000000I
a = 0
b = 1.000000I
c = −1.00000
d = − 1.000000I
−4.93480 −12.0000
v = − 1.000000I
a = 0
b = − 1.000000I
c = −1.00000
d = 1.000000I
−4.93480 −12.0000
84
XX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
u
2
(u − 1)
6
(u
3
+ 3u
2
+ 2u − 1)
2
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
5
· (u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
5
· (u
8
+ 6u
7
+ 13u
6
+ 10u
5
− 2u
4
− 4u
3
+ u
2
+ 3u + 4)
· (u
10
+ 4u
9
+ 10u
8
+ 14u
7
+ 15u
6
+ 10u
5
+ 7u
4
+ 5u
3
+ 11u
2
+ 11u + 4)
2
· (u
10
+ 5u
9
+ 11u
8
+ 13u
7
+ 8u
6
+ 2u
5
+ u
4
− u
3
+ 16u + 16)
· (u
12
+ 5u
11
+ ··· + 6u + 1)
c
2
, c
5
, c
6
c
7
, c
10
, c
12
u
2
(u
2
+ 1)
3
(u
3
− u
2
+ 2u − 1)
2
(u
4
+ u
2
− u + 1)
5
· (u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
5
· (u
8
+ 3u
6
− 2u
5
+ 2u
4
− 4u
3
+ u
2
− u + 2)
· (u
10
− 2u
9
+ 4u
8
− 4u
7
+ 5u
6
− 6u
5
+ 7u
4
− 7u
3
+ 5u
2
− 3u + 2)
2
· (u
10
+ u
9
+ 3u
8
+ 3u
7
+ 4u
6
+ 4u
5
+ 3u
4
+ 5u
3
+ 4u
2
+ 4u + 4)
· (u
12
+ u
11
+ 3u
10
+ 3u
9
+ 7u
8
+ 7u
7
+ 8u
6
+ 7u
5
+ 9u
4
+ 6u
3
+ 3u
2
+ 1)
c
3
, c
4
, c
8
u
2
(u
2
+ 1)
3
(u
3
− u
2
+ 2u − 1)
6
(u
4
+ u
2
− u + 1)
· (u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
· (u
8
+ 3u
6
− 2u
5
+ 2u
4
− 4u
3
+ u
2
− u + 2)
3
· (u
10
+ u
9
+ 6u
8
+ 6u
7
+ 13u
6
+ 13u
5
+ 11u
4
+ 10u
3
+ 2u
2
+ 1)
3
· (u
12
+ u
11
+ ··· + 4u + 4)
85
XXI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
y
2
(y −1)
6
(y
3
− 5y
2
+ 10y −1)
2
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
5
· (y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
5
· (y
8
− 10y
7
+ 45y
6
− 102y
5
+ 82y
4
+ 24y
3
+ 9y
2
− y + 16)
· (y
10
− 3y
9
+ ··· − 256y + 256)(y
10
+ 4y
9
+ ··· − 33y + 16)
2
· (y
12
+ 9y
11
+ ··· + 18y + 1)
c
2
, c
5
, c
6
c
7
, c
10
, c
12
y
2
(y + 1)
6
(y
3
+ 3y
2
+ 2y −1)
2
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
5
· (y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
5
· (y
8
+ 6y
7
+ 13y
6
+ 10y
5
− 2y
4
− 4y
3
+ y
2
+ 3y + 4)
· (y
10
+ 4y
9
+ 10y
8
+ 14y
7
+ 15y
6
+ 10y
5
+ 7y
4
+ 5y
3
+ 11y
2
+ 11y + 4)
2
· (y
10
+ 5y
9
+ 11y
8
+ 13y
7
+ 8y
6
+ 2y
5
+ y
4
− y
3
+ 16y + 16)
· (y
12
+ 5y
11
+ ··· + 6y + 1)
c
3
, c
4
, c
8
y
2
(y + 1)
6
(y
3
+ 3y
2
+ 2y −1)
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
· (y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
· (y
8
+ 6y
7
+ 13y
6
+ 10y
5
− 2y
4
− 4y
3
+ y
2
+ 3y + 4)
3
· ((y
10
+ 11y
9
+ ··· + 4y + 1)
3
)(y
12
+ 11y
11
+ ··· + 48y + 16)
86
