12a
0750
(K12a
0750
)
A knot diagram
1
Linearized knot diagam
3 8 10 9 11 1 12 2 4 6 5 7
Solving Sequence
6,11
5
7,12
8 1
4,10
3 2 9
c
5
c
11
c
7
c
12
c
10
c
3
c
2
c
9
c
1
, c
4
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
2
+ d, −u
9
+ 2u
8
− 7u
7
+ 12u
6
− 18u
5
+ 23u
4
− 17u
3
+ 10u
2
+ 4c − u − 3,
− u
9
+ 2u
8
− 7u
7
+ 12u
6
− 18u
5
+ 23u
4
− 17u
3
+ 10u
2
+ 4b − u + 1,
− u
9
+ 2u
8
− 7u
7
+ 12u
6
− 18u
5
+ 23u
4
− 17u
3
+ 10u
2
+ 4a − u − 3,
u
10
− u
9
+ 7u
8
− 7u
7
+ 18u
6
− 17u
5
+ 18u
4
− 15u
3
+ 3u
2
+ 1i
I
u
2
= h−u
2
+ d, u
6
+ 2u
5
+ 5u
4
+ 6u
3
+ 5u
2
+ c + 3u + 1, b − 1, −u
7
− 2u
6
− 6u
5
− 6u
4
− 8u
3
− 3u
2
+ 2a − u − 1,
u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 10u
4
+ 9u
3
+ 5u
2
+ 3u + 2i
I
u
3
= h−u
6
− u
5
− 3u
4
− 2u
3
− u
2
+ d − u + 1, −u
7
− 2u
6
− 6u
5
− 6u
4
− 8u
3
− 3u
2
+ 2c − u − 1,
u
6
+ 2u
5
+ 5u
4
+ 6u
3
+ 5u
2
+ b + 3u + 2, u
6
+ 2u
5
+ 5u
4
+ 6u
3
+ 5u
2
+ a + 3u + 1,
u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 10u
4
+ 9u
3
+ 5u
2
+ 3u + 2i
I
u
4
= h−u
6
− 2u
4
+ u
3
+ 2d + 2u + 2, u
7
− u
6
+ 3u
5
− u
4
+ 3u
3
− u
2
+ 4c + 2u − 4, b − 1,
u
7
− u
6
+ 3u
5
− u
4
+ 3u
3
− u
2
+ 4a + 2u − 4, u
8
− u
7
+ 3u
6
− 3u
5
+ 3u
4
− 5u
3
+ 4u
2
− 4u + 4i
I
u
5
= h−u
2
+ d, −u
2
+ c + u, b − 1, a
2
+ 2u
2
− a − u + 5, u
3
+ 2u + 1i
I
u
6
= hu
2
c + d + 1, c
2
+ 2u
2
− c − u + 5, −u
2
+ b + u + 1, −u
2
+ a + u, u
3
+ 2u + 1i
I
u
7
= h−u
4
+ d − u + 1, −u
5
− u
3
+ 2c − u − 1, b − 1, −u
5
− u
3
+ 2a − u − 1, u
6
+ u
4
+ 2u
3
+ u
2
+ u + 2i
I
u
8
= h−u
2
+ d, −u
2
+ c + u, −u
2
+ b + u + 1, −u
2
+ a + u, u
3
+ 2u + 1i
I
u
9
= h−u
2
+ d, 2u
3
− 2u
2
+ c + 2u − 1, b − 1, u
3
+ a + 2u − 1, u
4
− u
3
+ 2u
2
− 2u + 1i
I
u
10
= h−u
3
+ u
2
+ d − u + 2, u
3
+ c + 2u − 1, b − 1, −u
3
+ a − 2u, u
4
− u
3
+ 2u
2
− 2u + 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−u
3
+ u
2
+ d − u + 2, u
3
+ c + 2u − 1, b − 1, u
3
+ a + 2u − 1, u
4
− u
3
+ 2u
2
− 2u + 1i
I
u
12
= h−u
3
+ u
2
+ d − u + 2, u
3
+ c + 2u − 1, 2u
3
− 2u
2
+ b + 2u, 2u
3
− 2u
2
+ a + 2u − 1, u
4
− u
3
+ 2u
2
− 2u + 1i
I
u
13
= hu
3
+ d + u, −u
3
+ c − 2u, b − 1, u
3
+ a + 2u − 1, u
4
− u
3
+ 2u
2
− 2u + 1i
I
u
14
= hau + d + a − u, c + a − 1, b − 1, a
2
− a + u + 1, u
2
+ u + 1i
I
u
15
= hd + 1, c − u, b + u − 1, a + u, u
2
+ 1i
I
u
16
= hd, c − 1, b − u − 1, a − u, u
2
+ 1i
I
u
17
= hd + 1, c + u, b − 1, a − 1, u
2
+ 1i
I
u
18
= hd + 1, ca + u − 1, b − a − 1, u
2
+ 1i
I
v
1
= ha, d + 1, c + a − v −2, b −1, v
2
+ 1i
* 18 irreducible components of dim
C
= 0, with total 87 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.
2
I. I
u
1
= h−u
2
+ d, −u
9
+ 2u
8
+ · · · + 4c − 3, −u
9
+ 2u
8
+ · · · + 4b + 1, −u
9
+
2u
8
+ · · · + 4a − 3, u
10
− u
9
+ · · · + 3u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
1
4
u
9
−
1
2
u
8
+ ··· +
1
4
u +
3
4
u
2
a
12
=
−u
u
3
+ u
a
8
=
1
4
u
9
−
1
2
u
8
+ ··· +
1
4
u +
3
4
u
4
+ 2u
2
a
1
=
1
4
u
9
+
5
4
u
7
+ ··· −
7
4
u +
1
4
u
a
4
=
1
4
u
9
−
1
2
u
8
+ ··· +
1
4
u +
3
4
1
4
u
9
−
1
2
u
8
+ ··· +
1
4
u −
1
4
a
10
=
u
u
a
3
=
1
4
u
9
−
1
2
u
8
+ ··· +
1
4
u +
3
4
1
4
u
9
−
1
2
u
8
+ ··· +
1
4
u −
1
4
a
2
=
−u
3
− 2u + 1
−
1
4
u
9
−
7
4
u
7
+ ··· +
5
4
u +
1
4
a
9
=
−
1
4
u
9
−
5
4
u
7
+ ··· +
7
4
u −
1
4
−
1
4
u
9
−
5
4
u
7
+ ··· +
3
4
u −
1
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3u
8
− u
7
+ 18u
6
− 8u
5
+ 36u
4
− 19u
3
+ 20u
2
− 16u − 11
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ 3u
9
+ 8u
8
+ 10u
7
+ 14u
6
+ 8u
5
+ 5u
4
+ 15u
3
+ 48u
2
+ 48u + 16
c
2
, c
8
u
10
− u
9
+ 2u
8
− 2u
7
+ 4u
6
− 6u
5
+ 5u
4
− 7u
3
+ 8u
2
− 4u + 4
c
3
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
u
10
− u
9
+ 7u
8
− 7u
7
+ 18u
6
− 17u
5
+ 18u
4
− 15u
3
+ 3u
2
+ 1
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
+ 7y
9
+ ··· − 768y + 256
c
2
, c
8
y
10
+ 3y
9
+ 8y
8
+ 10y
7
+ 14y
6
+ 8y
5
+ 5y
4
+ 15y
3
+ 48y
2
+ 48y + 16
c
3
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y
10
+ 13y
9
+ ··· + 6y + 1
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.679448 + 0.180150I
a = 0.359501 − 0.232867I
b = −0.640499 − 0.232867I
c = 0.359501 − 0.232867I
d = 0.429196 + 0.244805I
−3.36992 − 3.42590I −13.9202 + 5.8734I
u = 0.679448 − 0.180150I
a = 0.359501 + 0.232867I
b = −0.640499 + 0.232867I
c = 0.359501 + 0.232867I
d = 0.429196 − 0.244805I
−3.36992 + 3.42590I −13.9202 − 5.8734I
u = 0.40586 + 1.47601I
a = −1.82314 − 0.97271I
b = −2.82314 − 0.97271I
c = −1.82314 − 0.97271I
d = −2.01389 + 1.19812I
12.8882 − 16.0216I −1.20715 + 8.19647I
u = 0.40586 − 1.47601I
a = −1.82314 + 0.97271I
b = −2.82314 + 0.97271I
c = −1.82314 + 0.97271I
d = −2.01389 − 1.19812I
12.8882 + 16.0216I −1.20715 − 8.19647I
u = −0.34141 + 1.51774I
a = −1.95611 + 0.83479I
b = −2.95611 + 0.83479I
c = −1.95611 + 0.83479I
d = −2.18697 − 1.03634I
15.7344 + 9.7447I 1.47516 − 4.40501I
u = −0.34141 − 1.51774I
a = −1.95611 − 0.83479I
b = −2.95611 − 0.83479I
c = −1.95611 − 0.83479I
d = −2.18697 + 1.03634I
15.7344 − 9.7447I 1.47516 + 4.40501I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.05876 + 1.63300I
a = −2.18667 + 0.13692I
b = −3.18667 + 0.13692I
c = −2.18667 + 0.13692I
d = −2.66324 − 0.19191I
−19.6670 + 3.4566I 2.19060 − 2.42157I
u = −0.05876 − 1.63300I
a = −2.18667 − 0.13692I
b = −3.18667 − 0.13692I
c = −2.18667 − 0.13692I
d = −2.66324 + 0.19191I
−19.6670 − 3.4566I 2.19060 + 2.42157I
u = −0.185141 + 0.315240I
a = 1.106430 + 0.262999I
b = 0.106427 + 0.262999I
c = 1.106430 + 0.262999I
d = −0.0650991 − 0.1167280I
−0.650910 + 0.940213I −10.53842 − 6.80546I
u = −0.185141 − 0.315240I
a = 1.106430 − 0.262999I
b = 0.106427 − 0.262999I
c = 1.106430 − 0.262999I
d = −0.0650991 + 0.1167280I
−0.650910 − 0.940213I −10.53842 + 6.80546I
7
II. I
u
2
= h−u
2
+ d, u
6
+ 2u
5
+ · · · + c + 1, b − 1, −u
7
− 2u
6
+ · · · + 2a −
1, u
8
+ 2u
7
+ · · · + 3u + 2i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
−u
6
− 2u
5
− 5u
4
− 6u
3
− 5u
2
− 3u − 1
u
2
a
12
=
−u
u
3
+ u
a
8
=
−u
6
− 2u
5
− 5u
4
− 6u
3
− 6u
2
− 3u − 1
u
4
+ 2u
2
a
1
=
u
7
+ 2u
6
+ 5u
5
+ 6u
4
+ 5u
3
+ 3u
2
u
a
4
=
1
2
u
7
+ u
6
+ ··· +
1
2
u +
1
2
1
a
10
=
u
u
a
3
=
1
2
u
7
+ 2u
6
+ ··· +
3
2
u +
1
2
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u + 1
a
2
=
1
2
u
7
+ u
6
+ ··· −
3
2
u −
1
2
−u
7
− u
6
− 4u
5
− 3u
4
− 4u
3
− 2u
2
− 1
a
9
=
1
2
u
7
+ u
6
+ ··· +
5
2
u +
3
2
−u
5
− u
4
− 3u
3
− 2u
2
− u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
− 2u
6
− 12u
5
− 2u
4
− 4u
3
+ 2u
2
+ 6u − 2
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ 3u
7
+ 8u
6
+ 10u
5
+ 14u
4
+ 11u
3
+ 12u
2
+ 4u + 1
c
2
, c
8
u
8
− u
7
+ 2u
6
− 2u
5
+ 4u
4
− 3u
3
+ 2u
2
+ 1
c
3
, c
4
, c
9
u
8
− u
7
+ 3u
6
− 3u
5
+ 3u
4
− 5u
3
+ 4u
2
− 4u + 4
c
5
, c
6
, c
7
c
10
, c
11
, c
12
u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 10u
4
+ 9u
3
+ 5u
2
+ 3u + 2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
+ 7y
7
+ 32y
6
+ 82y
5
+ 146y
4
+ 151y
3
+ 84y
2
+ 8y + 1
c
2
, c
8
y
8
+ 3y
7
+ 8y
6
+ 10y
5
+ 14y
4
+ 11y
3
+ 12y
2
+ 4y + 1
c
3
, c
4
, c
9
y
8
+ 5y
7
+ 9y
6
+ 7y
5
+ 3y
4
− y
3
+ 16y + 16
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
8
+ 8y
7
+ 24y
6
+ 30y
5
+ 8y
4
− 5y
3
+ 11y
2
+ 11y + 4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.832019 + 0.315048I
a = 0.187629 + 1.339450I
b = 1.00000
c = 0.132804 + 0.372803I
d = 0.593000 − 0.524253I
1.55583 + 6.79402I −7.11839 − 7.09473I
u = −0.832019 − 0.315048I
a = 0.187629 − 1.339450I
b = 1.00000
c = 0.132804 − 0.372803I
d = 0.593000 + 0.524253I
1.55583 − 6.79402I −7.11839 + 7.09473I
u = 0.251759 + 0.670878I
a = −0.545199 − 0.612937I
b = 1.00000
c = 1.50200 − 1.37807I
d = −0.386695 + 0.337799I
3.51088 − 1.27680I −2.16898 + 5.88514I
u = 0.251759 − 0.670878I
a = −0.545199 + 0.612937I
b = 1.00000
c = 1.50200 + 1.37807I
d = −0.386695 − 0.337799I
3.51088 + 1.27680I −2.16898 − 5.88514I
u = −0.09342 + 1.48598I
a = 0.448861 + 0.552340I
b = 1.00000
c = −2.58269 + 0.36635I
d = −2.19941 − 0.27763I
10.73060 − 0.66722I 0.81639 + 2.10627I
u = −0.09342 − 1.48598I
a = 0.448861 − 0.552340I
b = 1.00000
c = −2.58269 − 0.36635I
d = −2.19941 + 0.27763I
10.73060 + 0.66722I 0.81639 − 2.10627I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.32632 + 1.45375I
a = 0.658708 − 0.606572I
b = 1.00000
c = −2.05212 + 0.99140I
d = −2.00689 − 0.94878I
7.23180 + 10.98940I −3.52901 − 7.14773I
u = −0.32632 − 1.45375I
a = 0.658708 + 0.606572I
b = 1.00000
c = −2.05212 − 0.99140I
d = −2.00689 + 0.94878I
7.23180 − 10.98940I −3.52901 + 7.14773I
12
III. I
u
3
= h−u
6
− u
5
+ · · · + d + 1, −u
7
− 2u
6
+ · · · + 2c − 1, u
6
+ 2u
5
+ · · · +
b + 2, u
6
+ 2u
5
+ · · · + a + 1, u
8
+ 2u
7
+ · · · + 3u + 2i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
1
2
u
7
+ u
6
+ ··· +
1
2
u +
1
2
u
6
+ u
5
+ 3u
4
+ 2u
3
+ u
2
+ u − 1
a
12
=
−u
u
3
+ u
a
8
=
1
2
u
7
+ 2u
6
+ ··· +
3
2
u +
1
2
u
7
+ 3u
6
+ 6u
5
+ 8u
4
+ 8u
3
+ 4u
2
+ 3u + 1
a
1
=
−
1
2
u
7
− u
6
+ ··· −
5
2
u −
3
2
−u
5
− u
4
− 3u
3
− 2u
2
− 2u − 1
a
4
=
−u
6
− 2u
5
− 5u
4
− 6u
3
− 5u
2
− 3u − 1
−u
6
− 2u
5
− 5u
4
− 6u
3
− 5u
2
− 3u − 2
a
10
=
u
u
a
3
=
−u
6
− 2u
5
− 5u
4
− 6u
3
− 6u
2
− 3u − 1
−u
6
− 2u
5
− 5u
4
− 6u
3
− 6u
2
− 3u − 2
a
2
=
1
2
u
7
− 2u
4
+ ··· −
3
2
u −
1
2
u
7
+ u
5
− 2u
4
− 3u
3
− 3u
2
− 2u − 1
a
9
=
−u
7
− 2u
6
− 5u
5
− 6u
4
− 5u
3
− 3u
2
−u
7
− 2u
6
− 5u
5
− 6u
4
− 5u
3
− 3u
2
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
− 2u
6
− 12u
5
− 2u
4
− 4u
3
+ 2u
2
+ 6u − 2
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ 3u
7
+ 8u
6
+ 10u
5
+ 14u
4
+ 11u
3
+ 12u
2
+ 4u + 1
c
2
, c
8
u
8
− u
7
+ 2u
6
− 2u
5
+ 4u
4
− 3u
3
+ 2u
2
+ 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 10u
4
+ 9u
3
+ 5u
2
+ 3u + 2
c
6
, c
7
, c
12
u
8
− u
7
+ 3u
6
− 3u
5
+ 3u
4
− 5u
3
+ 4u
2
− 4u + 4
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
+ 7y
7
+ 32y
6
+ 82y
5
+ 146y
4
+ 151y
3
+ 84y
2
+ 8y + 1
c
2
, c
8
y
8
+ 3y
7
+ 8y
6
+ 10y
5
+ 14y
4
+ 11y
3
+ 12y
2
+ 4y + 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
8
+ 8y
7
+ 24y
6
+ 30y
5
+ 8y
4
− 5y
3
+ 11y
2
+ 11y + 4
c
6
, c
7
, c
12
y
8
+ 5y
7
+ 9y
6
+ 7y
5
+ 3y
4
− y
3
+ 16y + 16
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.832019 + 0.315048I
a = 0.132804 + 0.372803I
b = −0.867196 + 0.372803I
c = 0.187629 + 1.339450I
d = −1.81347 − 0.69593I
1.55583 + 6.79402I −7.11839 − 7.09473I
u = −0.832019 − 0.315048I
a = 0.132804 − 0.372803I
b = −0.867196 − 0.372803I
c = 0.187629 − 1.339450I
d = −1.81347 + 0.69593I
1.55583 − 6.79402I −7.11839 + 7.09473I
u = 0.251759 + 0.670878I
a = 1.50200 − 1.37807I
b = 0.50200 − 1.37807I
c = −0.545199 − 0.612937I
d = −1.41788 − 0.05285I
3.51088 − 1.27680I −2.16898 + 5.88514I
u = 0.251759 − 0.670878I
a = 1.50200 + 1.37807I
b = 0.50200 + 1.37807I
c = −0.545199 + 0.612937I
d = −1.41788 + 0.05285I
3.51088 + 1.27680I −2.16898 − 5.88514I
u = −0.09342 + 1.48598I
a = −2.58269 + 0.36635I
b = −3.58269 + 0.36635I
c = 0.448861 + 0.552340I
d = −0.166115 + 1.339440I
10.73060 − 0.66722I 0.81639 + 2.10627I
u = −0.09342 − 1.48598I
a = −2.58269 − 0.36635I
b = −3.58269 − 0.36635I
c = 0.448861 − 0.552340I
d = −0.166115 − 1.339440I
10.73060 + 0.66722I 0.81639 − 2.10627I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.32632 + 1.45375I
a = −2.05212 + 0.99140I
b = −3.05212 + 0.99140I
c = 0.658708 − 0.606572I
d = 0.897463 − 0.592355I
7.23180 + 10.98940I −3.52901 − 7.14773I
u = −0.32632 − 1.45375I
a = −2.05212 − 0.99140I
b = −3.05212 − 0.99140I
c = 0.658708 + 0.606572I
d = 0.897463 + 0.592355I
7.23180 − 10.98940I −3.52901 + 7.14773I
17
IV. I
u
4
= h−u
6
− 2u
4
+ · · · + 2d + 2, u
7
− u
6
+ · · · + 4c − 4, b − 1, u
7
− u
6
+
· · · + 4a − 4, u
8
− u
7
+ · · · − 4u + 4i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
−
1
4
u
7
+
1
4
u
6
+ ··· −
1
2
u + 1
1
2
u
6
+ u
4
−
1
2
u
3
− u − 1
a
12
=
−u
u
3
+ u
a
8
=
−
1
4
u
7
+
3
4
u
6
+ ··· −
3
2
u + 1
−
1
2
u
7
+
1
2
u
6
+ ··· − 2u + 1
a
1
=
−
1
4
u
7
+
1
4
u
6
+ ··· − u + 1
−
1
2
u
5
− u
3
+
1
2
u
2
− u + 1
a
4
=
−
1
4
u
7
+
1
4
u
6
+ ··· −
1
2
u + 1
1
a
10
=
u
u
a
3
=
−
1
4
u
7
+
3
4
u
6
+ ··· −
3
2
u + 1
1
2
u
6
+ u
4
−
1
2
u
3
+ u
2
− u + 1
a
2
=
1
2
u
6
−
1
2
u
5
+ ··· −
1
2
u + 1
1
2
u
7
+
1
2
u
6
+ ··· −
1
2
u
2
− u
a
9
=
1
4
u
7
−
1
4
u
6
+ ··· + u − 1
−
1
2
u
5
− u
3
+
1
2
u
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
7
+ 3u
6
+ u
5
+ 3u
4
− u
3
+ u
2
− 6u + 2
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ 3u
7
+ 8u
6
+ 10u
5
+ 14u
4
+ 11u
3
+ 12u
2
+ 4u + 1
c
2
, c
8
u
8
− u
7
+ 2u
6
− 2u
5
+ 4u
4
− 3u
3
+ 2u
2
+ 1
c
3
, c
4
, c
6
c
7
, c
9
, c
12
u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 10u
4
+ 9u
3
+ 5u
2
+ 3u + 2
c
5
, c
10
, c
11
u
8
− u
7
+ 3u
6
− 3u
5
+ 3u
4
− 5u
3
+ 4u
2
− 4u + 4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
+ 7y
7
+ 32y
6
+ 82y
5
+ 146y
4
+ 151y
3
+ 84y
2
+ 8y + 1
c
2
, c
8
y
8
+ 3y
7
+ 8y
6
+ 10y
5
+ 14y
4
+ 11y
3
+ 12y
2
+ 4y + 1
c
3
, c
4
, c
6
c
7
, c
9
, c
12
y
8
+ 8y
7
+ 24y
6
+ 30y
5
+ 8y
4
− 5y
3
+ 11y
2
+ 11y + 4
c
5
, c
10
, c
11
y
8
+ 5y
7
+ 9y
6
+ 7y
5
+ 3y
4
− y
3
+ 16y + 16
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.993174 + 0.298213I
a = 0.295449 − 1.252190I
b = 1.00000
c = 0.295449 − 1.252190I
d = −2.00689 + 0.94878I
7.23180 − 10.98940I −3.52901 + 7.14773I
u = 0.993174 − 0.298213I
a = 0.295449 + 1.252190I
b = 1.00000
c = 0.295449 + 1.252190I
d = −2.00689 − 0.94878I
7.23180 + 10.98940I −3.52901 − 7.14773I
u = −0.769280 + 0.870579I
a = 0.094762 + 0.907210I
b = 1.00000
c = 0.094762 + 0.907210I
d = −2.19941 + 0.27763I
10.73060 + 0.66722I 0.81639 − 2.10627I
u = −0.769280 − 0.870579I
a = 0.094762 − 0.907210I
b = 1.00000
c = 0.094762 − 0.907210I
d = −2.19941 − 0.27763I
10.73060 − 0.66722I 0.81639 + 2.10627I
u = 0.022189 + 1.190950I
a = 0.440820 − 0.221811I
b = 1.00000
c = 0.440820 − 0.221811I
d = −0.386695 − 0.337799I
3.51088 + 1.27680I −2.16898 − 5.88514I
u = 0.022189 − 1.190950I
a = 0.440820 + 0.221811I
b = 1.00000
c = 0.440820 + 0.221811I
d = −0.386695 + 0.337799I
3.51088 − 1.27680I −2.16898 + 5.88514I
21
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.253917 + 1.370380I
a = 0.668969 + 0.545807I
b = 1.00000
c = 0.668969 + 0.545807I
d = 0.593000 + 0.524253I
1.55583 − 6.79402I −7.11839 + 7.09473I
u = 0.253917 − 1.370380I
a = 0.668969 − 0.545807I
b = 1.00000
c = 0.668969 − 0.545807I
d = 0.593000 − 0.524253I
1.55583 + 6.79402I −7.11839 − 7.09473I
22
V. I
u
5
= h−u
2
+ d, −u
2
+ c + u, b − 1, a
2
+ 2u
2
− a − u + 5, u
3
+ 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
u
2
− u
u
2
a
12
=
−u
−u − 1
a
8
=
−u
−u
a
1
=
u
2
+ u + 1
u
a
4
=
a
1
a
10
=
u
u
a
3
=
−u
2
a + u
2
+ a
−u
2
a + u
2
+ 1
a
2
=
a
1
a
9
=
u
2
+ 2
au
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
+ 4u − 10
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ u
2
+ 3u + 4
c
2
, c
3
, c
4
c
8
, c
9
u
6
+ u
4
+ 2u
3
+ u
2
+ u + 2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
(u
3
+ 2u + 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
+ 2y
5
+ 3y
4
− 2y
3
+ 13y
2
− y + 16
c
2
, c
3
, c
4
c
8
, c
9
y
6
+ 2y
5
+ 3y
4
+ 2y
3
+ y
2
+ 3y + 4
c
5
, c
6
, c
7
c
10
, c
11
, c
12
(y
3
+ 4y
2
+ 4y −1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22670 + 1.46771I
a = 0.618738 + 0.576047I
b = 1.00000
c = −2.32948 − 0.80225I
d = −2.10278 + 0.66546I
9.44074 − 5.13794I −0.68207 + 3.20902I
u = 0.22670 + 1.46771I
a = 0.381262 − 0.576047I
b = 1.00000
c = −2.32948 − 0.80225I
d = −2.10278 + 0.66546I
9.44074 − 5.13794I −0.68207 + 3.20902I
u = 0.22670 − 1.46771I
a = 0.618738 − 0.576047I
b = 1.00000
c = −2.32948 + 0.80225I
d = −2.10278 − 0.66546I
9.44074 + 5.13794I −0.68207 − 3.20902I
u = 0.22670 − 1.46771I
a = 0.381262 + 0.576047I
b = 1.00000
c = −2.32948 + 0.80225I
d = −2.10278 − 0.66546I
9.44074 + 5.13794I −0.68207 − 3.20902I
u = −0.453398
a = 0.50000 + 2.36950I
b = 1.00000
c = 0.658967
d = 0.205569
−0.787199 −12.6360
u = −0.453398
a = 0.50000 − 2.36950I
b = 1.00000
c = 0.658967
d = 0.205569
−0.787199 −12.6360
26
VI.
I
u
6
= hu
2
c+d+1, c
2
+2u
2
−c−u+5, −u
2
+b+u+1, −u
2
+a+u, u
3
+2u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
c
−u
2
c − 1
a
12
=
−u
−u − 1
a
8
=
−u
2
c + u
2
+ c
−2u
2
c − cu + u
2
+ u − 1
a
1
=
−u
2
− 2
cu − u
a
4
=
u
2
− u
u
2
− u − 1
a
10
=
u
u
a
3
=
−u
−u − 1
a
2
=
2cu − u
2
+ c − u − 2
−u
2
c + 3cu + c − 2u − 1
a
9
=
−u
2
− u − 1
−u
2
− 2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
+ 4u − 10
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ u
2
+ 3u + 4
c
2
, c
6
, c
7
c
8
, c
12
u
6
+ u
4
+ 2u
3
+ u
2
+ u + 2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(u
3
+ 2u + 1)
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
+ 2y
5
+ 3y
4
− 2y
3
+ 13y
2
− y + 16
c
2
, c
6
, c
7
c
8
, c
12
y
6
+ 2y
5
+ 3y
4
+ 2y
3
+ y
2
+ 3y + 4
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y
3
+ 4y
2
+ 4y −1)
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22670 + 1.46771I
a = −2.32948 − 0.80225I
b = −3.32948 − 0.80225I
c = 0.618738 + 0.576047I
d = 0.684408 + 0.799560I
9.44074 − 5.13794I −0.68207 + 3.20902I
u = 0.22670 + 1.46771I
a = −2.32948 − 0.80225I
b = −3.32948 − 0.80225I
c = 0.381262 − 0.576047I
d = −0.58162 − 1.46502I
9.44074 − 5.13794I −0.68207 + 3.20902I
u = 0.22670 − 1.46771I
a = −2.32948 + 0.80225I
b = −3.32948 + 0.80225I
c = 0.618738 − 0.576047I
d = 0.684408 − 0.799560I
9.44074 + 5.13794I −0.68207 − 3.20902I
u = 0.22670 − 1.46771I
a = −2.32948 + 0.80225I
b = −3.32948 + 0.80225I
c = 0.381262 + 0.576047I
d = −0.58162 + 1.46502I
9.44074 + 5.13794I −0.68207 − 3.20902I
u = −0.453398
a = 0.658967
b = −0.341033
c = 0.50000 + 2.36950I
d = −1.102790 − 0.487097I
−0.787199 −12.6360
u = −0.453398
a = 0.658967
b = −0.341033
c = 0.50000 − 2.36950I
d = −1.102790 + 0.487097I
−0.787199 −12.6360
30
VII. I
u
7
= h−u
4
+ d − u + 1, −u
5
− u
3
+ 2c − u − 1, b − 1, −u
5
− u
3
+ 2a −
u − 1, u
6
+ u
4
+ 2u
3
+ u
2
+ u + 2i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
1
2
u
5
+
1
2
u
3
+
1
2
u +
1
2
u
4
+ u − 1
a
12
=
−u
u
3
+ u
a
8
=
1
2
u
5
+ u
4
+ ··· +
3
2
u +
1
2
u
3
+ u + 1
a
1
=
−
1
2
u
5
−
1
2
u
3
− u
2
−
1
2
u −
1
2
−u
3
− u − 1
a
4
=
1
2
u
5
+
1
2
u
3
+
1
2
u +
1
2
1
a
10
=
u
u
a
3
=
1
2
u
5
+ u
4
+ ··· +
3
2
u +
1
2
u
4
+ u
2
+ u + 1
a
2
=
−
1
2
u
5
+ u
4
+
1
2
u
3
+
3
2
u +
3
2
1
a
9
=
1
2
u
5
+
1
2
u
3
+ u
2
+
1
2
u +
1
2
−u
3
− 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
− 4u
3
− 8u − 10
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ u
2
+ 3u + 4
c
2
, c
5
, c
8
c
10
, c
11
u
6
+ u
4
+ 2u
3
+ u
2
+ u + 2
c
3
, c
4
, c
6
c
7
, c
9
, c
12
(u
3
+ 2u + 1)
2
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
+ 2y
5
+ 3y
4
− 2y
3
+ 13y
2
− y + 16
c
2
, c
5
, c
8
c
10
, c
11
y
6
+ 2y
5
+ 3y
4
+ 2y
3
+ y
2
+ 3y + 4
c
3
, c
4
, c
6
c
7
, c
9
, c
12
(y
3
+ 4y
2
+ 4y −1)
2
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.931903 + 0.428993I
a = 0.201029 + 1.207160I
b = 1.00000
c = 0.201029 + 1.207160I
d = −2.10278 − 0.66546I
9.44074 + 5.13794I −0.68207 − 3.20902I
u = −0.931903 − 0.428993I
a = 0.201029 − 1.207160I
b = 1.00000
c = 0.201029 − 1.207160I
d = −2.10278 + 0.66546I
9.44074 − 5.13794I −0.68207 + 3.20902I
u = 0.226699 + 1.074330I
a = 0.914742 + 0.404039I
b = 1.00000
c = 0.914742 + 0.404039I
d = 0.205569
−0.787199 −12.63587 + 0.I
u = 0.226699 − 1.074330I
a = 0.914742 − 0.404039I
b = 1.00000
c = 0.914742 − 0.404039I
d = 0.205569
−0.787199 −12.63587 + 0.I
u = 0.705204 + 1.038720I
a = 0.134229 − 0.806035I
b = 1.00000
c = 0.134229 − 0.806035I
d = −2.10278 − 0.66546I
9.44074 + 5.13794I −0.68207 − 3.20902I
u = 0.705204 − 1.038720I
a = 0.134229 + 0.806035I
b = 1.00000
c = 0.134229 + 0.806035I
d = −2.10278 + 0.66546I
9.44074 − 5.13794I −0.68207 + 3.20902I
34
VIII. I
u
8
= h−u
2
+ d, −u
2
+ c + u, −u
2
+ b + u + 1, −u
2
+ a + u, u
3
+ 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
u
2
− u
u
2
a
12
=
−u
−u − 1
a
8
=
−u
−u
a
1
=
u
2
+ u + 1
u
a
4
=
u
2
− u
u
2
− u − 1
a
10
=
u
u
a
3
=
−u
−u − 1
a
2
=
u
2
− u
u
2
− u − 1
a
9
=
−u
2
− u − 1
−u
2
− 2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
+ 4u − 10
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ 4u
2
+ 4u − 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u
3
+ 2u + 1
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
− 8y
2
+ 24y −1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
y
3
+ 4y
2
+ 4y −1
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22670 + 1.46771I
a = −2.32948 − 0.80225I
b = −3.32948 − 0.80225I
c = −2.32948 − 0.80225I
d = −2.10278 + 0.66546I
9.44074 − 5.13794I −0.68207 + 3.20902I
u = 0.22670 − 1.46771I
a = −2.32948 + 0.80225I
b = −3.32948 + 0.80225I
c = −2.32948 + 0.80225I
d = −2.10278 − 0.66546I
9.44074 + 5.13794I −0.68207 − 3.20902I
u = −0.453398
a = 0.658967
b = −0.341033
c = 0.658967
d = 0.205569
−0.787199 −12.6360
38
IX.
I
u
9
= h−u
2
+d, 2u
3
−2u
2
+c+2u−1, b−1, u
3
+a+2u−1, u
4
−u
3
+2u
2
−2u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
−2u
3
+ 2u
2
− 2u + 1
u
2
a
12
=
−u
u
3
+ u
a
8
=
−2u
3
+ u
2
− 2u + 1
u
3
+ 2u − 1
a
1
=
−2u
2
+ 2u − 2
u
a
4
=
−u
3
− 2u + 1
1
a
10
=
u
u
a
3
=
−u
u
3
+ u
a
2
=
u
3
− 2u
2
+ 2u − 2
1
a
9
=
u
3
− u
2
+ 2u − 2
−u
3
− u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u − 6
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 3u
3
+ 2u
2
+ 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u
4
− u
3
+ 2u
2
− 2u + 1
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 5y
3
+ 6y
2
+ 4y + 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621744 + 0.440597I
a = −0.121744 − 1.306620I
b = 1.00000
c = 0.384881 − 0.636296I
d = 0.192440 + 0.547877I
3.28987 − 2.02988I −4.00000 + 3.46410I
u = 0.621744 − 0.440597I
a = −0.121744 + 1.306620I
b = 1.00000
c = 0.384881 + 0.636296I
d = 0.192440 − 0.547877I
3.28987 + 2.02988I −4.00000 − 3.46410I
u = −0.121744 + 1.306620I
a = 0.621744 − 0.440597I
b = 1.00000
c = −3.38488 + 1.09575I
d = −1.69244 − 0.31815I
3.28987 + 2.02988I −4.00000 − 3.46410I
u = −0.121744 − 1.306620I
a = 0.621744 + 0.440597I
b = 1.00000
c = −3.38488 − 1.09575I
d = −1.69244 + 0.31815I
3.28987 − 2.02988I −4.00000 + 3.46410I
42
X. I
u
10
=
h−u
3
+u
2
+d−u+2, u
3
+c+2u−1, b−1, −u
3
+a−2u, u
4
−u
3
+2u
2
−2u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
−u
3
− 2u + 1
u
3
− u
2
+ u − 2
a
12
=
−u
u
3
+ u
a
8
=
−u
−u
a
1
=
−u
3
+ u
2
− 2u + 2
−u
3
− 2u + 1
a
4
=
u
3
+ 2u
1
a
10
=
u
u
a
3
=
u
2
+ u + 1
−u
3
+ u
2
− u + 2
a
2
=
u
3
+ 2u
1
a
9
=
u
3
− u
2
+ 2u − 2
u
3
+ 2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u − 6
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
, c
9
(u
2
+ u + 1)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
u
4
− u
3
+ 2u
2
− 2u + 1
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
, c
9
(y
2
+ y + 1)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621744 + 0.440597I
a = 1.12174 + 1.30662I
b = 1.00000
c = −0.121744 − 1.306620I
d = −1.69244 + 0.31815I
3.28987 − 2.02988I −4.00000 + 3.46410I
u = 0.621744 − 0.440597I
a = 1.12174 − 1.30662I
b = 1.00000
c = −0.121744 + 1.306620I
d = −1.69244 − 0.31815I
3.28987 + 2.02988I −4.00000 − 3.46410I
u = −0.121744 + 1.306620I
a = 0.378256 + 0.440597I
b = 1.00000
c = 0.621744 − 0.440597I
d = 0.192440 − 0.547877I
3.28987 + 2.02988I −4.00000 − 3.46410I
u = −0.121744 − 1.306620I
a = 0.378256 − 0.440597I
b = 1.00000
c = 0.621744 + 0.440597I
d = 0.192440 + 0.547877I
3.28987 − 2.02988I −4.00000 + 3.46410I
46
XI. I
u
11
=
h−u
3
+u
2
+d−u+2, u
3
+c+2u−1, b−1, u
3
+a+2u−1, u
4
−u
3
+2u
2
−2u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
−u
3
− 2u + 1
u
3
− u
2
+ u − 2
a
12
=
−u
u
3
+ u
a
8
=
−u
−u
a
1
=
−u
3
+ u
2
− 2u + 2
−u
3
− 2u + 1
a
4
=
−u
3
− 2u + 1
1
a
10
=
u
u
a
3
=
−u
u
3
+ u
a
2
=
−u
3
− 2u + 1
1
a
9
=
u
3
− u
2
+ 2u − 2
−u
3
− u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u − 6
47
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 3u
3
+ 2u
2
+ 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u
4
− u
3
+ 2u
2
− 2u + 1
48
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 5y
3
+ 6y
2
+ 4y + 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
49
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621744 + 0.440597I
a = −0.121744 − 1.306620I
b = 1.00000
c = −0.121744 − 1.306620I
d = −1.69244 + 0.31815I
3.28987 − 2.02988I −4.00000 + 3.46410I
u = 0.621744 − 0.440597I
a = −0.121744 + 1.306620I
b = 1.00000
c = −0.121744 + 1.306620I
d = −1.69244 − 0.31815I
3.28987 + 2.02988I −4.00000 − 3.46410I
u = −0.121744 + 1.306620I
a = 0.621744 − 0.440597I
b = 1.00000
c = 0.621744 − 0.440597I
d = 0.192440 − 0.547877I
3.28987 + 2.02988I −4.00000 − 3.46410I
u = −0.121744 − 1.306620I
a = 0.621744 + 0.440597I
b = 1.00000
c = 0.621744 + 0.440597I
d = 0.192440 + 0.547877I
3.28987 − 2.02988I −4.00000 + 3.46410I
50
XII. I
u
12
= h−u
3
+ u
2
+ d − u + 2, u
3
+ c + 2u − 1, 2u
3
− 2u
2
+ b + 2u, 2u
3
−
2u
2
+ a + 2u − 1, u
4
− u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
−u
3
− 2u + 1
u
3
− u
2
+ u − 2
a
12
=
−u
u
3
+ u
a
8
=
−u
−u
a
1
=
−u
3
+ u
2
− 2u + 2
−u
3
− 2u + 1
a
4
=
−2u
3
+ 2u
2
− 2u + 1
−2u
3
+ 2u
2
− 2u
a
10
=
u
u
a
3
=
−2u
3
+ u
2
− 2u + 1
−2u
3
+ u
2
− 2u
a
2
=
−2u
3
+ 2u
2
− 2u + 1
−2u
3
+ 2u
2
− 2u
a
9
=
2u
2
− 2u + 2
2u
2
− 3u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u − 6
51
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 3u
3
+ 2u
2
+ 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u
4
− u
3
+ 2u
2
− 2u + 1
52
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 5y
3
+ 6y
2
+ 4y + 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
53
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621744 + 0.440597I
a = 0.384881 − 0.636296I
b = −0.615119 − 0.636296I
c = −0.121744 − 1.306620I
d = −1.69244 + 0.31815I
3.28987 − 2.02988I −4.00000 + 3.46410I
u = 0.621744 − 0.440597I
a = 0.384881 + 0.636296I
b = −0.615119 + 0.636296I
c = −0.121744 + 1.306620I
d = −1.69244 − 0.31815I
3.28987 + 2.02988I −4.00000 − 3.46410I
u = −0.121744 + 1.306620I
a = −3.38488 + 1.09575I
b = −4.38488 + 1.09575I
c = 0.621744 − 0.440597I
d = 0.192440 − 0.547877I
3.28987 + 2.02988I −4.00000 − 3.46410I
u = −0.121744 − 1.306620I
a = −3.38488 − 1.09575I
b = −4.38488 − 1.09575I
c = 0.621744 + 0.440597I
d = 0.192440 + 0.547877I
3.28987 − 2.02988I −4.00000 + 3.46410I
54
XIII.
I
u
13
= hu
3
+ d + u, −u
3
+ c − 2u, b − 1, u
3
+ a + 2u − 1, u
4
− u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
7
=
u
3
+ 2u
−u
3
− u
a
12
=
−u
u
3
+ u
a
8
=
u
2
+ u + 1
−u
3
− u − 1
a
1
=
−u
3
+ u
2
− 2u + 2
u
3
+ u − 1
a
4
=
−u
3
− 2u + 1
1
a
10
=
u
u
a
3
=
−u
u
3
+ u
a
2
=
−2u
3
+ 2u
2
− 4u + 3
2u
3
+ 2u − 2
a
9
=
u
3
− u
2
+ 2u − 2
−u
3
− u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u − 6
55
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
(u
2
+ u + 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
4
− u
3
+ 2u
2
− 2u + 1
56
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
(y
2
+ y + 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
4
+ 3y
3
+ 2y
2
+ 1
57
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
13
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621744 + 0.440597I
a = −0.121744 − 1.306620I
b = 1.00000
c = 1.12174 + 1.30662I
d = −0.500000 − 0.866025I
3.28987 − 2.02988I −4.00000 + 3.46410I
u = 0.621744 − 0.440597I
a = −0.121744 + 1.306620I
b = 1.00000
c = 1.12174 − 1.30662I
d = −0.500000 + 0.866025I
3.28987 + 2.02988I −4.00000 − 3.46410I
u = −0.121744 + 1.306620I
a = 0.621744 − 0.440597I
b = 1.00000
c = 0.378256 + 0.440597I
d = −0.500000 + 0.866025I
3.28987 + 2.02988I −4.00000 − 3.46410I
u = −0.121744 − 1.306620I
a = 0.621744 + 0.440597I
b = 1.00000
c = 0.378256 − 0.440597I
d = −0.500000 − 0.866025I
3.28987 − 2.02988I −4.00000 + 3.46410I
58
XIV. I
u
14
= hau + d + a − u, c + a − 1, b − 1, a
2
− a + u + 1, u
2
+ u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
u + 1
a
7
=
−a + 1
−au − a + u
a
12
=
−u
u + 1
a
8
=
−au − 2a + 1
−au + u
a
1
=
−u − 1
−au
a
4
=
a
1
a
10
=
u
u
a
3
=
au + 2a − u − 1
au + a − u
a
2
=
2au + a − 2u − 1
1
a
9
=
u + 1
au
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u − 2
59
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
8
, c
10
, c
11
(u
2
+ u + 1)
2
c
3
, c
4
, c
6
c
7
, c
9
, c
12
u
4
− u
3
+ 2u
2
− 2u + 1
60
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
8
, c
10
, c
11
(y
2
+ y + 1)
2
c
3
, c
4
, c
6
c
7
, c
9
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
61
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
14
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.070696 + 0.758745I
b = 1.00000
c = 1.070700 − 0.758745I
d = 0.192440 + 0.547877I
3.28987 − 2.02988I −4.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 1.070700 − 0.758745I
b = 1.00000
c = −0.070696 + 0.758745I
d = −1.69244 + 0.31815I
3.28987 − 2.02988I −4.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = −0.070696 − 0.758745I
b = 1.00000
c = 1.070700 + 0.758745I
d = 0.192440 − 0.547877I
3.28987 + 2.02988I −4.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 1.070700 + 0.758745I
b = 1.00000
c = −0.070696 − 0.758745I
d = −1.69244 − 0.31815I
3.28987 + 2.02988I −4.00000 − 3.46410I
62
XV. I
u
15
= hd + 1, c − u, b + u − 1, a + u, u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
1
a
7
=
u
−1
a
12
=
−u
0
a
8
=
u − 1
−1
a
1
=
−u − 1
−u
a
4
=
−u
−u + 1
a
10
=
u
u
a
3
=
−u − 1
−u
a
2
=
−u − 1
−u
a
9
=
u − 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
63
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
u
2
c
3
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
u
2
+ 1
64
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
8
y
2
c
3
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
(y + 1)
2
65
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
15
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = − 1.000000I
b = 1.00000 − 1.00000I
c = 1.000000I
d = −1.00000
4.93480 4.00000
u = − 1.000000I
a = 1.000000I
b = 1.00000 + 1.00000I
c = − 1.000000I
d = −1.00000
4.93480 4.00000
66
XVI. I
u
16
= hd, c − 1, b − u − 1, a − u, u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
1
a
7
=
1
0
a
12
=
−u
0
a
8
=
1
0
a
1
=
−u
0
a
4
=
u
u + 1
a
10
=
u
u
a
3
=
u − 1
u
a
2
=
−1
u
a
9
=
u + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
67
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
3
, c
4
c
5
, c
8
, c
9
c
10
, c
11
u
2
+ 1
c
6
, c
7
, c
12
u
2
68
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
2
c
2
, c
3
, c
4
c
5
, c
8
, c
9
c
10
, c
11
(y + 1)
2
c
6
, c
7
, c
12
y
2
69
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
16
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.000000I
b = 1.00000 + 1.00000I
c = 1.00000
d = 0
1.64493 −8.00000
u = − 1.000000I
a = − 1.000000I
b = 1.00000 − 1.00000I
c = 1.00000
d = 0
1.64493 −8.00000
70
XVII. I
u
17
= hd + 1, c + u, b − 1, a − 1, u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
1
a
7
=
−u
−1
a
12
=
−u
0
a
8
=
−u − 1
−1
a
1
=
−u + 1
−u
a
4
=
1
1
a
10
=
u
u
a
3
=
1
1
a
2
=
−u + 2
−u + 1
a
9
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
71
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
5
, c
6
c
7
, c
8
, c
10
c
11
, c
12
u
2
+ 1
c
3
, c
4
, c
9
u
2
72
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
2
c
2
, c
5
, c
6
c
7
, c
8
, c
10
c
11
, c
12
(y + 1)
2
c
3
, c
4
, c
9
y
2
73
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
17
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.00000
b = 1.00000
c = − 1.000000I
d = −1.00000
1.64493 −8.00000
u = − 1.000000I
a = 1.00000
b = 1.00000
c = 1.000000I
d = −1.00000
1.64493 −8.00000
74
XVIII. I
u
18
= hd + 1, ca + u − 1, b − a − 1, u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
1
a
7
=
c
−1
a
12
=
−u
0
a
8
=
c − 1
−1
a
1
=
cu − u
−u
a
4
=
a
a + 1
a
10
=
u
u
a
3
=
a − 1
a
a
2
=
cu + a − u − 1
a − u
a
9
=
−au + u
−au
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2
(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.
75
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
18
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
c = ···
d = ···
3.28987 −2.00000
76
XIX. I
v
1
= ha, d + 1, c + a − v − 2, b − 1, v
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
v
0
a
5
=
1
0
a
7
=
v + 2
−1
a
12
=
v
0
a
8
=
v + 1
−1
a
1
=
−v + 1
v
a
4
=
0
1
a
10
=
v
0
a
3
=
−1
1
a
2
=
−v
v + 1
a
9
=
v
−v
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
77
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
9
, c
12
u
2
+ 1
c
5
, c
10
, c
11
u
2
78
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
2
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
9
, c
12
(y + 1)
2
c
5
, c
10
, c
11
y
2
79
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.000000I
a = 0
b = 1.00000
c = 2.00000 + 1.00000I
d = −1.00000
1.64493 −8.00000
v = − 1.000000I
a = 0
b = 1.00000
c = 2.00000 − 1.00000I
d = −1.00000
1.64493 −8.00000
80
XX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 1)
6
(u
2
+ u + 1)
6
(u
3
+ 4u
2
+ 4u − 1)(u
4
+ 3u
3
+ 2u
2
+ 1)
3
· (u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ u
2
+ 3u + 4)
3
· (u
8
+ 3u
7
+ 8u
6
+ 10u
5
+ 14u
4
+ 11u
3
+ 12u
2
+ 4u + 1)
3
· (u
10
+ 3u
9
+ 8u
8
+ 10u
7
+ 14u
6
+ 8u
5
+ 5u
4
+ 15u
3
+ 48u
2
+ 48u + 16)
c
2
, c
8
u
2
(u
2
+ 1)
3
(u
2
+ u + 1)
6
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
3
· (u
6
+ u
4
+ 2u
3
+ u
2
+ u + 2)
3
· (u
8
− u
7
+ 2u
6
− 2u
5
+ 4u
4
− 3u
3
+ 2u
2
+ 1)
3
· (u
10
− u
9
+ 2u
8
− 2u
7
+ 4u
6
− 6u
5
+ 5u
4
− 7u
3
+ 8u
2
− 4u + 4)
c
3
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
u
2
(u
2
+ 1)
3
(u
2
+ u + 1)
2
(u
3
+ 2u + 1)
5
(u
4
− u
3
+ 2u
2
− 2u + 1)
5
· (u
6
+ u
4
+ 2u
3
+ u
2
+ u + 2)
· (u
8
− u
7
+ 3u
6
− 3u
5
+ 3u
4
− 5u
3
+ 4u
2
− 4u + 4)
· (u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 10u
4
+ 9u
3
+ 5u
2
+ 3u + 2)
2
· (u
10
− u
9
+ 7u
8
− 7u
7
+ 18u
6
− 17u
5
+ 18u
4
− 15u
3
+ 3u
2
+ 1)
81
XXI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y −1)
6
(y
2
+ y + 1)
6
(y
3
− 8y
2
+ 24y −1)
· (y
4
− 5y
3
+ 6y
2
+ 4y + 1)
3
(y
6
+ 2y
5
+ 3y
4
− 2y
3
+ 13y
2
− y + 16)
3
· (y
8
+ 7y
7
+ 32y
6
+ 82y
5
+ 146y
4
+ 151y
3
+ 84y
2
+ 8y + 1)
3
· (y
10
+ 7y
9
+ ··· − 768y + 256)
c
2
, c
8
y
2
(y + 1)
6
(y
2
+ y + 1)
6
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
3
· (y
6
+ 2y
5
+ 3y
4
+ 2y
3
+ y
2
+ 3y + 4)
3
· (y
8
+ 3y
7
+ 8y
6
+ 10y
5
+ 14y
4
+ 11y
3
+ 12y
2
+ 4y + 1)
3
· (y
10
+ 3y
9
+ 8y
8
+ 10y
7
+ 14y
6
+ 8y
5
+ 5y
4
+ 15y
3
+ 48y
2
+ 48y + 16)
c
3
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y
2
(y + 1)
6
(y
2
+ y + 1)
2
(y
3
+ 4y
2
+ 4y −1)
5
(y
4
+ 3y
3
+ 2y
2
+ 1)
5
· (y
6
+ 2y
5
+ 3y
4
+ 2y
3
+ y
2
+ 3y + 4)
· (y
8
+ 5y
7
+ 9y
6
+ 7y
5
+ 3y
4
− y
3
+ 16y + 16)
· (y
8
+ 8y
7
+ 24y
6
+ 30y
5
+ 8y
4
− 5y
3
+ 11y
2
+ 11y + 4)
2
· (y
10
+ 13y
9
+ ··· + 6y + 1)
82
