12n
0555
(K12n
0555
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 12 2 4 3 11 4 1 5
Solving Sequence
4,8
3
2,9
1 7
6,11
10 5 12
c
3
c
8
c
1
c
7
c
6
c
10
c
4
c
12
c
2
, c
5
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hd − u, −u
4
+ u
3
+ 2c − u − 1, u
4
+ u
3
+ 2b + u − 1, −u
4
− u
3
+ 2a − u − 1, u
5
+ u
3
+ u
2
+ 2u − 1i
I
u
2
= hd − u, u
7
+ 2u
3
+ u
2
+ 2c − 3u + 1, b + 1, u
7
+ u
2
+ 2a − 3u + 1, u
8
− u
7
+ 2u
6
− 2u
5
+ 4u
4
− 3u
3
+ 2u
2
+ 1i
I
u
3
= hd − u, u
7
+ 2u
3
+ u
2
+ 2c − 3u + 1, u
7
− 2u
6
+ 2u
5
− 2u
4
+ 4u
3
− 5u
2
+ 2b + u − 1,
− u
7
+ 2u
6
− 2u
5
+ 2u
4
− 4u
3
+ 5u
2
+ 2a − u − 1, u
8
− u
7
+ 2u
6
− 2u
5
+ 4u
4
− 3u
3
+ 2u
2
+ 1i
I
u
4
= h−u
5
− 2u
3
+ u
2
+ 2d + 2, −u
7
+ u
6
− 3u
5
+ 3u
4
− 3u
3
+ 5u
2
+ 4c − 4u + 4, b + 1,
− u
7
+ u
6
− 3u
5
+ u
4
− 3u
3
+ u
2
+ 4a − 2u, u
8
− u
7
+ 3u
6
− 3u
5
+ 3u
4
− 5u
3
+ 4u
2
− 4u + 4i
I
u
5
= hu
7
− 2u
6
+ 2u
5
− 4u
4
+ 4u
3
− 5u
2
+ 2d + 3u − 1, −u
7
+ u
6
− 2u
5
+ 2u
4
− 4u
3
+ 3u
2
+ c − 2u,
u
7
− 2u
6
+ 2u
5
− 2u
4
+ 4u
3
− 5u
2
+ 2b + u − 1, −u
7
+ 2u
6
− 2u
5
+ 2u
4
− 4u
3
+ 5u
2
+ 2a − u − 1,
u
8
− u
7
+ 2u
6
− 2u
5
+ 4u
4
− 3u
3
+ 2u
2
+ 1i
I
u
6
= hd − u, u
5
− u
4
+ 2u
2
+ c − u − 2, b + 1, u
5
+ u
3
+ 2a + u − 1, u
6
+ u
4
+ 2u
3
+ u
2
+ u + 2i
I
u
7
= h−u
3
+ d − 1, −u
5
− u
3
− 2u
2
+ 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
3
+ d − 1, −u
5
− u
3
− 2u
2
+ 2c − u − 1, −u
5
− u
4
− 2u
2
+ b − 3u − 2, u
5
+ u
4
+ 2u
2
+ a + 3u + 1,
u
6
+ u
4
+ 2u
3
+ u
2
+ u + 2i
I
u
9
= hd − u, c + 2, b + 1, a
2
− a + u + 1, u
2
+ u + 1i
I
u
10
= h−u
3
+ d − u + 1, −u
3
+ u
2
+ c − 2u + 2, 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
+ d − u + 1, −u
3
+ u
2
+ c − 2u + 2, b + 1, u
3
+ a + 2u − 1, u
4
− u
3
+ 2u
2
− 2u + 1i
I
u
12
= hu
3
+ d + 2u − 1, −u
3
+ u
2
+ c − 2u + 2, b + 1, −u
3
+ a − 2u, u
4
− u
3
+ 2u
2
− 2u + 1i
I
u
13
= hau + d, c − u − 1, b + 1, a
2
− a + u + 1, u
2
+ u + 1i
I
u
14
= hd
2
+ du − u, c − u − 1, b + 2u, a − 2u − 1, u
2
+ u + 1i
I
u
15
= hd, c − u, b + u + 1, a − u, u
2
+ 1i
I
u
16
= hd + u, c − u + 1, b + 1, a − 1, u
2
+ 1i
I
u
17
= hd + u, c − u + 1, b + u + 1, a − u, u
2
+ 1i
I
u
18
= hd + u, ca − au + u + 1, b + a + 1, u
2
+ 1i
I
v
1
= ha, d + v, −av + c + v + 1, 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
= hd − u, −u
4
+ u
3
+ 2c − u − 1, u
4
+ u
3
+ 2b + u − 1, −u
4
− u
3
+
2a − u − 1, u
5
+ u
3
+ u
2
+ 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
2
=
1
2
u
4
+
1
2
u
3
+
1
2
u +
1
2
−
1
2
u
4
−
1
2
u
3
−
1
2
u +
1
2
a
9
=
u
u
3
+ u
a
1
=
1
2
u
4
+
1
2
u
3
+ u
2
+
1
2
u +
1
2
1
2
u
4
−
1
2
u
3
−
1
2
u +
1
2
a
7
=
−u
u
a
6
=
−
1
2
u
4
+
1
2
u
3
−
1
2
u −
1
2
1
2
u
4
−
1
2
u
3
−
1
2
u +
1
2
a
11
=
1
2
u
4
−
1
2
u
3
+
1
2
u +
1
2
u
a
10
=
1
2
u
4
−
1
2
u
3
−
1
2
u +
1
2
u
a
5
=
1
2
u
4
+
1
2
u
3
+ u
2
+
1
2
u +
1
2
−u
2
a
12
=
u
2
+ u
1
2
u
4
+
1
2
u
3
−
1
2
u +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
4
+ 4u
3
+ 4u + 14
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
u
5
+ 2u
4
+ 5u
3
+ 3u
2
+ 6u − 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
u
5
+ u
3
+ u
2
+ 2u − 1
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
y
5
+ 6y
4
+ 25y
3
+ 55y
2
+ 42y −1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
y
5
+ 2y
4
+ 5y
3
+ 3y
2
+ 6y −1
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.828442 + 0.812698I
a = −0.284015 + 0.939824I
b = 1.28401 − 0.93982I
c = −1.356950 − 0.196710I
d = −0.828442 + 0.812698I
4.34615 − 6.57943I 7.72788 + 7.51859I
u = −0.828442 − 0.812698I
a = −0.284015 − 0.939824I
b = 1.28401 + 0.93982I
c = −1.356950 + 0.196710I
d = −0.828442 − 0.812698I
4.34615 + 6.57943I 7.72788 − 7.51859I
u = 0.633508 + 1.226040I
a = −1.08404 − 1.28198I
b = 2.08404 + 1.28198I
c = 1.51852 − 0.91518I
d = 0.633508 + 1.226040I
−2.1892 + 16.8691I 1.32766 − 10.25585I
u = 0.633508 − 1.226040I
a = −1.08404 + 1.28198I
b = 2.08404 − 1.28198I
c = 1.51852 + 0.91518I
d = 0.633508 − 1.226040I
−2.1892 − 16.8691I 1.32766 + 10.25585I
u = 0.389868
a = 0.736115
b = 0.263885
c = 0.676856
d = 0.389868
0.620982 15.8890
6
II. I
u
2
=
hd−u, u
7
+2u
3
+· · ·+2c+1, b+1, u
7
+u
2
+2a−3u+1, u
8
−u
7
+· · ·+2u
2
+1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
2
=
−
1
2
u
7
−
1
2
u
2
+
3
2
u −
1
2
−1
a
9
=
u
u
3
+ u
a
1
=
−u
7
− u
5
− u
3
− u
2
+ u − 2
−
1
2
u
7
− u
3
−
1
2
u
2
+
1
2
u −
1
2
a
7
=
−u
u
a
6
=
−u
7
+ u
6
− 2u
5
+ 2u
4
− 4u
3
+ 3u
2
− 2u
−
1
2
u
7
+ u
6
+ ··· −
1
2
u +
1
2
a
11
=
−
1
2
u
7
− u
3
−
1
2
u
2
+
3
2
u −
1
2
u
a
10
=
−
1
2
u
7
− u
3
−
1
2
u
2
+
1
2
u −
1
2
u
a
5
=
1
2
u
7
− u
6
+ ··· +
1
2
u +
1
2
−u
2
a
12
=
−
1
2
u
7
− u
5
+ ··· +
1
2
u −
3
2
−
1
2
u
7
−
1
2
u
2
+
1
2
u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
6
+ 2u
5
− 4u
4
+ 6u
3
− 12u
2
+ 6u + 4
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ 5u
7
+ 9u
6
+ 7u
5
+ 3u
4
− u
3
+ 16u + 16
c
2
, c
6
u
8
− u
7
+ 3u
6
− 3u
5
+ 3u
4
− 5u
3
+ 4u
2
− 4u + 4
c
3
, c
4
, c
5
c
7
, c
8
, c
10
c
12
u
8
− u
7
+ 2u
6
− 2u
5
+ 4u
4
− 3u
3
+ 2u
2
+ 1
c
9
, c
11
u
8
+ 3u
7
+ 8u
6
+ 10u
5
+ 14u
4
+ 11u
3
+ 12u
2
+ 4u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 7y
7
+ 17y
6
+ 15y
5
− 105y
4
+ 63y
3
+ 128y
2
− 256y + 256
c
2
, c
6
y
8
+ 5y
7
+ 9y
6
+ 7y
5
+ 3y
4
− y
3
+ 16y + 16
c
3
, c
4
, c
5
c
7
, c
8
, c
10
c
12
y
8
+ 3y
7
+ 8y
6
+ 10y
5
+ 14y
4
+ 11y
3
+ 12y
2
+ 4y + 1
c
9
, c
11
y
8
+ 7y
7
+ 32y
6
+ 82y
5
+ 146y
4
+ 151y
3
+ 84y
2
+ 8y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.862697 + 0.615401I
a = 0.886105 + 1.090380I
b = −1.00000
c = 1.224210 − 0.050581I
d = 0.862697 + 0.615401I
4.15083 + 0.66722I 8.81639 − 2.10627I
u = 0.862697 − 0.615401I
a = 0.886105 − 1.090380I
b = −1.00000
c = 1.224210 + 0.050581I
d = 0.862697 − 0.615401I
4.15083 − 0.66722I 8.81639 + 2.10627I
u = 0.578102 + 1.055330I
a = 0.102567 − 0.732209I
b = −1.00000
c = 1.84091 − 0.61494I
d = 0.578102 + 1.055330I
−5.02390 + 6.79402I 0.88161 − 7.09473I
u = 0.578102 − 1.055330I
a = 0.102567 + 0.732209I
b = −1.00000
c = 1.84091 + 0.61494I
d = 0.578102 − 1.055330I
−5.02390 − 6.79402I 0.88161 + 7.09473I
u = −0.666851 + 1.155530I
a = 0.821510 − 0.756488I
b = −1.00000
c = −1.55320 − 0.75511I
d = −0.666851 + 1.155530I
0.65207 − 10.98940I 4.47099 + 7.14773I
u = −0.666851 − 1.155530I
a = 0.821510 + 0.756488I
b = −1.00000
c = −1.55320 + 0.75511I
d = −0.666851 − 1.155530I
0.65207 + 10.98940I 4.47099 − 7.14773I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.273948 + 0.520074I
a = −0.810182 + 0.910843I
b = −1.00000
c = −1.011910 + 0.934421I
d = −0.273948 + 0.520074I
−3.06886 − 1.27680I 5.83102 + 5.88514I
u = −0.273948 − 0.520074I
a = −0.810182 − 0.910843I
b = −1.00000
c = −1.011910 − 0.934421I
d = −0.273948 − 0.520074I
−3.06886 + 1.27680I 5.83102 − 5.88514I
11
III. I
u
3
= hd − u, u
7
+ 2u
3
+ · · · + 2c + 1, u
7
− 2u
6
+ · · · + 2b − 1, −u
7
+
2u
6
+ · · · + 2a − 1, u
8
− u
7
+ · · · + 2u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
2
=
1
2
u
7
− u
6
+ ··· +
1
2
u +
1
2
−
1
2
u
7
+ u
6
+ ··· −
1
2
u +
1
2
a
9
=
u
u
3
+ u
a
1
=
1
2
u
7
− u
6
+ ··· +
1
2
u +
1
2
−
1
2
u
7
+ u
6
+ ··· −
1
2
u +
1
2
a
7
=
−u
u
a
6
=
1
2
u
7
+ u
3
+
1
2
u
2
−
3
2
u +
1
2
−
1
2
u
7
− u
3
−
1
2
u
2
+
1
2
u −
1
2
a
11
=
−
1
2
u
7
− u
3
−
1
2
u
2
+
3
2
u −
1
2
u
a
10
=
−
1
2
u
7
− u
3
−
1
2
u
2
+
1
2
u −
1
2
u
a
5
=
1
2
u
7
− u
6
+ ··· +
1
2
u +
1
2
−u
2
a
12
=
−u
6
+ u
5
− u
4
+ 2u
3
− 3u
2
+ 2u
u
6
+ u
4
− u
3
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
6
+ 2u
5
− 4u
4
+ 6u
3
− 12u
2
+ 6u + 4
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
8
+ 3u
7
+ 8u
6
+ 10u
5
+ 14u
4
+ 11u
3
+ 12u
2
+ 4u + 1
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
10
u
8
− u
7
+ 2u
6
− 2u
5
+ 4u
4
− 3u
3
+ 2u
2
+ 1
c
5
, c
12
u
8
− u
7
+ 3u
6
− 3u
5
+ 3u
4
− 5u
3
+ 4u
2
− 4u + 4
c
11
u
8
+ 5u
7
+ 9u
6
+ 7u
5
+ 3u
4
− u
3
+ 16u + 16
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
8
+ 7y
7
+ 32y
6
+ 82y
5
+ 146y
4
+ 151y
3
+ 84y
2
+ 8y + 1
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
10
y
8
+ 3y
7
+ 8y
6
+ 10y
5
+ 14y
4
+ 11y
3
+ 12y
2
+ 4y + 1
c
5
, c
12
y
8
+ 5y
7
+ 9y
6
+ 7y
5
+ 3y
4
− y
3
+ 16y + 16
c
11
y
8
− 7y
7
+ 17y
6
+ 15y
5
− 105y
4
+ 63y
3
+ 128y
2
− 256y + 256
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.862697 + 0.615401I
a = −0.087246 − 0.709742I
b = 1.087250 + 0.709742I
c = 1.224210 − 0.050581I
d = 0.862697 + 0.615401I
4.15083 + 0.66722I 8.81639 − 2.10627I
u = 0.862697 − 0.615401I
a = −0.087246 + 0.709742I
b = 1.087250 − 0.709742I
c = 1.224210 + 0.050581I
d = 0.862697 − 0.615401I
4.15083 − 0.66722I 8.81639 + 2.10627I
u = 0.578102 + 1.055330I
a = −0.71320 − 1.58728I
b = 1.71320 + 1.58728I
c = 1.84091 − 0.61494I
d = 0.578102 + 1.055330I
−5.02390 + 6.79402I 0.88161 − 7.09473I
u = 0.578102 − 1.055330I
a = −0.71320 + 1.58728I
b = 1.71320 − 1.58728I
c = 1.84091 + 0.61494I
d = 0.578102 − 1.055330I
−5.02390 − 6.79402I 0.88161 + 7.09473I
u = −0.666851 + 1.155530I
a = −0.90831 + 1.29123I
b = 1.90831 − 1.29123I
c = −1.55320 − 0.75511I
d = −0.666851 + 1.155530I
0.65207 − 10.98940I 4.47099 + 7.14773I
u = −0.666851 − 1.155530I
a = −0.90831 − 1.29123I
b = 1.90831 + 1.29123I
c = −1.55320 + 0.75511I
d = −0.666851 − 1.155530I
0.65207 + 10.98940I 4.47099 − 7.14773I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.273948 + 0.520074I
a = 1.20876 + 0.78225I
b = −0.208757 − 0.782252I
c = −1.011910 + 0.934421I
d = −0.273948 + 0.520074I
−3.06886 − 1.27680I 5.83102 + 5.88514I
u = −0.273948 − 0.520074I
a = 1.20876 − 0.78225I
b = −0.208757 + 0.782252I
c = −1.011910 − 0.934421I
d = −0.273948 − 0.520074I
−3.06886 + 1.27680I 5.83102 − 5.88514I
16
IV. I
u
4
= h−u
5
− 2u
3
+ u
2
+ 2d + 2, −u
7
+ u
6
+ · · · + 4c + 4, b + 1, −u
7
+
u
6
+ · · · + 4a − 2u, u
8
− u
7
+ · · · − 4u + 4i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
2
=
1
4
u
7
−
1
4
u
6
+ ··· −
1
4
u
2
+
1
2
u
−1
a
9
=
u
u
3
+ u
a
1
=
1
4
u
7
−
3
4
u
6
+ ··· +
3
2
u − 1
−
1
2
u
7
+
1
2
u
6
+ ··· − 2u + 1
a
7
=
−u
u
a
6
=
−
1
4
u
7
+
1
4
u
6
+ ··· − u + 1
1
2
u
5
+ u
3
−
1
2
u
2
+ u − 1
a
11
=
1
4
u
7
−
1
4
u
6
+ ··· + u − 1
1
2
u
5
+ u
3
−
1
2
u
2
− 1
a
10
=
1
4
u
7
−
1
4
u
6
+ ··· −
3
4
u
2
+ u
1
2
u
5
+ u
3
−
1
2
u
2
− 1
a
5
=
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
12
=
−
1
2
u
6
+
1
2
u
5
+ ··· +
1
2
u − 1
−
1
2
u
7
+
1
2
u
6
+ ··· − u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
7
+ 3u
6
+ u
5
+ 3u
4
− u
3
+ u
2
− 6u + 10
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
u
8
+ 3u
7
+ 8u
6
+ 10u
5
+ 14u
4
+ 11u
3
+ 12u
2
+ 4u + 1
c
2
, c
4
, c
5
c
6
, c
10
, c
12
u
8
− u
7
+ 2u
6
− 2u
5
+ 4u
4
− 3u
3
+ 2u
2
+ 1
c
3
, c
7
, c
8
u
8
− u
7
+ 3u
6
− 3u
5
+ 3u
4
− 5u
3
+ 4u
2
− 4u + 4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
y
8
+ 7y
7
+ 32y
6
+ 82y
5
+ 146y
4
+ 151y
3
+ 84y
2
+ 8y + 1
c
2
, c
4
, c
5
c
6
, c
10
, c
12
y
8
+ 3y
7
+ 8y
6
+ 10y
5
+ 14y
4
+ 11y
3
+ 12y
2
+ 4y + 1
c
3
, c
7
, c
8
y
8
+ 5y
7
+ 9y
6
+ 7y
5
+ 3y
4
− y
3
+ 16y + 16
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.993174 + 0.298213I
a = 0.70455 + 1.25219I
b = −1.00000
c = −0.923603 + 0.277324I
d = −0.666851 + 1.155530I
0.65207 − 10.98940I 4.47099 + 7.14773I
u = 0.993174 − 0.298213I
a = 0.70455 − 1.25219I
b = −1.00000
c = −0.923603 − 0.277324I
d = −0.666851 − 1.155530I
0.65207 + 10.98940I 4.47099 − 7.14773I
u = −0.769280 + 0.870579I
a = 0.905238 − 0.907210I
b = −1.00000
c = 0.569964 + 0.645017I
d = 0.862697 + 0.615401I
4.15083 + 0.66722I 8.81639 − 2.10627I
u = −0.769280 − 0.870579I
a = 0.905238 + 0.907210I
b = −1.00000
c = 0.569964 − 0.645017I
d = 0.862697 − 0.615401I
4.15083 − 0.66722I 8.81639 + 2.10627I
u = 0.022189 + 1.190950I
a = 0.559180 + 0.221811I
b = −1.00000
c = −0.015639 + 0.839373I
d = −0.273948 − 0.520074I
−3.06886 + 1.27680I 5.83102 − 5.88514I
u = 0.022189 − 1.190950I
a = 0.559180 − 0.221811I
b = −1.00000
c = −0.015639 − 0.839373I
d = −0.273948 + 0.520074I
−3.06886 − 1.27680I 5.83102 + 5.88514I
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.253917 + 1.370380I
a = 0.331031 − 0.545807I
b = −1.00000
c = −0.130722 + 0.705502I
d = 0.578102 − 1.055330I
−5.02390 − 6.79402I 0.88161 + 7.09473I
u = 0.253917 − 1.370380I
a = 0.331031 + 0.545807I
b = −1.00000
c = −0.130722 − 0.705502I
d = 0.578102 + 1.055330I
−5.02390 + 6.79402I 0.88161 − 7.09473I
21
V. I
u
5
= hu
7
− 2u
6
+ · · · + 2d − 1, −u
7
+ u
6
+ · · · + c − 2u, u
7
− 2u
6
+ · · · +
2b − 1, −u
7
+ 2u
6
+ · · · + 2a − 1, u
8
− u
7
+ · · · + 2u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
2
=
1
2
u
7
− u
6
+ ··· +
1
2
u +
1
2
−
1
2
u
7
+ u
6
+ ··· −
1
2
u +
1
2
a
9
=
u
u
3
+ u
a
1
=
1
2
u
7
− u
6
+ ··· +
1
2
u +
1
2
−
1
2
u
7
+ u
6
+ ··· −
1
2
u +
1
2
a
7
=
−u
u
a
6
=
1
2
u
7
+ u
3
+
1
2
u
2
−
3
2
u +
1
2
−
1
2
u
7
− u
3
−
1
2
u
2
+
1
2
u −
1
2
a
11
=
u
7
− u
6
+ 2u
5
− 2u
4
+ 4u
3
− 3u
2
+ 2u
−
1
2
u
7
+ u
6
+ ··· −
3
2
u +
1
2
a
10
=
3
2
u
7
− 2u
6
+ ··· +
7
2
u −
1
2
−
1
2
u
7
+ u
6
+ ··· −
3
2
u +
1
2
a
5
=
−u
7
− u
5
− u
3
− u
2
+ u − 2
1
2
u
7
+ u
5
+ ··· +
1
2
u +
3
2
a
12
=
3
2
u
7
− 2u
6
+ ··· +
5
2
u −
1
2
−u
7
+ u
6
− 2u
5
+ 3u
4
− 4u
3
+ 3u
2
− 2u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
6
+ 2u
5
− 4u
4
+ 6u
3
− 12u
2
+ 6u + 4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
8
+ 3u
7
+ 8u
6
+ 10u
5
+ 14u
4
+ 11u
3
+ 12u
2
+ 4u + 1
c
2
, c
3
, c
5
c
6
, c
7
, c
8
c
12
u
8
− u
7
+ 2u
6
− 2u
5
+ 4u
4
− 3u
3
+ 2u
2
+ 1
c
4
, c
10
u
8
− u
7
+ 3u
6
− 3u
5
+ 3u
4
− 5u
3
+ 4u
2
− 4u + 4
c
9
u
8
+ 5u
7
+ 9u
6
+ 7u
5
+ 3u
4
− u
3
+ 16u + 16
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
8
+ 7y
7
+ 32y
6
+ 82y
5
+ 146y
4
+ 151y
3
+ 84y
2
+ 8y + 1
c
2
, c
3
, c
5
c
6
, c
7
, c
8
c
12
y
8
+ 3y
7
+ 8y
6
+ 10y
5
+ 14y
4
+ 11y
3
+ 12y
2
+ 4y + 1
c
4
, c
10
y
8
+ 5y
7
+ 9y
6
+ 7y
5
+ 3y
4
− y
3
+ 16y + 16
c
9
y
8
− 7y
7
+ 17y
6
+ 15y
5
− 105y
4
+ 63y
3
+ 128y
2
− 256y + 256
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.862697 + 0.615401I
a = −0.087246 − 0.709742I
b = 1.087250 + 0.709742I
c = −0.768231 + 0.548015I
d = −0.769280 + 0.870579I
4.15083 + 0.66722I 8.81639 − 2.10627I
u = 0.862697 − 0.615401I
a = −0.087246 + 0.709742I
b = 1.087250 − 0.709742I
c = −0.768231 − 0.548015I
d = −0.769280 − 0.870579I
4.15083 − 0.66722I 8.81639 + 2.10627I
u = 0.578102 + 1.055330I
a = −0.71320 − 1.58728I
b = 1.71320 + 1.58728I
c = −0.399261 + 0.728856I
d = 0.253917 − 1.370380I
−5.02390 + 6.79402I 0.88161 − 7.09473I
u = 0.578102 − 1.055330I
a = −0.71320 + 1.58728I
b = 1.71320 − 1.58728I
c = −0.399261 − 0.728856I
d = 0.253917 + 1.370380I
−5.02390 − 6.79402I 0.88161 + 7.09473I
u = −0.666851 + 1.155530I
a = −0.90831 + 1.29123I
b = 1.90831 − 1.29123I
c = 0.374646 + 0.649195I
d = 0.993174 + 0.298213I
0.65207 − 10.98940I 4.47099 + 7.14773I
u = −0.666851 − 1.155530I
a = −0.90831 − 1.29123I
b = 1.90831 + 1.29123I
c = 0.374646 − 0.649195I
d = 0.993174 − 0.298213I
0.65207 + 10.98940I 4.47099 − 7.14773I
25
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.273948 + 0.520074I
a = 1.20876 + 0.78225I
b = −0.208757 − 0.782252I
c = 0.79285 + 1.50517I
d = 0.022189 − 1.190950I
−3.06886 − 1.27680I 5.83102 + 5.88514I
u = −0.273948 − 0.520074I
a = 1.20876 − 0.78225I
b = −0.208757 + 0.782252I
c = 0.79285 − 1.50517I
d = 0.022189 + 1.190950I
−3.06886 + 1.27680I 5.83102 − 5.88514I
26
VI. I
u
6
=
hd−u, u
5
−u
4
+2u
2
+c−u−2, b+1, u
5
+u
3
+2a+u−1, u
6
+u
4
+2u
3
+u
2
+u+2i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
2
=
−
1
2
u
5
−
1
2
u
3
−
1
2
u +
1
2
−1
a
9
=
u
u
3
+ u
a
1
=
−
1
2
u
5
− u
4
+ ··· −
3
2
u −
1
2
u
3
+ u + 1
a
7
=
−u
u
a
6
=
−
1
2
u
5
−
1
2
u
3
− u
2
−
1
2
u −
1
2
u
3
+ u + 1
a
11
=
−u
5
+ u
4
− 2u
2
+ u + 2
u
a
10
=
−u
5
+ u
4
− 2u
2
+ 2
u
a
5
=
−u
5
− u
4
− u
2
− 3u − 1
−u
2
a
12
=
−
3
2
u
5
+ u
4
+ ··· +
1
2
u +
5
2
u
5
+ u
3
+ u
2
+ u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
− 4u
3
− 8u − 2
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ u
2
+ 3u + 4
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
u
6
+ u
4
+ 2u
3
+ u
2
+ u + 2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
y
6
+ 2y
5
+ 3y
4
− 2y
3
+ 13y
2
− y + 16
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
y
6
+ 2y
5
+ 3y
4
+ 2y
3
+ y
2
+ 3y + 4
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.931903 + 0.428993I
a = 0.79897 − 1.20716I
b = −1.00000
c = −1.100360 − 0.012951I
d = −0.931903 + 0.428993I
2.86100 + 5.13794I 7.31793 − 3.20902I
u = −0.931903 − 0.428993I
a = 0.79897 + 1.20716I
b = −1.00000
c = −1.100360 + 0.012951I
d = −0.931903 − 0.428993I
2.86100 − 5.13794I 7.31793 + 3.20902I
u = 0.226699 + 1.074330I
a = 0.085258 − 0.404039I
b = −1.00000
c = 4.03505 − 1.78227I
d = 0.226699 + 1.074330I
−7.36693 −4.63587 + 0.I
u = 0.226699 − 1.074330I
a = 0.085258 + 0.404039I
b = −1.00000
c = 4.03505 + 1.78227I
d = 0.226699 − 1.074330I
−7.36693 −4.63587 + 0.I
u = 0.705204 + 1.038720I
a = 0.865771 + 0.806035I
b = −1.00000
c = 1.56530 − 0.51571I
d = 0.705204 + 1.038720I
2.86100 + 5.13794I 7.31793 − 3.20902I
u = 0.705204 − 1.038720I
a = 0.865771 − 0.806035I
b = −1.00000
c = 1.56530 + 0.51571I
d = 0.705204 − 1.038720I
2.86100 − 5.13794I 7.31793 + 3.20902I
30
VII. I
u
7
= h−u
3
+ d − 1, −u
5
− u
3
+ · · · + 2c − 1, b + 1, u
5
+ u
3
+ 2a + u −
1, u
6
+ u
4
+ 2u
3
+ u
2
+ u + 2i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
2
=
−
1
2
u
5
−
1
2
u
3
−
1
2
u +
1
2
−1
a
9
=
u
u
3
+ u
a
1
=
−
1
2
u
5
− u
4
+ ··· −
3
2
u −
1
2
u
3
+ u + 1
a
7
=
−u
u
a
6
=
−
1
2
u
5
−
1
2
u
3
− u
2
−
1
2
u −
1
2
u
3
+ u + 1
a
11
=
1
2
u
5
+
1
2
u
3
+ u
2
+
1
2
u +
1
2
u
3
+ 1
a
10
=
1
2
u
5
−
1
2
u
3
+ u
2
+
1
2
u −
1
2
u
3
+ 1
a
5
=
−
1
2
u
5
− u
4
+ ··· −
3
2
u −
1
2
u
4
+ u
2
+ u + 1
a
12
=
1
2
u
5
− u
4
−
1
2
u
3
−
3
2
u −
3
2
−u
5
− u
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
− 4u
3
− 8u − 2
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ u
2
+ 3u + 4
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
u
6
+ u
4
+ 2u
3
+ u
2
+ u + 2
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
y
6
+ 2y
5
+ 3y
4
− 2y
3
+ 13y
2
− y + 16
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
y
6
+ 2y
5
+ 3y
4
+ 2y
3
+ y
2
+ 3y + 4
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.931903 + 0.428993I
a = 0.79897 − 1.20716I
b = −1.00000
c = 0.885437 + 0.407603I
d = 0.705204 + 1.038720I
2.86100 + 5.13794I 7.31793 − 3.20902I
u = −0.931903 − 0.428993I
a = 0.79897 + 1.20716I
b = −1.00000
c = 0.885437 − 0.407603I
d = 0.705204 − 1.038720I
2.86100 − 5.13794I 7.31793 + 3.20902I
u = 0.226699 + 1.074330I
a = 0.085258 − 0.404039I
b = −1.00000
c = −0.188043 + 0.891136I
d = 0.226699 − 1.074330I
−7.36693 −4.63587 + 0.I
u = 0.226699 − 1.074330I
a = 0.085258 + 0.404039I
b = −1.00000
c = −0.188043 − 0.891136I
d = 0.226699 + 1.074330I
−7.36693 −4.63587 + 0.I
u = 0.705204 + 1.038720I
a = 0.865771 + 0.806035I
b = −1.00000
c = −0.447394 + 0.658981I
d = −0.931903 + 0.428993I
2.86100 + 5.13794I 7.31793 − 3.20902I
u = 0.705204 − 1.038720I
a = 0.865771 − 0.806035I
b = −1.00000
c = −0.447394 − 0.658981I
d = −0.931903 − 0.428993I
2.86100 − 5.13794I 7.31793 + 3.20902I
34
VIII. I
u
8
= h−u
3
+ d − 1, −u
5
− u
3
+ · · · + 2c − 1, −u
5
− u
4
+ · · · + b −
2, u
5
+ u
4
+ 2u
2
+ a + 3u + 1, u
6
+ u
4
+ 2u
3
+ u
2
+ u + 2i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
2
=
−u
5
− u
4
− 2u
2
− 3u − 1
u
5
+ u
4
+ 2u
2
+ 3u + 2
a
9
=
u
u
3
+ u
a
1
=
−u
5
− u
4
− u
2
− 3u − 1
u
5
+ 2u
4
+ 2u
2
+ 3u + 2
a
7
=
−u
u
a
6
=
u
5
− u
4
+ 2u
2
− u − 2
−u
5
+ u
4
− 2u
2
+ 2
a
11
=
1
2
u
5
+
1
2
u
3
+ u
2
+
1
2
u +
1
2
u
3
+ 1
a
10
=
1
2
u
5
−
1
2
u
3
+ u
2
+
1
2
u −
1
2
u
3
+ 1
a
5
=
−
1
2
u
5
− u
4
+ ··· −
3
2
u −
1
2
u
4
+ u
2
+ u + 1
a
12
=
−
3
2
u
5
− u
4
+ ··· −
7
2
u −
1
2
u
5
+ 2u
4
+ 2u
2
+ 4u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
− 4u
3
− 8u − 2
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ u
2
+ 3u + 4
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
u
6
+ u
4
+ 2u
3
+ u
2
+ u + 2
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
y
6
+ 2y
5
+ 3y
4
− 2y
3
+ 13y
2
− y + 16
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
y
6
+ 2y
5
+ 3y
4
+ 2y
3
+ y
2
+ 3y + 4
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −0.931903 + 0.428993I
a = −0.030982 + 0.459976I
b = 1.030980 − 0.459976I
c = 0.885437 + 0.407603I
d = 0.705204 + 1.038720I
2.86100 + 5.13794I 7.31793 − 3.20902I
u = −0.931903 − 0.428993I
a = −0.030982 − 0.459976I
b = 1.030980 + 0.459976I
c = 0.885437 − 0.407603I
d = 0.705204 − 1.038720I
2.86100 − 5.13794I 7.31793 + 3.20902I
u = 0.226699 + 1.074330I
a = −1.82948 − 3.93092I
b = 2.82948 + 3.93092I
c = −0.188043 + 0.891136I
d = 0.226699 − 1.074330I
−7.36693 −4.63587 + 0.I
u = 0.226699 − 1.074330I
a = −1.82948 + 3.93092I
b = 2.82948 − 3.93092I
c = −0.188043 − 0.891136I
d = 0.226699 + 1.074330I
−7.36693 −4.63587 + 0.I
u = 0.705204 + 1.038720I
a = −0.63953 − 1.26223I
b = 1.63953 + 1.26223I
c = −0.447394 + 0.658981I
d = −0.931903 + 0.428993I
2.86100 + 5.13794I 7.31793 − 3.20902I
u = 0.705204 − 1.038720I
a = −0.63953 + 1.26223I
b = 1.63953 − 1.26223I
c = −0.447394 − 0.658981I
d = −0.931903 − 0.428993I
2.86100 − 5.13794I 7.31793 + 3.20902I
38
IX. I
u
9
= hd − u, c + 2, b + 1, a
2
− a + u + 1, u
2
+ u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
−u − 1
a
2
=
a
−1
a
9
=
u
u + 1
a
1
=
au + 2a − 1
−au + u
a
7
=
−u
u
a
6
=
−u − 1
au
a
11
=
−2
u
a
10
=
−u − 2
u
a
5
=
u
u + 1
a
12
=
a − 1
−au − a + u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u + 6
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
4
+ 3u
3
+ 2u
2
+ 1
c
2
, c
5
, c
6
c
12
u
4
− u
3
+ 2u
2
− 2u + 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
(u
2
+ u + 1)
2
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
4
− 5y
3
+ 6y
2
+ 4y + 1
c
2
, c
5
, c
6
c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
(y
2
+ y + 1)
2
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.070696 + 0.758745I
b = −1.00000
c = −2.00000
d = −0.500000 + 0.866025I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 1.070700 − 0.758745I
b = −1.00000
c = −2.00000
d = −0.500000 + 0.866025I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = −0.070696 − 0.758745I
b = −1.00000
c = −2.00000
d = −0.500000 − 0.866025I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 1.070700 + 0.758745I
b = −1.00000
c = −2.00000
d = −0.500000 − 0.866025I
−3.28987 + 2.02988I 4.00000 − 3.46410I
42
X. I
u
10
=
h−u
3
+d−u+1, −u
3
+u
2
+c−2u+2, b+1, −u
3
+a−2u, u
4
−u
3
+2u
2
−2u+1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
2
=
u
3
+ 2u
−1
a
9
=
u
u
3
+ u
a
1
=
u
−u
a
7
=
−u
u
a
6
=
−u
3
+ u
2
− 2u + 2
u
3
+ 2u − 1
a
11
=
u
3
− u
2
+ 2u − 2
u
3
+ u − 1
a
10
=
−u
2
+ u − 1
u
3
+ u − 1
a
5
=
u
u
3
+ u
a
12
=
u
3
+ 2u − 1
u
3
− u
2
+ u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u + 2
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
9
, c
10
(u
2
+ u + 1)
2
c
3
, c
5
, c
7
c
8
, c
12
u
4
− u
3
+ 2u
2
− 2u + 1
c
11
u
4
+ 3u
3
+ 2u
2
+ 1
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
9
, c
10
(y
2
+ y + 1)
2
c
3
, c
5
, c
7
c
8
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
11
y
4
− 5y
3
+ 6y
2
+ 4y + 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 = −1.070700 + 0.758745I
d = −0.500000 + 0.866025I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = 0.621744 − 0.440597I
a = 1.12174 − 1.30662I
b = −1.00000
c = −1.070700 − 0.758745I
d = −0.500000 − 0.866025I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = −0.121744 + 1.306620I
a = 0.378256 + 0.440597I
b = −1.00000
c = 0.070696 + 0.758745I
d = −0.500000 − 0.866025I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = −0.121744 − 1.306620I
a = 0.378256 − 0.440597I
b = −1.00000
c = 0.070696 − 0.758745I
d = −0.500000 + 0.866025I
−3.28987 − 2.02988I 4.00000 + 3.46410I
46
XI. I
u
11
=
h−u
3
+d−u+1, −u
3
+u
2
+c−2u+2, b+1, u
3
+a+2u−1, u
4
−u
3
+2u
2
−2u+1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
2
=
−u
3
− 2u + 1
−1
a
9
=
u
u
3
+ u
a
1
=
−u
2
− u − 1
−u
3
− u − 1
a
7
=
−u
u
a
6
=
−u
3
+ u
2
− 2u + 2
−u
3
− u + 1
a
11
=
u
3
− u
2
+ 2u − 2
u
3
+ u − 1
a
10
=
−u
2
+ u − 1
u
3
+ u − 1
a
5
=
u
u
3
+ u
a
12
=
−u
3
− 2u
−u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u + 2
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
6
c
7
, c
8
u
4
− u
3
+ 2u
2
− 2u + 1
c
4
, c
5
, c
9
c
10
, c
11
, c
12
(u
2
+ u + 1)
2
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
6
c
7
, c
8
y
4
+ 3y
3
+ 2y
2
+ 1
c
4
, c
5
, c
9
c
10
, c
11
, c
12
(y
2
+ y + 1)
2
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 = −1.070700 + 0.758745I
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 = −1.070700 − 0.758745I
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 = 0.070696 + 0.758745I
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 = 0.070696 − 0.758745I
d = −0.500000 + 0.866025I
−3.28987 − 2.02988I 4.00000 + 3.46410I
50
XII. I
u
12
=
hu
3
+d+2u−1, −u
3
+u
2
+c−2u+2, b+1, −u
3
+a−2u, u
4
−u
3
+2u
2
−2u+1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
2
=
u
3
+ 2u
−1
a
9
=
u
u
3
+ u
a
1
=
u
−u
a
7
=
−u
u
a
6
=
−u
3
+ u
2
− 2u + 2
u
3
+ 2u − 1
a
11
=
u
3
− u
2
+ 2u − 2
−u
3
− 2u + 1
a
10
=
2u
3
− u
2
+ 4u − 3
−u
3
− 2u + 1
a
5
=
−u
2
− u − 1
−u
3
+ u
2
− u + 2
a
12
=
2u
3
− 2u
2
+ 4u − 3
−2u
3
+ u
2
− 4u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u + 2
51
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(u
2
+ u + 1)
2
c
3
, c
4
, c
7
c
8
, c
10
u
4
− u
3
+ 2u
2
− 2u + 1
c
9
u
4
+ 3u
3
+ 2u
2
+ 1
52
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y
2
+ y + 1)
2
c
3
, c
4
, c
7
c
8
, c
10
y
4
+ 3y
3
+ 2y
2
+ 1
c
9
y
4
− 5y
3
+ 6y
2
+ 4y + 1
53
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621744 + 0.440597I
a = 1.12174 + 1.30662I
b = −1.00000
c = −1.070700 + 0.758745I
d = −0.121744 − 1.306620I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = 0.621744 − 0.440597I
a = 1.12174 − 1.30662I
b = −1.00000
c = −1.070700 − 0.758745I
d = −0.121744 + 1.306620I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = −0.121744 + 1.306620I
a = 0.378256 + 0.440597I
b = −1.00000
c = 0.070696 + 0.758745I
d = 0.621744 − 0.440597I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = −0.121744 − 1.306620I
a = 0.378256 − 0.440597I
b = −1.00000
c = 0.070696 − 0.758745I
d = 0.621744 + 0.440597I
−3.28987 − 2.02988I 4.00000 + 3.46410I
54
XIII. I
u
13
= hau + d, c − u − 1, b + 1, a
2
− a + u + 1, u
2
+ u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
−u − 1
a
2
=
a
−1
a
9
=
u
u + 1
a
1
=
au + 2a − 1
−au + u
a
7
=
−u
u
a
6
=
−u − 1
au
a
11
=
u + 1
−au
a
10
=
au + u + 1
−au
a
5
=
−au − 2a + u + 1
au + a − u
a
12
=
2au + a
−au + a − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u + 6
55
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
4
+ 3u
3
+ 2u
2
+ 1
c
2
, c
4
, c
6
c
10
u
4
− u
3
+ 2u
2
− 2u + 1
c
3
, c
5
, c
7
c
8
, c
11
, c
12
(u
2
+ u + 1)
2
56
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
4
− 5y
3
+ 6y
2
+ 4y + 1
c
2
, c
4
, c
6
c
10
y
4
+ 3y
3
+ 2y
2
+ 1
c
3
, c
5
, c
7
c
8
, c
11
, c
12
(y
2
+ y + 1)
2
57
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
13
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.070696 + 0.758745I
b = −1.00000
c = 0.500000 + 0.866025I
d = 0.621744 + 0.440597I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 1.070700 − 0.758745I
b = −1.00000
c = 0.500000 + 0.866025I
d = −0.121744 − 1.306620I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = −0.070696 − 0.758745I
b = −1.00000
c = 0.500000 − 0.866025I
d = 0.621744 − 0.440597I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 1.070700 + 0.758745I
b = −1.00000
c = 0.500000 − 0.866025I
d = −0.121744 + 1.306620I
−3.28987 + 2.02988I 4.00000 − 3.46410I
58
XIV. I
u
14
= hd
2
+ du − u, c − u − 1, b + 2u, a − 2u − 1, u
2
+ u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
−u − 1
a
2
=
2u + 1
−2u
a
9
=
u
u + 1
a
1
=
u
−u
a
7
=
−u
u
a
6
=
2
−u − 2
a
11
=
u + 1
d
a
10
=
−d + u + 1
d
a
5
=
−2du − d + u + 1
du − u
a
12
=
du + d + 2u + 1
−du − u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u + 6
59
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
(u
2
+ u + 1)
2
c
4
, c
5
, c
10
c
12
u
4
− u
3
+ 2u
2
− 2u + 1
c
9
, c
11
u
4
+ 3u
3
+ 2u
2
+ 1
60
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
(y
2
+ y + 1)
2
c
4
, c
5
, c
10
c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
9
, c
11
y
4
− 5y
3
+ 6y
2
+ 4y + 1
61
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
14
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.73205I
b = 1.00000 − 1.73205I
c = 0.500000 + 0.866025I
d = 0.621744 + 0.440597I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 1.73205I
b = 1.00000 − 1.73205I
c = 0.500000 + 0.866025I
d = −0.121744 − 1.306620I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = − 1.73205I
b = 1.00000 + 1.73205I
c = 0.500000 − 0.866025I
d = 0.621744 − 0.440597I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = − 1.73205I
b = 1.00000 + 1.73205I
c = 0.500000 − 0.866025I
d = −0.121744 + 1.306620I
−3.28987 + 2.02988I 4.00000 − 3.46410I
62
XV. I
u
15
= hd, c − u, b + u + 1, a − u, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
−1
a
2
=
u
−u − 1
a
9
=
u
0
a
1
=
u − 1
−u
a
7
=
−u
u
a
6
=
−u − 1
1
a
11
=
u
0
a
10
=
u
0
a
5
=
1
0
a
12
=
2u − 1
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
63
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u − 1)
2
c
2
, c
3
, c
5
c
6
, c
7
, c
8
c
12
u
2
+ 1
c
4
, c
9
, c
10
u
2
64
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y −1)
2
c
2
, c
3
, c
5
c
6
, c
7
, c
8
c
12
(y + 1)
2
c
4
, c
9
, c
10
y
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 = 0
−4.93480 0
u = − 1.000000I
a = − 1.000000I
b = −1.00000 + 1.00000I
c = − 1.000000I
d = 0
−4.93480 0
66
XVI. I
u
16
= hd + u, c − u + 1, b + 1, a − 1, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
−1
a
2
=
1
−1
a
9
=
u
0
a
1
=
1
−1
a
7
=
−u
u
a
6
=
−u
u
a
11
=
u − 1
−u
a
10
=
2u − 1
−u
a
5
=
−u − 1
1
a
12
=
u
−u − 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
6
u
2
c
3
, c
4
, c
5
c
7
, 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
6
y
2
c
3
, c
4
, c
5
c
7
, 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
16
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.00000
b = −1.00000
c = −1.00000 + 1.00000I
d = − 1.000000I
−4.93480 0
u = − 1.000000I
a = 1.00000
b = −1.00000
c = −1.00000 − 1.00000I
d = 1.000000I
−4.93480 0
70
XVII. I
u
17
= hd + u, c − u + 1, b + u + 1, a − u, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
−1
a
2
=
u
−u − 1
a
9
=
u
0
a
1
=
u − 1
−u
a
7
=
−u
u
a
6
=
−u − 1
1
a
11
=
u − 1
−u
a
10
=
2u − 1
−u
a
5
=
−u − 1
1
a
12
=
u − 1
−u
(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
6
, c
7
, c
8
c
10
u
2
+ 1
c
5
, 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
6
, c
7
, c
8
c
10
(y + 1)
2
c
5
, c
11
, c
12
y
2
73
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
17
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.000000I
b = −1.00000 − 1.00000I
c = −1.00000 + 1.00000I
d = − 1.000000I
−4.93480 0
u = − 1.000000I
a = − 1.000000I
b = −1.00000 + 1.00000I
c = −1.00000 − 1.00000I
d = 1.000000I
−4.93480 0
74
XVIII. I
u
18
= hd + u, ca − au + u + 1, b + a + 1, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
−1
a
2
=
a
−a − 1
a
9
=
u
0
a
1
=
a − 1
−a
a
7
=
−u
u
a
6
=
au − u
−au
a
11
=
c
−u
a
10
=
c + u
−u
a
5
=
cu
1
a
12
=
c + a − 1
−a − u
(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.
75
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
18
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
c = ···
d = ···
−6.57974 −6.00000
76
XIX. I
v
1
= ha, d + v, −av + c + v + 1, b + 1, v
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
v
0
a
3
=
1
0
a
2
=
0
−1
a
9
=
v
0
a
1
=
−1
−1
a
7
=
v
0
a
6
=
v
v
a
11
=
−v −1
−v
a
10
=
−1
−v
a
5
=
−v + 1
1
a
12
=
−v −2
−v −1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
77
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
(u − 1)
2
c
2
, c
4
, c
5
c
6
, c
10
, c
12
u
2
+ 1
c
3
, c
7
, c
8
u
2
78
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
(y −1)
2
c
2
, c
4
, c
5
c
6
, c
10
, c
12
(y + 1)
2
c
3
, c
7
, c
8
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 = −1.00000 − 1.00000I
d = − 1.000000I
−4.93480 0
v = − 1.000000I
a = 0
b = −1.00000
c = −1.00000 + 1.00000I
d = 1.000000I
−4.93480 0
80
XX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
u
2
(u − 1)
6
(u
2
+ u + 1)
6
(u
4
+ 3u
3
+ 2u
2
+ 1)
3
· (u
5
+ 2u
4
+ 5u
3
+ 3u
2
+ 6u − 1)(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
8
+ 5u
7
+ 9u
6
+ 7u
5
+ 3u
4
− u
3
+ 16u + 16)
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
u
2
(u
2
+ 1)
3
(u
2
+ u + 1)
6
(u
4
− u
3
+ 2u
2
− 2u + 1)
3
· (u
5
+ u
3
+ u
2
+ 2u − 1)(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
8
− u
7
+ 3u
6
− 3u
5
+ 3u
4
− 5u
3
+ 4u
2
− 4u + 4)
81
XXI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
y
2
(y −1)
6
(y
2
+ y + 1)
6
(y
4
− 5y
3
+ 6y
2
+ 4y + 1)
3
· (y
5
+ 6y
4
+ 25y
3
+ 55y
2
+ 42y −1)
· (y
6
+ 2y
5
+ 3y
4
− 2y
3
+ 13y
2
− y + 16)
3
· (y
8
− 7y
7
+ 17y
6
+ 15y
5
− 105y
4
+ 63y
3
+ 128y
2
− 256y + 256)
· (y
8
+ 7y
7
+ 32y
6
+ 82y
5
+ 146y
4
+ 151y
3
+ 84y
2
+ 8y + 1)
3
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
12
y
2
(y + 1)
6
(y
2
+ y + 1)
6
(y
4
+ 3y
3
+ 2y
2
+ 1)
3
· (y
5
+ 2y
4
+ 5y
3
+ 3y
2
+ 6y −1)(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
8
+ 5y
7
+ 9y
6
+ 7y
5
+ 3y
4
− y
3
+ 16y + 16)
82
