12n
0554
(K12n
0554
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 12 2 4 3 5 9 1 5
Solving Sequence
5,9
10
3,4 1,8
12 6 2 7 11
c
9
c
4
c
8
c
12
c
5
c
2
c
6
c
11
c
1
, c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
5
− u
4
− 5u
3
− 5u
2
+ 6d − 4u − 2, u
5
+ u
4
− u
3
− u
2
+ 12c − 8u − 4,
− u
5
− 4u
4
− 5u
3
− 8u
2
+ 6b − 4u − 2, u
5
+ u
4
+ 5u
3
− u
2
+ 12a − 2u − 4,
u
6
+ 3u
5
+ 7u
4
+ 9u
3
+ 8u
2
+ 4u + 4i
I
u
2
= h−u
3
+ u
2
+ 2d − 3u − 1, c + 1, b + u, u
3
− u
2
+ 2a + 5u − 1, u
4
+ 4u
2
+ 2u + 1i
I
u
3
= h−u
3
+ u
2
+ 2d − 3u − 1, c + 1, −u
3
− u
2
+ 2b − 5u − 5, −u
3
+ u
2
+ 2a − 5u + 3, u
4
+ 4u
2
+ 2u + 1i
I
u
4
= hu
3
− u
2
+ 2d + 5u + 1, 5u
3
− u
2
+ 2c + 19u + 5, b + u, u
3
− u
2
+ 2a + 5u − 1, u
4
+ 4u
2
+ 2u + 1i
I
u
5
= hd + 1, 2c − u − 1, b, a − 1, u
2
− u + 2i
I
u
6
= hd + 1, 2c − u − 1, b − u + 1, 2a − u + 1, u
2
− u + 2i
I
u
7
= hd − u, c, b − u + 1, 2a − u + 1, u
2
− u + 2i
I
u
8
= hd + 1, c, b, a − 1, u + 1i
I
u
9
= hd, c − u, b − u, a − 1, u
2
+ 1i
I
u
10
= hd − u, c − 1, b + 1, a, u
2
+ 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
= hd − u, c − 1, b − u, a − 1, u
2
+ 1i
I
u
12
= hd − u, cb − u + 1, a − 1, u
2
+ 1i
I
v
1
= ha, d − v, −av + c + 1, b − 1, v
2
+ 1i
* 12 irreducible components of dim
C
= 0, with total 33 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
5
− u
4
+ · · · + 6d − 2, u
5
+ u
4
+ · · · + 12c − 4, −u
5
− 4u
4
+ · · · +
6b − 2, u
5
+ u
4
+ · · · + 12a − 4, u
6
+ 3u
5
+ · · · + 4u + 4i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
−
1
12
u
5
−
1
12
u
4
+ ··· +
2
3
u +
1
3
1
6
u
5
+
1
6
u
4
+ ··· +
2
3
u +
1
3
a
4
=
u
u
3
+ u
a
1
=
−
1
12
u
5
−
1
12
u
4
+ ··· +
1
6
u +
1
3
1
6
u
5
+
2
3
u
4
+ ··· +
2
3
u +
1
3
a
8
=
−
1
4
u
5
−
3
4
u
4
+ ··· −
5
4
u
2
−
1
2
u
1
3
u
5
+
1
3
u
4
+ ··· +
1
3
u −
1
3
a
12
=
−
1
12
u
5
−
1
12
u
4
+ ··· +
1
6
u +
1
3
−
1
6
u
5
+
1
3
u
4
+ ··· +
1
3
u −
1
3
a
6
=
1
12
u
5
+
7
12
u
4
+ ··· +
1
3
u +
2
3
−
2
3
u
5
−
7
6
u
4
+ ··· −
2
3
u −
1
3
a
2
=
1
2
u
3
+ u
2
+
1
2
u + 1
1
3
u
5
+
5
6
u
4
+ ··· +
1
3
u +
2
3
a
7
=
7
12
u
5
+
13
12
u
4
+ ··· +
5
6
u +
2
3
1
3
u
5
+
7
3
u
4
+ ··· +
4
3
u +
11
3
a
11
=
u
2
+ 1
u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
5
− u
4
− u
3
+ 5u
2
+ 6u + 10
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
6
+ 2u
5
+ 11u
4
+ 8u
3
+ 35u
2
+ 6u + 1
c
2
, c
3
, c
5
c
6
, c
7
, c
8
c
12
u
6
+ u
4
+ 2u
3
+ 5u
2
− 2u + 1
c
4
, c
9
u
6
− 3u
5
+ 7u
4
− 9u
3
+ 8u
2
− 4u + 4
c
10
u
6
− 5u
5
+ 11u
4
− 15u
3
+ 48u
2
− 48u + 16
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
6
+ 18y
5
+ 159y
4
+ 684y
3
+ 1151y
2
+ 34y + 1
c
2
, c
3
, c
5
c
6
, c
7
, c
8
c
12
y
6
+ 2y
5
+ 11y
4
+ 8y
3
+ 35y
2
+ 6y + 1
c
4
, c
9
y
6
+ 5y
5
+ 11y
4
+ 15y
3
+ 48y
2
+ 48y + 16
c
10
y
6
− 3y
5
+ 67y
4
+ 383y
3
+ 1216y
2
− 768y + 256
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.161386 + 0.788818I
a = 0.386240 + 0.341797I
b = −0.360068 + 0.335344I
c = 0.318404 + 0.521609I
d = −0.207282 + 0.359834I
0.555934 − 1.031130I 7.70744 + 6.55849I
u = 0.161386 − 0.788818I
a = 0.386240 − 0.341797I
b = −0.360068 − 0.335344I
c = 0.318404 − 0.521609I
d = −0.207282 − 0.359834I
0.555934 + 1.031130I 7.70744 − 6.55849I
u = −1.161390 + 0.788818I
a = −0.263365 − 0.996502I
b = 0.040620 − 1.297830I
c = −0.543326 + 0.748451I
d = 1.09193 + 0.94958I
3.25859 + 6.90945I 3.50627 − 5.32738I
u = −1.161390 − 0.788818I
a = −0.263365 + 0.996502I
b = 0.040620 + 1.297830I
c = −0.543326 − 0.748451I
d = 1.09193 − 0.94958I
3.25859 − 6.90945I 3.50627 + 5.32738I
u = −0.50000 + 1.69717I
a = −0.622875 + 0.704751I
b = −0.18055 + 2.20615I
c = 1.224920 − 0.254488I
d = −0.88465 − 1.40950I
10.9899 + 13.3339I 2.78630 − 6.00559I
u = −0.50000 − 1.69717I
a = −0.622875 − 0.704751I
b = −0.18055 − 2.20615I
c = 1.224920 + 0.254488I
d = −0.88465 + 1.40950I
10.9899 − 13.3339I 2.78630 + 6.00559I
6
II.
I
u
2
= h−u
3
+u
2
+2d−3u−1, c+1, b+u, u
3
−u
2
+2a+5u−1, u
4
+4u
2
+2u+1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
−1
1
2
u
3
−
1
2
u
2
+
3
2
u +
1
2
a
4
=
u
u
3
+ u
a
1
=
−
1
2
u
3
+
1
2
u
2
−
5
2
u +
1
2
−u
a
8
=
−
1
2
u
3
+
1
2
u
2
−
3
2
u +
1
2
1
2
u
3
−
1
2
u
2
+
1
2
u −
1
2
a
12
=
−
1
2
u
3
+
1
2
u
2
−
5
2
u +
1
2
−
1
2
u
3
−
1
2
u
2
−
3
2
u −
1
2
a
6
=
1
2
u
3
+
1
2
u
2
+
3
2
u +
3
2
−u
2
a
2
=
−u
3
− 3u − 1
u
3
+ u
2
+ 2u + 1
a
7
=
u
3
+ 2u
−
3
2
u
3
−
3
2
u
2
−
3
2
u +
1
2
a
11
=
u
2
+ 1
u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 14u − 4
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− u
3
+ 16u + 16
c
2
, c
6
u
4
− 3u
3
+ 4u
2
− 4u + 4
c
3
, c
5
, c
7
c
8
, c
12
u
4
+ 3u
3
+ 5u
2
+ 3u + 2
c
4
, c
9
u
4
+ 4u
2
− 2u + 1
c
10
u
4
− 8u
3
+ 18u
2
− 4u + 1
c
11
u
4
+ u
3
+ 11u
2
+ 11u + 4
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− y
3
+ 64y
2
− 256y + 256
c
2
, c
6
y
4
− y
3
+ 16y + 16
c
3
, c
5
, c
7
c
8
, c
12
y
4
+ y
3
+ 11y
2
+ 11y + 4
c
4
, c
9
y
4
+ 8y
3
+ 18y
2
+ 4y + 1
c
10
y
4
− 28y
3
+ 262y
2
+ 20y + 1
c
11
y
4
+ 21y
3
+ 107y
2
− 33y + 16
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.264316 + 0.422125I
a = 1.04521 − 1.17351I
b = 0.264316 − 0.422125I
c = −1.00000
d = 0.219104 + 0.751390I
−3.71660 + 1.17563I −0.79089 − 5.96277I
u = −0.264316 − 0.422125I
a = 1.04521 + 1.17351I
b = 0.264316 + 0.422125I
c = −1.00000
d = 0.219104 − 0.751390I
−3.71660 − 1.17563I −0.79089 + 5.96277I
u = 0.26432 + 1.99036I
a = −0.545213 − 0.715953I
b = −0.26432 − 1.99036I
c = −1.00000
d = 1.28090 − 1.27441I
13.5862 − 4.7517I 4.79089 + 2.00586I
u = 0.26432 − 1.99036I
a = −0.545213 + 0.715953I
b = −0.26432 + 1.99036I
c = −1.00000
d = 1.28090 + 1.27441I
13.5862 + 4.7517I 4.79089 − 2.00586I
10
III. I
u
3
= h−u
3
+ u
2
+ 2d − 3u − 1, c + 1, −u
3
− u
2
+ 2b − 5u − 5, −u
3
+
u
2
+ 2a − 5u + 3, u
4
+ 4u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
−1
1
2
u
3
−
1
2
u
2
+
3
2
u +
1
2
a
4
=
u
u
3
+ u
a
1
=
1
2
u
3
−
1
2
u
2
+
5
2
u −
3
2
1
2
u
3
+
1
2
u
2
+
5
2
u +
5
2
a
8
=
−
1
2
u
3
+
1
2
u
2
−
3
2
u +
1
2
1
2
u
3
−
1
2
u
2
+
1
2
u −
1
2
a
12
=
1
2
u
3
−
1
2
u
2
+
5
2
u −
3
2
u
3
+ 3u + 3
a
6
=
3
2
u
3
−
1
2
u
2
+
11
2
u +
5
2
−
3
2
u
3
+
3
2
u
2
−
9
2
u +
1
2
a
2
=
u
3
− u
2
+ 3u − 2
3u + 3
a
7
=
u
3
+ 2u
−
3
2
u
3
−
3
2
u
2
−
3
2
u +
1
2
a
11
=
u
2
+ 1
u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 14u − 4
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ u
3
+ 11u
2
+ 11u + 4
c
2
, c
3
, c
6
c
7
, c
8
u
4
+ 3u
3
+ 5u
2
+ 3u + 2
c
4
, c
9
u
4
+ 4u
2
− 2u + 1
c
5
, c
12
u
4
− 3u
3
+ 4u
2
− 4u + 4
c
10
u
4
− 8u
3
+ 18u
2
− 4u + 1
c
11
u
4
− u
3
+ 16u + 16
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
+ 21y
3
+ 107y
2
− 33y + 16
c
2
, c
3
, c
6
c
7
, c
8
y
4
+ y
3
+ 11y
2
+ 11y + 4
c
4
, c
9
y
4
+ 8y
3
+ 18y
2
+ 4y + 1
c
5
, c
12
y
4
− y
3
+ 16y + 16
c
10
y
4
− 28y
3
+ 262y
2
+ 20y + 1
c
11
y
4
− y
3
+ 64y
2
− 256y + 256
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.264316 + 0.422125I
a = −2.04521 + 1.17351I
b = 1.84646 + 0.95037I
c = −1.00000
d = 0.219104 + 0.751390I
−3.71660 + 1.17563I −0.79089 − 5.96277I
u = −0.264316 − 0.422125I
a = −2.04521 − 1.17351I
b = 1.84646 − 0.95037I
c = −1.00000
d = 0.219104 − 0.751390I
−3.71660 − 1.17563I −0.79089 + 5.96277I
u = 0.26432 + 1.99036I
a = −0.454787 + 0.715953I
b = −0.34646 + 1.76812I
c = −1.00000
d = 1.28090 − 1.27441I
13.5862 − 4.7517I 4.79089 + 2.00586I
u = 0.26432 − 1.99036I
a = −0.454787 − 0.715953I
b = −0.34646 − 1.76812I
c = −1.00000
d = 1.28090 + 1.27441I
13.5862 + 4.7517I 4.79089 − 2.00586I
14
IV. I
u
4
= hu
3
− u
2
+ 2d + 5u + 1, 5u
3
− u
2
+ 2c + 19u + 5, b + u, u
3
− u
2
+
2a + 5u − 1, u
4
+ 4u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
−
5
2
u
3
+
1
2
u
2
−
19
2
u −
5
2
−
1
2
u
3
+
1
2
u
2
−
5
2
u −
1
2
a
4
=
u
u
3
+ u
a
1
=
−
1
2
u
3
+
1
2
u
2
−
5
2
u +
1
2
−u
a
8
=
−u
2
− 4
−
1
2
u
3
−
1
2
u
2
−
1
2
u −
3
2
a
12
=
−
1
2
u
3
+
1
2
u
2
−
5
2
u +
1
2
−
1
2
u
3
−
1
2
u
2
−
3
2
u −
1
2
a
6
=
1
2
u
3
+
1
2
u
2
+
3
2
u +
3
2
−u
2
a
2
=
−2u
3
+ u
2
− 7u − 2
−u
2
− 3u − 1
a
7
=
−
1
2
u
3
+
3
2
u
2
−
1
2
u +
7
2
3
2
u
3
−
1
2
u
2
−
1
2
u +
1
2
a
11
=
u
2
+ 1
u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 14u − 4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
4
+ u
3
+ 11u
2
+ 11u + 4
c
2
, c
5
, c
6
c
12
u
4
+ 3u
3
+ 5u
2
+ 3u + 2
c
3
, c
7
, c
8
u
4
− 3u
3
+ 4u
2
− 4u + 4
c
4
, c
9
u
4
+ 4u
2
− 2u + 1
c
10
u
4
− 8u
3
+ 18u
2
− 4u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
4
+ 21y
3
+ 107y
2
− 33y + 16
c
2
, c
5
, c
6
c
12
y
4
+ y
3
+ 11y
2
+ 11y + 4
c
3
, c
7
, c
8
y
4
− y
3
+ 16y + 16
c
4
, c
9
y
4
+ 8y
3
+ 18y
2
+ 4y + 1
c
10
y
4
− 28y
3
+ 262y
2
+ 20y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.264316 + 0.422125I
a = 1.04521 − 1.17351I
b = 0.264316 − 0.422125I
c = −0.35023 − 4.15490I
d = 0.045213 − 1.173520I
−3.71660 + 1.17563I −0.79089 − 5.96277I
u = −0.264316 − 0.422125I
a = 1.04521 + 1.17351I
b = 0.264316 + 0.422125I
c = −0.35023 + 4.15490I
d = 0.045213 + 1.173520I
−3.71660 − 1.17563I −0.79089 + 5.96277I
u = 0.26432 + 1.99036I
a = −0.545213 − 0.715953I
b = −0.26432 − 1.99036I
c = 0.850232 + 0.286979I
d = −1.54521 − 0.71595I
13.5862 − 4.7517I 4.79089 + 2.00586I
u = 0.26432 − 1.99036I
a = −0.545213 + 0.715953I
b = −0.26432 + 1.99036I
c = 0.850232 − 0.286979I
d = −1.54521 + 0.71595I
13.5862 + 4.7517I 4.79089 − 2.00586I
18
V. I
u
5
= hd + 1, 2c − u − 1, b, a − 1, u
2
− u + 2i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u − 2
a
3
=
1
2
u +
1
2
−1
a
4
=
u
−2
a
1
=
1
0
a
8
=
−
1
2
u +
1
2
1
a
12
=
1
u − 2
a
6
=
u
−2
a
2
=
−
1
2
u +
1
2
1
a
7
=
3
2
u −
1
2
−3
a
11
=
u − 1
u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
19
(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 − 1)
2
c
4
, c
5
, c
9
c
12
u
2
+ u + 2
c
10
u
2
− 3u + 4
c
11
u
2
+ 3u + 4
20
(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 −1)
2
c
4
, c
5
, c
9
c
12
y
2
+ 3y + 4
c
10
, c
11
y
2
− y + 16
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.50000 + 1.32288I
a = 1.00000
b = 0
c = 0.750000 + 0.661438I
d = −1.00000
1.64493 6.00000
u = 0.50000 − 1.32288I
a = 1.00000
b = 0
c = 0.750000 − 0.661438I
d = −1.00000
1.64493 6.00000
22
VI. I
u
6
= hd + 1, 2c − u − 1, b − u + 1, 2a − u + 1, u
2
− u + 2i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u − 2
a
3
=
1
2
u +
1
2
−1
a
4
=
u
−2
a
1
=
1
2
u −
1
2
u − 1
a
8
=
−
1
2
u +
1
2
1
a
12
=
1
2
u −
1
2
−1
a
6
=
−
1
2
u +
1
2
u + 1
a
2
=
1
2
u +
3
2
2u − 3
a
7
=
3
2
u −
1
2
−3
a
11
=
u − 1
u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
+ 3u + 4
c
2
, c
4
, c
6
c
9
u
2
+ u + 2
c
3
, c
5
, c
7
c
8
, c
11
, c
12
(u − 1)
2
c
10
u
2
− 3u + 4
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
2
− y + 16
c
2
, c
4
, c
6
c
9
y
2
+ 3y + 4
c
3
, c
5
, c
7
c
8
, c
11
, c
12
(y −1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.50000 + 1.32288I
a = −0.250000 + 0.661438I
b = −0.50000 + 1.32288I
c = 0.750000 + 0.661438I
d = −1.00000
1.64493 6.00000
u = 0.50000 − 1.32288I
a = −0.250000 − 0.661438I
b = −0.50000 − 1.32288I
c = 0.750000 − 0.661438I
d = −1.00000
1.64493 6.00000
26
VII. I
u
7
= hd − u, c, b − u + 1, 2a − u + 1, u
2
− u + 2i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u − 2
a
3
=
0
u
a
4
=
u
−2
a
1
=
1
2
u −
1
2
u − 1
a
8
=
1
u − 2
a
12
=
1
2
u −
1
2
−1
a
6
=
−
1
2
u +
1
2
u + 1
a
2
=
1
2
u −
1
2
−1
a
7
=
−u + 1
u + 2
a
11
=
u − 1
u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
27
(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 − 1)
2
c
3
, c
4
, c
7
c
8
, c
9
u
2
+ u + 2
c
10
u
2
− 3u + 4
28
(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 −1)
2
c
3
, c
4
, c
7
c
8
, c
9
y
2
+ 3y + 4
c
10
y
2
− y + 16
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.50000 + 1.32288I
a = −0.250000 + 0.661438I
b = −0.50000 + 1.32288I
c = 0
d = 0.50000 + 1.32288I
1.64493 6.00000
u = 0.50000 − 1.32288I
a = −0.250000 − 0.661438I
b = −0.50000 − 1.32288I
c = 0
d = 0.50000 − 1.32288I
1.64493 6.00000
30
VIII. I
u
8
= hd + 1, c, b, a − 1, u + 1i
(i) Arc colorings
a
5
=
0
−1
a
9
=
1
0
a
10
=
1
1
a
3
=
0
−1
a
4
=
−1
−2
a
1
=
1
0
a
8
=
1
1
a
12
=
1
1
a
6
=
−1
−2
a
2
=
1
1
a
7
=
−2
−3
a
11
=
2
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
11
, c
12
u − 1
c
10
u + 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 0
c = 0
d = −1.00000
1.64493 6.00000
34
IX. I
u
9
= hd, c − u, b − u, a − 1, u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−1
a
3
=
u
0
a
4
=
u
0
a
1
=
1
u
a
8
=
1
0
a
12
=
1
u − 1
a
6
=
u
−1
a
2
=
u + 1
u
a
7
=
1
0
a
11
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
, c
11
(u − 1)
2
c
2
, c
4
, c
5
c
6
, c
9
, c
12
u
2
+ 1
c
3
, c
7
, c
8
u
2
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
, c
11
(y −1)
2
c
2
, c
4
, c
5
c
6
, c
9
, c
12
(y + 1)
2
c
3
, c
7
, c
8
y
2
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.00000
b = 1.000000I
c = 1.000000I
d = 0
−1.64493 4.00000
u = − 1.000000I
a = 1.00000
b = − 1.000000I
c = − 1.000000I
d = 0
−1.64493 4.00000
38
X. I
u
10
= hd − u, c − 1, b + 1, a, u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−1
a
3
=
1
u
a
4
=
u
0
a
1
=
0
−1
a
8
=
u + 1
−1
a
12
=
0
−1
a
6
=
0
u
a
2
=
1
u − 1
a
7
=
u
−1
a
11
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u − 1)
2
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
9
u
2
+ 1
c
5
, c
11
, c
12
u
2
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y −1)
2
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
9
(y + 1)
2
c
5
, c
11
, c
12
y
2
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0
b = −1.00000
c = 1.00000
d = 1.000000I
−1.64493 4.00000
u = − 1.000000I
a = 0
b = −1.00000
c = 1.00000
d = − 1.000000I
−1.64493 4.00000
42
XI. I
u
11
= hd − u, c − 1, b − u, a − 1, u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−1
a
3
=
1
u
a
4
=
u
0
a
1
=
1
u
a
8
=
u + 1
−1
a
12
=
1
u − 1
a
6
=
u
−1
a
2
=
1
u
a
7
=
u
−1
a
11
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
43
(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
9
c
12
u
2
+ 1
c
10
, c
11
(u − 1)
2
44
(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
9
c
12
(y + 1)
2
c
10
, c
11
(y −1)
2
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.00000
b = 1.000000I
c = 1.00000
d = 1.000000I
−1.64493 4.00000
u = − 1.000000I
a = 1.00000
b = − 1.000000I
c = 1.00000
d = − 1.000000I
−1.64493 4.00000
46
XII. I
u
12
= hd − u, cb − u + 1, a − 1, u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−1
a
3
=
c
u
a
4
=
u
0
a
1
=
1
b
a
8
=
cu + 1
−1
a
12
=
1
b − 1
a
6
=
u
bu
a
2
=
c + 1
b + u
a
7
=
−cu
1
a
11
=
0
−1
(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.
47
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
c = ···
d = ···
−3.28987 −2.00000
48
XIII. I
v
1
= ha, d − v, −av + c + 1, b − 1, v
2
+ 1i
(i) Arc colorings
a
5
=
v
0
a
9
=
1
0
a
10
=
1
0
a
3
=
−1
v
a
4
=
v
0
a
1
=
0
1
a
8
=
−v + 1
−1
a
12
=
1
1
a
6
=
0
−v
a
2
=
−1
v + 1
a
7
=
−v
−1
a
11
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
49
(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
50
(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
51
(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
d = 1.000000I
−4.93480 −8.00000
v = − 1.000000I
a = 0
b = 1.00000
c = −1.00000
d = − 1.000000I
−4.93480 −8.00000
52
XIV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
u
2
(u − 1)
11
(u
2
+ 3u + 4)(u
4
− u
3
+ 16u + 16)
· ((u
4
+ u
3
+ 11u
2
+ 11u + 4)
2
)(u
6
+ 2u
5
+ ··· + 6u + 1)
c
2
, c
3
, c
5
c
6
, c
7
, c
8
c
12
u
2
(u − 1)
5
(u
2
+ 1)
3
(u
2
+ u + 2)(u
4
− 3u
3
+ 4u
2
− 4u + 4)
· (u
4
+ 3u
3
+ 5u
2
+ 3u + 2)
2
(u
6
+ u
4
+ 2u
3
+ 5u
2
− 2u + 1)
c
4
, c
9
u
2
(u − 1)(u
2
+ 1)
3
(u
2
+ u + 2)
3
(u
4
+ 4u
2
− 2u + 1)
3
· (u
6
− 3u
5
+ 7u
4
− 9u
3
+ 8u
2
− 4u + 4)
c
10
u
2
(u − 1)
6
(u + 1)(u
2
− 3u + 4)
3
(u
4
− 8u
3
+ 18u
2
− 4u + 1)
3
· (u
6
− 5u
5
+ 11u
4
− 15u
3
+ 48u
2
− 48u + 16)
53
XV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
2
(y −1)
11
(y
2
− y + 16)(y
4
− y
3
+ 64y
2
− 256y + 256)
· (y
4
+ 21y
3
+ 107y
2
− 33y + 16)
2
· (y
6
+ 18y
5
+ 159y
4
+ 684y
3
+ 1151y
2
+ 34y + 1)
c
2
, c
3
, c
5
c
6
, c
7
, c
8
c
12
y
2
(y −1)
5
(y + 1)
6
(y
2
+ 3y + 4)(y
4
− y
3
+ 16y + 16)
· ((y
4
+ y
3
+ 11y
2
+ 11y + 4)
2
)(y
6
+ 2y
5
+ ··· + 6y + 1)
c
4
, c
9
y
2
(y −1)(y + 1)
6
(y
2
+ 3y + 4)
3
(y
4
+ 8y
3
+ 18y
2
+ 4y + 1)
3
· (y
6
+ 5y
5
+ 11y
4
+ 15y
3
+ 48y
2
+ 48y + 16)
c
10
y
2
(y −1)
7
(y
2
− y + 16)
3
(y
4
− 28y
3
+ 262y
2
+ 20y + 1)
3
· (y
6
− 3y
5
+ 67y
4
+ 383y
3
+ 1216y
2
− 768y + 256)
54
