12n
0881
(K12n
0881
)
A knot diagram
1
Linearized knot diagam
4 12 7 1 8 4 11 5 12 8 3 9
Solving Sequence
3,7 4,11
8 12 2 1 6 5 10 9
c
3
c
7
c
11
c
2
c
1
c
6
c
5
c
10
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, a + 1, u
3
+ u
2
+ 2u − 1i
I
u
2
= hb − u, −2u
15
+ 4u
14
+ ··· + 2a + 5,
u
16
− u
15
+ 6u
14
− 3u
13
+ 17u
12
− 5u
11
+ 30u
10
− 4u
9
+ 33u
8
− 3u
7
+ 22u
6
− 4u
5
+ 8u
4
− 5u
3
+ 3u
2
− 3u + 1i
I
u
3
= h−2u
15
− 8u
13
− 5u
12
− 20u
11
− 14u
10
− 28u
9
− 24u
8
− 22u
7
− 14u
6
− u
4
+ 6u
3
+ 2u
2
+ 2b + u − 2, a + 1,
u
16
− u
15
+ 6u
14
− 3u
13
+ 17u
12
− 5u
11
+ 30u
10
− 4u
9
+ 33u
8
− 3u
7
+ 22u
6
− 4u
5
+ 8u
4
− 5u
3
+ 3u
2
− 3u + 1i
I
u
4
= h14971u
15
+ 114227u
14
+ ··· + 20848b + 188080, 11755u
15
+ 75853u
14
+ ··· + 41696a − 119840,
u
16
+ 9u
15
+ ··· + 64u + 32i
I
u
5
= hb + u, a + 1, u
4
+ u
2
+ 2u + 1i
I
u
6
= hb − 2u − 1, a + 1, u
2
+ u + 1i
I
u
7
= hb + u, a + u − 1, u
2
+ u + 1i
I
u
8
= h2b − u − 1, 6a + u − 3, u
2
+ 3i
I
u
9
= hb + 1, a + 1, u
2
− u + 1i
I
u
10
= hb − u, a + u − 1, u
2
− u + 1i
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
1
I
u
11
= hb − a, a
2
− a + 1, u + 1i
I
u
12
= hu
3
− au − u
2
+ b + 3u − 2, 2u
4
a − 2u
3
a + 7u
2
a + u
3
+ a
2
− 5au + 3a + 3u, u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1i
I
u
13
= hu
8
− 2u
7
+ 2u
6
− 4u
5
+ 6u
4
− 3u
3
+ 4u
2
+ 2b − 3u,
− 2u
9
+ 3u
8
− 4u
7
+ 10u
6
− 12u
5
+ 10u
4
− 17u
3
+ 10u
2
+ 2a − 9u + 4,
u
10
− 2u
9
+ 3u
8
− 6u
7
+ 8u
6
− 8u
5
+ 11u
4
− 8u
3
+ 7u
2
− 4u + 1i
I
u
14
= hu
9
− 2u
8
+ 2u
7
− 4u
6
+ 6u
5
− 5u
4
+ 6u
3
− 5u
2
+ 2b + 4u − 2,
− u
7
+ 2u
6
− 2u
5
+ 4u
4
− 6u
3
+ 3u
2
+ 2a − 4u + 3,
u
10
− 2u
9
+ 3u
8
− 6u
7
+ 8u
6
− 8u
5
+ 11u
4
− 8u
3
+ 7u
2
− 4u + 1i
I
u
15
= hb + u, a + 1, u
3
− u
2
+ 2u − 1i
I
u
16
= hb + u, 2u
5
+ 5u
3
− 3u
2
+ a + 3u − 2, u
6
− u
5
+ 3u
4
− 4u
3
+ 4u
2
− 3u + 1i
I
u
17
= h−u
5
+ u
4
+ b − u, −u
4
+ u
3
+ a − 1, u
6
− 2u
5
+ 2u
4
− 2u
3
+ 2u
2
− u + 1i
I
u
18
= h2u
5
− u
4
+ 5u
3
− 5u
2
+ b + 4u − 2, a + 1, u
6
− u
5
+ 3u
4
− 4u
3
+ 4u
2
− 3u + 1i
I
u
19
= hb − u, a + 1, u
4
+ 2u
3
+ 3u
2
+ 2u + 1i
* 19 irreducible components of dim
C
= 0, with total 122 representations.
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= hb − u, a + 1, u
3
+ u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
−1
u
a
8
=
−u
u
2
+ u
a
12
=
−u − 1
u
a
2
=
u
2
+ u + 1
−u
2
a
1
=
u
2
+ 1
2u − 1
a
6
=
u
−u
2
− u + 1
a
5
=
u
2
+ u
−u
2
+ u
a
10
=
−u
2
− 1
−u + 1
a
9
=
u − 1
−u
2
− u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6u − 9
3
(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
10
, c
11
, c
12
u
3
− u
2
+ 2u + 1
4
(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
3
+ 3y
2
+ 6y −1
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.69632 + 1.43595I
a = −1.00000
b = −0.69632 + 1.43595I
8.6715 + 17.0103I −4.82206 − 8.61570I
u = −0.69632 − 1.43595I
a = −1.00000
b = −0.69632 − 1.43595I
8.6715 − 17.0103I −4.82206 + 8.61570I
u = 0.392647
a = −1.00000
b = 0.392647
−0.893590 −11.3560
6
II. I
u
2
= hb − u, −2u
15
+ 4u
14
+ · · · + 2a + 5, u
16
− u
15
+ · · · − 3u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
u
15
− 2u
14
+ ··· + 4u −
5
2
u
a
8
=
u
15
+ 2u
14
+ ··· − 5u + 2
u
15
− 2u
14
+ ··· + 5u − 1
a
12
=
u
15
− 2u
14
+ ··· + 3u −
5
2
u
a
2
=
u
15
+ 4u
13
+ ··· −
1
2
u + 2
−u
2
a
1
=
2u
15
+
1
2
u
14
+ ··· −
5
2
u + 3
−
1
2
u
15
− u
14
+ ··· +
7
2
u −
3
2
a
6
=
u
u
3
+ u
a
5
=
−
1
2
u
15
+
5
2
u
14
+ ··· −
9
2
u + 2
u
15
− u
14
+ ··· +
5
2
u −
1
2
a
10
=
−
3
2
u
15
− 6u
13
+ ··· + u −
5
2
1
2
u
15
+ u
14
+ ··· − 3u + 2
a
9
=
−
3
2
u
15
+ 2u
14
+ ··· − 5u +
1
2
u
15
−
1
2
u
14
+ ··· + u +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3u
15
+ 14u
13
+ 8u
12
+ 38u
11
+ 28u
10
+ 64u
9
+ 54u
8
+ 68u
7
+
48u
6
+ 35u
5
+ 12u
4
+ 2u
3
− 10u
2
− 5u − 8
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
16
− 9u
15
+ ··· − 64u + 32
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
u
16
+ u
15
+ ··· + 3u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
16
+ 11y
15
+ ··· − 2560y + 1024
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
16
+ 11y
15
+ ··· − 3y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.155071 + 0.982491I
a = 1.85344 − 0.16488I
b = 0.155071 + 0.982491I
11.07300 + 2.11324I −4.13579 − 3.29911I
u = 0.155071 − 0.982491I
a = 1.85344 + 0.16488I
b = 0.155071 − 0.982491I
11.07300 − 2.11324I −4.13579 + 3.29911I
u = 0.263127 + 0.911584I
a = −0.593560 − 1.154310I
b = 0.263127 + 0.911584I
1.97235 −2.75019 + 0.I
u = 0.263127 − 0.911584I
a = −0.593560 + 1.154310I
b = 0.263127 − 0.911584I
1.97235 −2.75019 + 0.I
u = −0.415478 + 1.074820I
a = −0.325650 − 1.226660I
b = −0.415478 + 1.074820I
4.56396 + 9.62189I −5.35347 − 7.22561I
u = −0.415478 − 1.074820I
a = −0.325650 + 1.226660I
b = −0.415478 − 1.074820I
4.56396 − 9.62189I −5.35347 + 7.22561I
u = −0.635797 + 0.475943I
a = −0.30659 − 1.45911I
b = −0.635797 + 0.475943I
2.73466 − 5.62392I −7.83043 + 1.63381I
u = −0.635797 − 0.475943I
a = −0.30659 + 1.45911I
b = −0.635797 − 0.475943I
2.73466 + 5.62392I −7.83043 − 1.63381I
u = −0.640425 + 1.031810I
a = −1.163390 + 0.606464I
b = −0.640425 + 1.031810I
11.07300 + 2.11324I −4.13579 − 3.29911I
u = −0.640425 − 1.031810I
a = −1.163390 − 0.606464I
b = −0.640425 − 1.031810I
11.07300 − 2.11324I −4.13579 + 3.29911I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.59989 + 1.32302I
a = 0.816913 − 0.091000I
b = 0.59989 + 1.32302I
2.73466 − 5.62392I −7.83043 + 1.63381I
u = 0.59989 − 1.32302I
a = 0.816913 + 0.091000I
b = 0.59989 − 1.32302I
2.73466 + 5.62392I −7.83043 − 1.63381I
u = 0.75412 + 1.29455I
a = 0.993241 + 0.183480I
b = 0.75412 + 1.29455I
4.56396 − 9.62189I −5.35347 + 7.22561I
u = 0.75412 − 1.29455I
a = 0.993241 − 0.183480I
b = 0.75412 − 1.29455I
4.56396 + 9.62189I −5.35347 − 7.22561I
u = 0.419493 + 0.126250I
a = −0.774408 + 0.831625I
b = 0.419493 + 0.126250I
−0.882161 −11.61043 + 0.I
u = 0.419493 − 0.126250I
a = −0.774408 − 0.831625I
b = 0.419493 − 0.126250I
−0.882161 −11.61043 + 0.I
11
III. I
u
3
= h−2u
15
− 8u
13
+ · · · + 2b − 2, a + 1, u
16
− u
15
+ · · · − 3u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
−1
u
15
+ 4u
13
+ ··· −
1
2
u + 1
a
8
=
−u
u
15
− 2u
14
+ ··· + 5u − 1
a
12
=
−u
15
− 4u
13
+ ··· +
1
2
u − 2
u
15
+ 4u
13
+ ··· −
1
2
u + 1
a
2
=
−2u
15
+
5
2
u
14
+ ··· −
11
2
u + 3
3u
15
−
5
2
u
14
+ ··· + 5u − 1
a
1
=
−
1
2
u
15
+
3
2
u
14
+ ··· − 4u +
5
2
2u
15
−
5
2
u
14
+ ··· + 5u −
3
2
a
6
=
u
u
3
+ u
a
5
=
−
3
2
u
15
+ 2u
14
+ ··· − 3u + 1
3
2
u
15
− u
14
+ ··· − 4u
2
+ 2u
a
10
=
−u
2
− 1
−
1
2
u
14
−
5
2
u
12
+ ··· + u
2
+
3
2
u
a
9
=
−
1
2
u
15
−
1
2
u
14
+ ··· +
3
2
u − 1
−u
15
+ u
14
+ ··· −
3
2
u +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3u
15
+ 14u
13
+ 8u
12
+ 38u
11
+ 28u
10
+ 64u
9
+ 54u
8
+ 68u
7
+
48u
6
+ 35u
5
+ 12u
4
+ 2u
3
− 10u
2
− 5u − 8
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
, c
12
u
16
+ u
15
+ ··· + 3u + 1
c
2
, c
5
, c
8
c
11
u
16
− 9u
15
+ ··· − 64u + 32
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
, c
12
y
16
+ 11y
15
+ ··· − 3y + 1
c
2
, c
5
, c
8
c
11
y
16
+ 11y
15
+ ··· − 2560y + 1024
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.155071 + 0.982491I
a = −1.00000
b = −0.44941 − 1.79542I
11.07300 + 2.11324I −4.13579 − 3.29911I
u = 0.155071 − 0.982491I
a = −1.00000
b = −0.44941 + 1.79542I
11.07300 − 2.11324I −4.13579 + 3.29911I
u = 0.263127 + 0.911584I
a = −1.00000
b = −0.896070 + 0.844811I
1.97235 −2.75019 + 0.I
u = 0.263127 − 0.911584I
a = −1.00000
b = −0.896070 − 0.844811I
1.97235 −2.75019 + 0.I
u = −0.415478 + 1.074820I
a = −1.00000
b = −1.45373 − 0.15964I
4.56396 + 9.62189I −5.35347 − 7.22561I
u = −0.415478 − 1.074820I
a = −1.00000
b = −1.45373 + 0.15964I
4.56396 − 9.62189I −5.35347 + 7.22561I
u = −0.635797 + 0.475943I
a = −1.00000
b = −0.889379 − 0.781779I
2.73466 − 5.62392I −7.83043 + 1.63381I
u = −0.635797 − 0.475943I
a = −1.00000
b = −0.889379 + 0.781779I
2.73466 + 5.62392I −7.83043 − 1.63381I
u = −0.640425 + 1.031810I
a = −1.00000
b = −0.11931 + 1.58879I
11.07300 + 2.11324I −4.13579 − 3.29911I
u = −0.640425 − 1.031810I
a = −1.00000
b = −0.11931 − 1.58879I
11.07300 − 2.11324I −4.13579 + 3.29911I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.59989 + 1.32302I
a = −1.00000
b = −0.610454 − 1.026200I
2.73466 − 5.62392I −7.83043 + 1.63381I
u = 0.59989 − 1.32302I
a = −1.00000
b = −0.610454 + 1.026200I
2.73466 + 5.62392I −7.83043 − 1.63381I
u = 0.75412 + 1.29455I
a = −1.00000
b = −0.51150 − 1.42416I
4.56396 − 9.62189I −5.35347 + 7.22561I
u = 0.75412 − 1.29455I
a = −1.00000
b = −0.51150 + 1.42416I
4.56396 + 9.62189I −5.35347 − 7.22561I
u = 0.419493 + 0.126250I
a = −1.00000
b = 0.429851 − 0.251093I
−0.882161 −11.61043 + 0.I
u = 0.419493 − 0.126250I
a = −1.00000
b = 0.429851 + 0.251093I
−0.882161 −11.61043 + 0.I
16
IV. I
u
4
= h14971u
15
+ 114227u
14
+ · · · + 20848b + 188080, 11755u
15
+
75853u
14
+ · · · + 41696a − 119840, u
16
+ 9u
15
+ · · · + 64u + 32i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
−0.281922u
15
− 1.81919u
14
+ ··· − 4.33596u + 2.87414
−0.718102u
15
− 5.47904u
14
+ ··· − 20.9171u − 9.02149
a
8
=
0.706255u
15
+ 5.65340u
14
+ ··· + 24.6506u + 9.22947
0.702897u
15
+ 6.15119u
14
+ ··· + 36.9708u + 22.6002
a
12
=
0.436181u
15
+ 3.65985u
14
+ ··· + 16.5812u + 11.8956
−0.718102u
15
− 5.47904u
14
+ ··· − 20.9171u − 9.02149
a
2
=
−0.00335764u
15
+ 0.497794u
14
+ ··· + 11.3202u + 14.3707
−0.702897u
15
− 6.15119u
14
+ ··· − 35.9708u − 22.6002
a
1
=
0.0881619u
15
+ 0.918649u
14
+ ··· + 9.03473u + 8.66692
−0.149367u
15
− 1.50173u
14
+ ··· − 13.1190u − 9.70990
a
6
=
u
u
3
+ u
a
5
=
−0.321901u
15
− 3.03118u
14
+ ··· − 19.7034u − 16.2621
−0.268755u
15
− 2.46590u
14
+ ··· − 14.9006u − 13.2295
a
10
=
0.141045u
15
+ 1.82840u
14
+ ··· + 17.8037u + 16.0787
0.424885u
15
+ 4.19350u
14
+ ··· + 29.8853u + 27.4927
a
9
=
0.333245u
15
+ 3.21899u
14
+ ··· + 19.1554u + 15.4597
0.333941u
15
+ 3.80516u
14
+ ··· + 33.7444u + 30.7329
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
16065
5212
u
15
−
133039
5212
u
14
+ ··· −
159664
1303
u −
98654
1303
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
10
, c
11
u
16
+ u
15
+ ··· + 3u + 1
c
3
, c
6
, c
9
c
12
u
16
− 9u
15
+ ··· − 64u + 32
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
10
, c
11
y
16
+ 11y
15
+ ··· − 3y + 1
c
3
, c
6
, c
9
c
12
y
16
+ 11y
15
+ ··· − 2560y + 1024
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.889379 + 0.781779I
a = −0.137916 − 0.656371I
b = −0.635797 − 0.475943I
2.73466 + 5.62392I −7.83043 − 1.63381I
u = −0.889379 − 0.781779I
a = −0.137916 + 0.656371I
b = −0.635797 + 0.475943I
2.73466 − 5.62392I −7.83043 + 1.63381I
u = −0.610454 + 1.026200I
a = 1.209120 − 0.134690I
b = 0.59989 − 1.32302I
2.73466 + 5.62392I −7.83043 − 1.63381I
u = −0.610454 − 1.026200I
a = 1.209120 + 0.134690I
b = 0.59989 + 1.32302I
2.73466 − 5.62392I −7.83043 + 1.63381I
u = −0.896070 + 0.844811I
a = −0.352314 + 0.685153I
b = 0.263127 + 0.911584I
1.97235 −2.75019 + 0.I
u = −0.896070 − 0.844811I
a = −0.352314 − 0.685153I
b = 0.263127 − 0.911584I
1.97235 −2.75019 + 0.I
u = −1.45373 + 0.15964I
a = −0.202173 − 0.761549I
b = −0.415478 − 1.074820I
4.56396 − 9.62189I −5.35347 + 7.22561I
u = −1.45373 − 0.15964I
a = −0.202173 + 0.761549I
b = −0.415478 + 1.074820I
4.56396 + 9.62189I −5.35347 − 7.22561I
u = 0.429851 + 0.251093I
a = −0.599708 + 0.644017I
b = 0.419493 − 0.126250I
−0.882161 −11.61043 + 0.I
u = 0.429851 − 0.251093I
a = −0.599708 − 0.644017I
b = 0.419493 + 0.126250I
−0.882161 −11.61043 + 0.I
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.51150 + 1.42416I
a = 0.973582 + 0.179848I
b = 0.75412 − 1.29455I
4.56396 + 9.62189I −5.35347 − 7.22561I
u = −0.51150 − 1.42416I
a = 0.973582 − 0.179848I
b = 0.75412 + 1.29455I
4.56396 − 9.62189I −5.35347 + 7.22561I
u = −0.11931 + 1.58879I
a = −0.675889 − 0.352334I
b = −0.640425 + 1.031810I
11.07300 + 2.11324I −4.13579 − 3.29911I
u = −0.11931 − 1.58879I
a = −0.675889 + 0.352334I
b = −0.640425 − 1.031810I
11.07300 − 2.11324I −4.13579 + 3.29911I
u = −0.44941 + 1.79542I
a = 0.535301 − 0.047620I
b = 0.155071 − 0.982491I
11.07300 − 2.11324I −4.13579 + 3.29911I
u = −0.44941 − 1.79542I
a = 0.535301 + 0.047620I
b = 0.155071 + 0.982491I
11.07300 + 2.11324I −4.13579 − 3.29911I
21
V. I
u
5
= hb + u, a + 1, u
4
+ u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
−1
−u
a
8
=
−u
−u
2
+ u
a
12
=
u − 1
−u
a
2
=
u
2
− u + 1
−u
2
a
1
=
u
3
+ u + 2
u
3
− u
2
+ u + 1
a
6
=
u
u
3
+ u
a
5
=
u
3
− u
2
+ 2u + 1
−u
3
+ u
2
− u − 2
a
10
=
−u
2
− 1
−u
3
+ u
2
− u
a
9
=
−2u
3
+ u
2
− 3u − 3
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
3
+ 6u
2
− 6u − 12
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
9
, c
11
u
4
+ u
2
+ 2u + 1
c
2
, c
4
, c
6
c
8
, c
10
, c
12
u
4
+ u
2
− 2u + 1
23
(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
4
+ 2y
3
+ 3y
2
− 2y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.624811 + 0.300243I
a = −1.00000
b = 0.624811 − 0.300243I
3.28987 + 7.32772I −6.00000 − 6.00000I
u = −0.624811 − 0.300243I
a = −1.00000
b = 0.624811 + 0.300243I
3.28987 − 7.32772I −6.00000 + 6.00000I
u = 0.62481 + 1.30024I
a = −1.00000
b = −0.62481 − 1.30024I
3.28987 − 7.32772I −6.00000 + 6.00000I
u = 0.62481 − 1.30024I
a = −1.00000
b = −0.62481 + 1.30024I
3.28987 + 7.32772I −6.00000 − 6.00000I
25
VI. I
u
6
= hb − 2u − 1, a + 1, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u − 1
a
11
=
−1
2u + 1
a
8
=
−u
−2
a
12
=
−2u − 2
2u + 1
a
2
=
2u − 1
3
a
1
=
u − 1
2
a
6
=
u
u + 1
a
5
=
2u + 2
−3u − 1
a
10
=
u
1
a
9
=
u − 2
u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u − 13
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
9
u
2
+ u + 1
c
2
, c
5
, c
8
c
11
u
2
+ 3
c
4
, c
6
, c
10
c
12
u
2
− u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
, c
12
y
2
+ y + 1
c
2
, c
5
, c
8
c
11
(y + 3)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.00000
b = 1.73205I
9.86960 + 4.05977I −9.00000 − 6.92820I
u = −0.500000 − 0.866025I
a = −1.00000
b = − 1.73205I
9.86960 − 4.05977I −9.00000 + 6.92820I
29
VII. I
u
7
= hb + u, a + u − 1, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u − 1
a
11
=
−u + 1
−u
a
8
=
−3u − 3
−2
a
12
=
1
−u
a
2
=
u + 1
u + 1
a
1
=
3u + 2
2
a
6
=
u
u + 1
a
5
=
u − 3
3u + 1
a
10
=
2u − 2
3u + 2
a
9
=
u − 2
2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u − 13
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
2
+ 3
c
2
, c
6
, c
8
c
12
u
2
− u + 1
c
3
, c
5
, c
9
c
11
u
2
+ u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(y + 3)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
2
+ y + 1
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.50000 − 0.86603I
b = 0.500000 − 0.866025I
9.86960 + 4.05977I −9.00000 − 6.92820I
u = −0.500000 − 0.866025I
a = 1.50000 + 0.86603I
b = 0.500000 + 0.866025I
9.86960 − 4.05977I −9.00000 + 6.92820I
33
VIII. I
u
8
= h2b − u − 1, 6a + u − 3, u
2
+ 3i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−3
a
11
=
−
1
6
u +
1
2
1
2
u +
1
2
a
8
=
−
1
6
u −
1
2
1
2
u +
1
2
a
12
=
−
2
3
u
1
2
u +
1
2
a
2
=
1
3
u
−
1
2
u +
1
2
a
1
=
5
6
u +
1
2
−2u − 1
a
6
=
u
−2u
a
5
=
2
3
u
−
3
2
u −
1
2
a
10
=
1
6
u +
1
2
1
a
9
=
1
6
u −
3
2
−
1
2
u +
5
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u − 9
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
11
u
2
+ u + 1
c
2
, c
4
, c
8
c
10
u
2
− u + 1
c
3
, c
6
, c
9
c
12
u
2
+ 3
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
10
, c
11
y
2
+ y + 1
c
3
, c
6
, c
9
c
12
(y + 3)
2
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73205I
a = 0.500000 − 0.288675I
b = 0.500000 + 0.866025I
9.86960 − 4.05977I −9.00000 + 6.92820I
u = − 1.73205I
a = 0.500000 + 0.288675I
b = 0.500000 − 0.866025I
9.86960 + 4.05977I −9.00000 − 6.92820I
37
IX. I
u
9
= hb + 1, a + 1, u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u − 1
a
11
=
−1
−1
a
8
=
−u
0
a
12
=
0
−1
a
2
=
1
−1
a
1
=
−u + 1
0
a
6
=
u
u − 1
a
5
=
0
u − 1
a
10
=
−u
−1
a
9
=
−u
u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8u − 13
38
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
, c
12
u
2
+ u + 1
c
2
, c
5
, c
8
c
11
(u − 1)
2
39
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
, c
12
y
2
+ y + 1
c
2
, c
5
, c
8
c
11
(y −1)
2
40
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.00000
b = −1.00000
− 4.05977I −9.00000 + 6.92820I
u = 0.500000 − 0.866025I
a = −1.00000
b = −1.00000
4.05977I −9.00000 − 6.92820I
41
X. I
u
10
= hb − u, a + u − 1, u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u − 1
a
11
=
−u + 1
u
a
8
=
u − 1
0
a
12
=
−2u + 1
u
a
2
=
u − 1
−u + 1
a
1
=
u
0
a
6
=
u
u − 1
a
5
=
u + 1
u − 1
a
10
=
−2u + 2
u
a
9
=
−u
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8u − 13
42
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(u − 1)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
u
2
+ u + 1
43
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(y −1)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
2
+ y + 1
44
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = 0.500000 + 0.866025I
− 4.05977I −9.00000 + 6.92820I
u = 0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = 0.500000 − 0.866025I
4.05977I −9.00000 − 6.92820I
45
XI. I
u
11
= hb − a, a
2
− a + 1, u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
−1
a
4
=
1
1
a
11
=
a
a
a
8
=
a − 1
a − 2
a
12
=
0
a
a
2
=
1
−a + 1
a
1
=
−a + 1
−2a + 1
a
6
=
−1
−2
a
5
=
0
a − 1
a
10
=
a − 1
−1
a
9
=
a − 1
a − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8a − 13
46
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
10
, c
11
u
2
+ u + 1
c
3
, c
6
, c
9
c
12
(u − 1)
2
47
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
10
, c
11
y
2
+ y + 1
c
3
, c
6
, c
9
c
12
(y −1)
2
48
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.500000 + 0.866025I
b = 0.500000 + 0.866025I
− 4.05977I −9.00000 + 6.92820I
u = −1.00000
a = 0.500000 − 0.866025I
b = 0.500000 − 0.866025I
4.05977I −9.00000 − 6.92820I
49
XII. I
u
12
=
hu
3
−au−u
2
+b+3u−2, 2u
4
a−2u
3
a+· · ·+a
2
+3a, u
5
−u
4
+4u
3
−3u
2
+3u−1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
a
−u
3
+ au + u
2
− 3u + 2
a
8
=
−u
3
a + u
4
+ u
2
a − 3au + 3u
2
+ 2a
u
4
− u
3
+ 3u
2
− 2u + 1
a
12
=
u
3
− au − u
2
+ a + 3u − 2
−u
3
+ au + u
2
− 3u + 2
a
2
=
−u
4
a + u
3
a + 2u
4
− 3u
2
a − 2u
3
+ 2au + 7u
2
− 5u + 3
u
4
a − u
3
a − u
4
+ 3u
2
a + 2u
3
− 2au − 4u
2
+ 5u − 2
a
1
=
−u
4
a + u
3
a + 2u
4
− 3u
2
a − u
3
+ au + 6u
2
− 2u + 1
u
4
a − 2u
3
a − u
4
+ 3u
2
a + u
3
− 2au − 3u
2
+ 2u − 1
a
6
=
u
u
3
+ u
a
5
=
−u
4
a + 2u
3
a − 4u
2
a − 2u
3
+ 5au + u
2
− 2a − 5u + 2
−u
3
a + u
2
a + u
3
− 2au + a + u
a
10
=
u
4
a − 2u
3
a + 4u
2
a + 2u
3
− 5au − u
2
+ 3a + 6u − 2
u
3
a − u
2
a − u
3
+ 3au + u
2
− a − 3u + 2
a
9
=
u
4
a − 2u
3
a − u
4
+ 5u
2
a + 3u
3
− 6au − 4u
2
+ 3a + 8u − 2
u
3
a + u
4
− 2u
2
a − 2u
3
+ 3au + 4u
2
− a − 5u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
+ 4u
3
− 16u
2
+ 12u − 14
50
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
10
, c
11
u
10
+ 2u
9
+ 3u
8
+ 6u
7
+ 8u
6
+ 8u
5
+ 11u
4
+ 8u
3
+ 7u
2
+ 4u + 1
c
3
, c
6
, c
9
c
12
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
2
51
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
10
, c
11
y
10
+ 2y
9
+ y
8
+ 2y
7
+ 16y
6
+ 44y
5
+ 63y
4
+ 42y
3
+ 7y
2
− 2y + 1
c
3
, c
6
, c
9
c
12
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
2
52
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = 0.233677 + 0.885557I
a = 1.310210 + 0.036071I
b = 1.38058 − 0.52471I
1.81981 − 2.21397I −3.11432 + 4.22289I
u = 0.233677 + 0.885557I
a = 0.16935 + 1.60369I
b = −0.274223 − 1.168700I
1.81981 − 2.21397I −3.11432 + 4.22289I
u = 0.233677 − 0.885557I
a = 1.310210 − 0.036071I
b = 1.38058 + 0.52471I
1.81981 + 2.21397I −3.11432 − 4.22289I
u = 0.233677 − 0.885557I
a = 0.16935 − 1.60369I
b = −0.274223 + 1.168700I
1.81981 + 2.21397I −3.11432 − 4.22289I
u = 0.416284
a = −1.023710 + 0.522511I
b = 0.426151 + 0.217513I
−0.882183 −11.6090
u = 0.416284
a = −1.023710 − 0.522511I
b = 0.426151 − 0.217513I
−0.882183 −11.6090
u = 0.05818 + 1.69128I
a = 0.612800 − 0.376865I
b = 0.140527 + 0.958055I
10.95830 − 3.33174I −2.08126 + 2.36228I
u = 0.05818 + 1.69128I
a = −0.568653 + 0.063527I
b = −0.673038 − 1.014490I
10.95830 − 3.33174I −2.08126 + 2.36228I
u = 0.05818 − 1.69128I
a = 0.612800 + 0.376865I
b = 0.140527 − 0.958055I
10.95830 + 3.33174I −2.08126 − 2.36228I
u = 0.05818 − 1.69128I
a = −0.568653 − 0.063527I
b = −0.673038 + 1.014490I
10.95830 + 3.33174I −2.08126 − 2.36228I
53
XIII.
I
u
13
= hu
8
−2u
7
+· · ·+2b−3u, −2u
9
+3u
8
+· · ·+2a+4, u
10
−2u
9
+· · ·−4u+1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
u
9
−
3
2
u
8
+ ··· +
9
2
u − 2
−
1
2
u
8
+ u
7
+ ··· − 2u
2
+
3
2
u
a
8
=
1
2
u
8
−
1
2
u
7
+ ··· +
1
2
u −
1
2
1
2
u
9
− u
8
+ ··· +
1
2
u +
1
2
a
12
=
u
9
− u
8
+ u
7
− 4u
6
+ 4u
5
− 2u
4
+ 7u
3
− 3u
2
+ 3u − 2
−
1
2
u
8
+ u
7
+ ··· − 2u
2
+
3
2
u
a
2
=
−u
9
+
5
2
u
8
+ ··· −
13
2
u + 3
1
2
u
9
− u
8
+ ··· + 2u −
1
2
a
1
=
−u
9
+
5
2
u
8
+ ··· −
15
2
u + 3
1
2
u
9
− u
8
+ ··· + 2u −
1
2
a
6
=
u
u
3
+ u
a
5
=
−
1
2
u
9
+
1
2
u
8
+ ··· +
1
2
u
2
+ u
1
2
u
8
−
1
2
u
7
+ ··· −
3
2
u +
1
2
a
10
=
u
9
−
3
2
u
8
+ ··· + 6u −
5
2
−
1
2
u
9
+ u
8
+ ··· −
3
2
u + 1
a
9
=
3
2
u
9
− 3u
8
+ ··· + 5u −
3
2
−u
9
+ 2u
8
+ ··· − u +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
9
− 6u
8
+ 8u
7
− 14u
6
+ 22u
5
− 22u
4
+ 24u
3
− 24u
2
+ 12u − 14
54
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
, c
12
u
10
+ 2u
9
+ 3u
8
+ 6u
7
+ 8u
6
+ 8u
5
+ 11u
4
+ 8u
3
+ 7u
2
+ 4u + 1
c
2
, c
5
, c
8
c
11
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
2
55
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
, c
12
y
10
+ 2y
9
+ y
8
+ 2y
7
+ 16y
6
+ 44y
5
+ 63y
4
+ 42y
3
+ 7y
2
− 2y + 1
c
2
, c
5
, c
8
c
11
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
2
56
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
13
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140527 + 0.958055I
a = 1.137480 − 0.535660I
b = 0.05818 + 1.69128I
10.95830 − 3.33174I −2.08126 + 2.36228I
u = 0.140527 − 0.958055I
a = 1.137480 + 0.535660I
b = 0.05818 − 1.69128I
10.95830 + 3.33174I −2.08126 − 2.36228I
u = −0.274223 + 1.168700I
a = −0.162827 + 1.219510I
b = 0.233677 − 0.885557I
1.81981 + 2.21397I −3.11432 − 4.22289I
u = −0.274223 − 1.168700I
a = −0.162827 − 1.219510I
b = 0.233677 + 0.885557I
1.81981 − 2.21397I −3.11432 + 4.22289I
u = −0.673038 + 1.014490I
a = 0.719565 − 0.338858I
b = 0.05818 − 1.69128I
10.95830 + 3.33174I −2.08126 − 2.36228I
u = −0.673038 − 1.014490I
a = 0.719565 + 0.338858I
b = 0.05818 + 1.69128I
10.95830 − 3.33174I −2.08126 + 2.36228I
u = 1.38058 + 0.52471I
a = −0.107568 − 0.805640I
b = 0.233677 − 0.885557I
1.81981 + 2.21397I −3.11432 − 4.22289I
u = 1.38058 − 0.52471I
a = −0.107568 + 0.805640I
b = 0.233677 + 0.885557I
1.81981 − 2.21397I −3.11432 + 4.22289I
u = 0.426151 + 0.217513I
a = −0.586646 + 0.809843I
b = 0.416284
−0.882183 −11.60884 + 0.I
u = 0.426151 − 0.217513I
a = −0.586646 − 0.809843I
b = 0.416284
−0.882183 −11.60884 + 0.I
57
XIV.
I
u
14
= hu
9
−2u
8
+· · ·+2b − 2, −u
7
+2u
6
+· · ·+2a + 3, u
10
−2u
9
+· · ·−4u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
1
2
u
7
− u
6
+ u
5
− 2u
4
+ 3u
3
−
3
2
u
2
+ 2u −
3
2
−
1
2
u
9
+ u
8
+ ··· − 2u + 1
a
8
=
1
2
u
9
−
1
2
u
8
+ ··· +
1
2
u
2
− u
1
2
u
9
− u
8
+ ··· +
1
2
u +
1
2
a
12
=
1
2
u
9
− u
8
+ ··· + 4u −
5
2
−
1
2
u
9
+ u
8
+ ··· − 2u + 1
a
2
=
−u
9
+ 2u
8
+ ··· − 4u +
5
2
1
2
u
9
−
1
2
u
8
+ ··· +
1
2
u
2
−
1
2
u
a
1
=
−u
9
+
5
2
u
8
+ ··· −
11
2
u +
5
2
1
2
u
9
− u
8
+ ··· +
3
2
u −
1
2
a
6
=
u
u
3
+ u
a
5
=
−
1
2
u
9
+ u
8
+ ··· − u +
1
2
1
2
u
8
− u
7
+ ··· −
3
2
u +
1
2
a
10
=
3
2
u
9
− 3u
8
+ ··· +
9
2
u − 2
−
1
2
u
9
+
1
2
u
8
+ ··· +
1
2
u +
1
2
a
9
=
1
2
u
9
− u
8
+ ··· +
1
2
u −
1
2
−
1
2
u
7
+ u
6
− u
5
+ u
4
− u
3
+
1
2
u
2
+
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
9
− 6u
8
+ 8u
7
− 14u
6
+ 22u
5
− 22u
4
+ 24u
3
− 24u
2
+ 12u − 14
58
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
u
10
+ 2u
9
+ 3u
8
+ 6u
7
+ 8u
6
+ 8u
5
+ 11u
4
+ 8u
3
+ 7u
2
+ 4u + 1
59
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
10
+ 2y
9
+ y
8
+ 2y
7
+ 16y
6
+ 44y
5
+ 63y
4
+ 42y
3
+ 7y
2
− 2y + 1
60
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
14
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140527 + 0.958055I
a = −1.73686 − 0.19403I
b = −0.673038 − 1.014490I
10.95830 − 3.33174I −2.08126 + 2.36228I
u = 0.140527 − 0.958055I
a = −1.73686 + 0.19403I
b = −0.673038 + 1.014490I
10.95830 + 3.33174I −2.08126 − 2.36228I
u = −0.274223 + 1.168700I
a = 0.762658 + 0.020997I
b = 1.38058 + 0.52471I
1.81981 + 2.21397I −3.11432 − 4.22289I
u = −0.274223 − 1.168700I
a = 0.762658 − 0.020997I
b = 1.38058 − 0.52471I
1.81981 − 2.21397I −3.11432 + 4.22289I
u = −0.673038 + 1.014490I
a = 1.184040 − 0.728171I
b = 0.140527 − 0.958055I
10.95830 + 3.33174I −2.08126 − 2.36228I
u = −0.673038 − 1.014490I
a = 1.184040 + 0.728171I
b = 0.140527 + 0.958055I
10.95830 − 3.33174I −2.08126 + 2.36228I
u = 1.38058 + 0.52471I
a = 0.065122 + 0.616687I
b = −0.274223 + 1.168700I
1.81981 + 2.21397I −3.11432 − 4.22289I
u = 1.38058 − 0.52471I
a = 0.065122 − 0.616687I
b = −0.274223 − 1.168700I
1.81981 − 2.21397I −3.11432 + 4.22289I
u = 0.426151 + 0.217513I
a = −0.774953 + 0.395545I
b = 0.426151 − 0.217513I
−0.882183 −11.60884 + 0.I
u = 0.426151 − 0.217513I
a = −0.774953 − 0.395545I
b = 0.426151 + 0.217513I
−0.882183 −11.60884 + 0.I
61
XV. I
u
15
= hb + u, a + 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
−1
−u
a
8
=
−u
−u
2
+ u
a
12
=
u − 1
−u
a
2
=
u
2
− u + 1
−u
2
a
1
=
u
2
− 2u + 1
−2u
2
+ 2u − 1
a
6
=
u
u
2
− u + 1
a
5
=
u
2
+ u
u
2
− 3u + 2
a
10
=
−u
2
− 1
u − 1
a
9
=
−2u
2
+ u − 1
u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12u
2
+ 6u − 21
62
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
9
, c
11
u
3
− u
2
+ 2u − 1
c
2
, c
4
, c
6
c
8
, c
10
, c
12
u
3
+ u
2
+ 2u + 1
63
(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
3
+ 3y
2
+ 2y −1
64
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
15
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −1.00000
b = −0.215080 − 1.307140I
14.0789 − 1.8854I 0.238787 + 1.095494I
u = 0.215080 − 1.307140I
a = −1.00000
b = −0.215080 + 1.307140I
14.0789 + 1.8854I 0.238787 − 1.095494I
u = 0.569840
a = −1.00000
b = −0.569840
−1.83893 −21.4780
65
XVI.
I
u
16
= hb + u, 2u
5
+ 5u
3
− 3u
2
+ a + 3u − 2, u
6
− u
5
+ 3u
4
− 4u
3
+ 4u
2
− 3u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
−2u
5
− 5u
3
+ 3u
2
− 3u + 2
−u
a
8
=
u
5
− u
4
+ 3u
3
− 3u
2
+ 4u − 1
−u
5
+ u
4
− 3u
3
+ 4u
2
− 3u + 2
a
12
=
−2u
5
− 5u
3
+ 3u
2
− 2u + 2
−u
a
2
=
−2u
5
+ u
4
− 5u
3
+ 6u
2
− 4u + 3
−u
2
a
1
=
−2u
5
− 5u
3
+ 4u
2
− 3u + 2
−u
5
+ u
4
− 3u
3
+ 2u
2
− 3u + 1
a
6
=
u
u
3
+ u
a
5
=
u
5
+ 3u
3
− 2u
2
+ 3u − 2
2u
5
− u
4
+ 6u
3
− 4u
2
+ 5u − 2
a
10
=
−2u
4
− 4u
2
+ 3u − 1
u
5
+ 3u
3
− 2u
2
+ 2u − 2
a
9
=
u
5
− u
4
+ 2u
3
− 3u
2
+ 3u − 1
u
3
− u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
5
− 6u
3
+ 3u
2
− 3u − 5
66
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
6
− 2u
5
+ 2u
4
− 2u
3
+ 2u
2
− u + 1
c
2
, c
6
, c
8
c
12
u
6
+ u
5
+ 3u
4
+ 4u
3
+ 4u
2
+ 3u + 1
c
3
, c
5
, c
9
c
11
u
6
− u
5
+ 3u
4
− 4u
3
+ 4u
2
− 3u + 1
c
4
, c
10
u
6
+ 2u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ u + 1
67
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
6
+ 2y
3
+ 4y
2
+ 3y + 1
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 2y
2
− y + 1
68
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
16
√
−1(vol +
√
−1CS) Cusp shape
u = 0.232606 + 0.943705I
a = 0.215080 + 1.307140I
b = −0.232606 − 0.943705I
0.459731 − 0.942707I −6.98708 + 1.68684I
u = 0.232606 − 0.943705I
a = 0.215080 − 1.307140I
b = −0.232606 + 0.943705I
0.459731 + 0.942707I −6.98708 − 1.68684I
u = 0.644833 + 0.198843I
a = 0.215080 − 1.307140I
b = −0.644833 − 0.198843I
0.459731 + 0.942707I −6.98708 − 1.68684I
u = 0.644833 − 0.198843I
a = 0.215080 + 1.307140I
b = −0.644833 + 0.198843I
0.459731 − 0.942707I −6.98708 + 1.68684I
u = −0.37744 + 1.47725I
a = 0.569840
b = 0.37744 − 1.47725I
12.2400 −6 − 1.025846 + 0.10I
u = −0.37744 − 1.47725I
a = 0.569840
b = 0.37744 + 1.47725I
12.2400 −6 − 1.025846 + 0.10I
69
XVII.
I
u
17
= h−u
5
+ u
4
+ b − u, −u
4
+ u
3
+ a − 1, u
6
− 2u
5
+ 2u
4
− 2u
3
+ 2u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
u
4
− u
3
+ 1
u
5
− u
4
+ u
a
8
=
−2u
5
+ 3u
4
− u
3
+ u
2
− 2u
−u
5
+ 3u
4
− 3u
3
+ 2u
2
− u + 2
a
12
=
−u
5
+ 2u
4
− u
3
− u + 1
u
5
− u
4
+ u
a
2
=
−u
5
+ 2u
3
− u
2
− 1
−u
5
+ 3u
4
− 3u
3
+ 2u
2
− 2u + 2
a
1
=
−2u
5
+ 2u
4
+ u
3
− u
2
− u − 1
u
4
− 2u
3
+ u
2
− u + 2
a
6
=
u
u
3
+ u
a
5
=
−2u
4
+ 3u
3
− u
2
+ 2u − 3
−2u
5
+ 4u
4
− 2u
3
+ 2u
2
− 3u + 1
a
10
=
u
5
− 3u
4
+ 3u
3
− 2u
2
+ 3u − 2
−2u
5
+ 3u
4
− 2u
3
+ 2u
2
− 2u
a
9
=
2u
5
− 4u
4
+ 2u
3
− u
2
+ 3u − 1
−2u
5
+ 2u
4
+ u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
4
− 6u
3
+ 3u
2
− 3u − 2
70
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
11
u
6
− u
5
+ 3u
4
− 4u
3
+ 4u
2
− 3u + 1
c
2
, c
4
, c
8
c
10
u
6
+ u
5
+ 3u
4
+ 4u
3
+ 4u
2
+ 3u + 1
c
3
, c
9
u
6
− 2u
5
+ 2u
4
− 2u
3
+ 2u
2
− u + 1
c
6
, c
12
u
6
+ 2u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ u + 1
71
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
10
, c
11
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 2y
2
− y + 1
c
3
, c
6
, c
9
c
12
y
6
+ 2y
3
+ 4y
2
+ 3y + 1
72
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
17
√
−1(vol +
√
−1CS) Cusp shape
u = −0.398606 + 0.800120I
a = 0.122561 + 0.744862I
b = −0.644833 − 0.198843I
0.459731 + 0.942707I −6.98708 − 1.68684I
u = −0.398606 − 0.800120I
a = 0.122561 − 0.744862I
b = −0.644833 + 0.198843I
0.459731 − 0.942707I −6.98708 + 1.68684I
u = 0.215080 + 0.841795I
a = 1.75488
b = 0.37744 + 1.47725I
12.2400 −6 − 1.025846 + 0.10I
u = 0.215080 − 0.841795I
a = 1.75488
b = 0.37744 − 1.47725I
12.2400 −6 − 1.025846 + 0.10I
u = 1.183530 + 0.507021I
a = 0.122561 + 0.744862I
b = −0.232606 + 0.943705I
0.459731 + 0.942707I −6.98708 − 1.68684I
u = 1.183530 − 0.507021I
a = 0.122561 − 0.744862I
b = −0.232606 − 0.943705I
0.459731 − 0.942707I −6.98708 + 1.68684I
73
XVIII.
I
u
18
= h2u
5
−u
4
+5u
3
−5u
2
+b+4u−2, a+1, u
6
−u
5
+3u
4
−4u
3
+4u
2
−3u+1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
−1
−2u
5
+ u
4
− 5u
3
+ 5u
2
− 4u + 2
a
8
=
−u
−u
5
+ u
4
− 3u
3
+ 4u
2
− 3u + 2
a
12
=
2u
5
− u
4
+ 5u
3
− 5u
2
+ 4u − 3
−2u
5
+ u
4
− 5u
3
+ 5u
2
− 4u + 2
a
2
=
−2u
5
+ u
4
− 6u
3
+ 5u
2
− 6u + 4
u
3
+ 2u − 1
a
1
=
−u
5
+ u
4
− 3u
3
+ 3u
2
− 3u + 2
u
5
− u
4
+ 4u
3
− 3u
2
+ 4u − 2
a
6
=
u
u
3
+ u
a
5
=
u
5
+ 2u
3
− u
2
+ 2u
u
3
− u
2
+ u − 1
a
10
=
−u
2
− 1
−2u
5
+ u
4
− 5u
3
+ 6u
2
− 5u + 3
a
9
=
−2u
5
− 5u
3
+ 2u
2
− 4u + 1
−u
5
+ u
4
− 3u
3
+ 5u
2
− 4u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
5
− 6u
3
+ 3u
2
− 3u − 5
74
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
9
u
6
− u
5
+ 3u
4
− 4u
3
+ 4u
2
− 3u + 1
c
2
, c
8
u
6
+ 2u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ u + 1
c
4
, c
6
, c
10
c
12
u
6
+ u
5
+ 3u
4
+ 4u
3
+ 4u
2
+ 3u + 1
c
5
, c
11
u
6
− 2u
5
+ 2u
4
− 2u
3
+ 2u
2
− u + 1
75
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
, c
12
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 2y
2
− y + 1
c
2
, c
5
, c
8
c
11
y
6
+ 2y
3
+ 4y
2
+ 3y + 1
76
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
18
√
−1(vol +
√
−1CS) Cusp shape
u = 0.232606 + 0.943705I
a = −1.00000
b = −1.183530 + 0.507021I
0.459731 − 0.942707I −6.98708 + 1.68684I
u = 0.232606 − 0.943705I
a = −1.00000
b = −1.183530 − 0.507021I
0.459731 + 0.942707I −6.98708 − 1.68684I
u = 0.644833 + 0.198843I
a = −1.00000
b = 0.398606 − 0.800120I
0.459731 + 0.942707I −6.98708 − 1.68684I
u = 0.644833 − 0.198843I
a = −1.00000
b = 0.398606 + 0.800120I
0.459731 − 0.942707I −6.98708 + 1.68684I
u = −0.37744 + 1.47725I
a = −1.00000
b = −0.215080 + 0.841795I
12.2400 −6 − 1.025846 + 0.10I
u = −0.37744 − 1.47725I
a = −1.00000
b = −0.215080 − 0.841795I
12.2400 −6 − 1.025846 + 0.10I
77
XIX. I
u
19
= hb − u, a + 1, u
4
+ 2u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
−1
u
a
8
=
−u
u
2
+ u
a
12
=
−u − 1
u
a
2
=
u
2
+ u + 1
−u
2
a
1
=
u
3
+ 2u
2
+ 3u + 2
u
3
+ u
2
+ u + 1
a
6
=
u
u
3
+ u
a
5
=
u
3
+ u
2
+ 2u + 1
u
3
+ u
2
+ u
a
10
=
−u
2
− 1
u
3
+ u
2
+ u
a
9
=
−u
2
− u − 1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6u
3
− 6u
2
− 6u − 6
78
(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
10
, c
11
, c
12
(u
2
− u + 1)
2
79
(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
2
+ y + 1)
2
80
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
19
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.00000
b = −0.500000 + 0.866025I
3.28987 −6.00000 + 0.I
u = −0.500000 + 0.866025I
a = −1.00000
b = −0.500000 + 0.866025I
3.28987 −6.00000 + 0.I
u = −0.500000 − 0.866025I
a = −1.00000
b = −0.500000 − 0.866025I
3.28987 −6.00000 + 0.I
u = −0.500000 − 0.866025I
a = −1.00000
b = −0.500000 − 0.866025I
3.28987 −6.00000 + 0.I
81
XX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
9
, c
11
(u − 1)
2
(u
2
+ 3)(u
2
− u + 1)
2
(u
2
+ u + 1)
4
(u
3
− u
2
+ 2u − 1)
· (u
3
− u
2
+ 2u + 1)(u
4
+ u
2
+ 2u + 1)(u
5
+ u
4
+ ··· + 3u + 1)
2
· (u
6
− 2u
5
+ 2u
4
− 2u
3
+ 2u
2
− u + 1)
· (u
6
− u
5
+ 3u
4
− 4u
3
+ 4u
2
− 3u + 1)
2
· (u
10
+ 2u
9
+ 3u
8
+ 6u
7
+ 8u
6
+ 8u
5
+ 11u
4
+ 8u
3
+ 7u
2
+ 4u + 1)
2
· (u
16
− 9u
15
+ ··· − 64u + 32)(u
16
+ u
15
+ ··· + 3u + 1)
2
c
2
, c
4
, c
6
c
8
, c
10
, c
12
(u − 1)
2
(u
2
+ 3)(u
2
− u + 1)
4
(u
2
+ u + 1)
2
(u
3
− u
2
+ 2u + 1)
· (u
3
+ u
2
+ 2u + 1)(u
4
+ u
2
− 2u + 1)(u
5
+ u
4
+ ··· + 3u + 1)
2
· (u
6
+ u
5
+ 3u
4
+ 4u
3
+ 4u
2
+ 3u + 1)
2
· (u
6
+ 2u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ u + 1)
· (u
10
+ 2u
9
+ 3u
8
+ 6u
7
+ 8u
6
+ 8u
5
+ 11u
4
+ 8u
3
+ 7u
2
+ 4u + 1)
2
· (u
16
− 9u
15
+ ··· − 64u + 32)(u
16
+ u
15
+ ··· + 3u + 1)
2
82
XXI. Riley Polynomials
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)
2
)(y + 3)
2
(y
2
+ y + 1)
6
(y
3
+ 3y
2
+ 2y −1)(y
3
+ 3y
2
+ 6y −1)
· (y
4
+ 2y
3
+ 3y
2
− 2y + 1)(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
2
· (y
6
+ 2y
3
+ 4y
2
+ 3y + 1)(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 2y
2
− y + 1)
2
· (y
10
+ 2y
9
+ y
8
+ 2y
7
+ 16y
6
+ 44y
5
+ 63y
4
+ 42y
3
+ 7y
2
− 2y + 1)
2
· (y
16
+ 11y
15
+ ··· − 2560y + 1024)(y
16
+ 11y
15
+ ··· − 3y + 1)
2
83
