12n
0380
(K12n
0380
)
A knot diagram
1
Linearized knot diagam
3 6 9 7 2 12 3 10 4 8 1 7
Solving Sequence
3,9
4
6,10
2 1 5 8 11 7 12
c
3
c
9
c
2
c
1
c
5
c
8
c
10
c
7
c
12
c
4
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
24
+ 2u
23
+ ··· + b − 1, −u
24
− u
23
+ ··· + 2a − 2, u
25
+ 3u
24
+ ··· − 4u − 2i
I
u
2
= h−36u
11
a + 71u
11
+ ··· + 286a − 731, −2u
11
a + 2u
10
a + ··· − 4a − 1,
u
12
− 2u
10
+ u
9
+ 4u
8
− u
7
− 3u
6
+ 3u
5
+ 3u
4
− u
3
− u
2
+ 2u + 1i
I
u
3
= hb + 1, −u
3
+ 2u
2
+ 2a + u − 2, u
4
− u
2
+ 2i
I
u
4
= hb − 1, a − u, u
4
+ 1i
I
u
5
= hb, a + 1, u − 1i
I
u
6
= hb + 1, a − 2, u − 1i
I
u
7
= hb + 1, a − 3, u − 1i
I
u
8
= hb + 1, a − 1, u + 1i
I
v
1
= ha, b − 1, v + 1i
* 9 irreducible components of dim
C
= 0, with total 62 representations.
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).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= hu
24
+2u
23
+· · ·+b−1, −u
24
−u
23
+· · ·+2a−2, u
25
+3u
24
+· · ·−4u−2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
6
=
1
2
u
24
+
1
2
u
23
+ ··· + u
2
+ 1
−u
24
− 2u
23
+ ··· + 2u + 1
a
10
=
u
−u
3
+ u
a
2
=
1
2
u
24
+
5
2
u
23
+ ··· − 3u − 2
−u
23
− u
22
+ ··· + 2u + 1
a
1
=
1
2
u
24
+
3
2
u
23
+ ··· − u − 1
−u
23
− u
22
+ ··· + 2u + 1
a
5
=
−u
12
+ u
10
− 3u
8
+ 2u
6
− 2u
4
+ u
2
+ 1
u
12
− 2u
10
+ 4u
8
− 4u
6
+ 3u
4
− 2u
2
a
8
=
−u
3
u
5
− u
3
+ u
a
11
=
u
5
+ u
−u
7
+ u
5
− 2u
3
+ u
a
7
=
−u
5
− u
u
5
− u
3
+ u
a
12
=
−
1
2
u
24
−
5
2
u
23
+ ··· + 4u + 3
u
23
+ u
22
+ ··· − u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −2u
24
+ 10u
22
+ 6u
21
− 30u
20
− 24u
19
+ 54u
18
+ 64u
17
− 72u
16
− 112u
15
+ 54u
14
+
150u
13
−12u
12
−142u
11
−42u
10
+100u
9
+66u
8
−34u
7
−56u
6
−6u
5
+22u
4
+18u
3
−2u −4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
25
+ 5u
24
+ ··· + 11u + 1
c
2
, c
5
, c
6
c
12
u
25
+ u
24
+ ··· + u − 1
c
3
, c
9
u
25
+ 3u
24
+ ··· − 4u − 2
c
4
u
25
+ 21u
24
+ ··· + 13332u + 2962
c
7
u
25
− 3u
24
+ ··· − 92u − 26
c
8
, c
10
u
25
− 9u
24
+ ··· − 8u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
25
+ 43y
24
+ ··· + 11y −1
c
2
, c
5
, c
6
c
12
y
25
− 5y
24
+ ··· + 11y −1
c
3
, c
9
y
25
− 9y
24
+ ··· − 8y −4
c
4
y
25
− 33y
24
+ ··· − 42476552y −8773444
c
7
y
25
− 21y
24
+ ··· − 4952y −676
c
8
, c
10
y
25
+ 15y
24
+ ··· + 320y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.980316 + 0.233102I
a = 0.44130 + 2.47602I
b = −0.622808 − 0.762022I
2.82058 − 3.81422I 4.98039 + 6.61368I
u = −0.980316 − 0.233102I
a = 0.44130 − 2.47602I
b = −0.622808 + 0.762022I
2.82058 + 3.81422I 4.98039 − 6.61368I
u = −0.568077 + 0.832369I
a = 0.51973 − 1.50739I
b = −1.13721 + 0.86526I
4.15791 + 8.74016I −1.84068 − 4.40634I
u = −0.568077 − 0.832369I
a = 0.51973 + 1.50739I
b = −1.13721 − 0.86526I
4.15791 − 8.74016I −1.84068 + 4.40634I
u = −0.733592 + 0.747057I
a = 0.337972 − 0.198014I
b = 0.611523 + 0.222308I
−3.30756 − 0.71712I −2.44059 + 3.90523I
u = −0.733592 − 0.747057I
a = 0.337972 + 0.198014I
b = 0.611523 − 0.222308I
−3.30756 + 0.71712I −2.44059 − 3.90523I
u = 0.932488 + 0.483370I
a = 0.96761 + 1.60037I
b = −0.206915 − 0.805921I
1.59893 + 1.80276I 4.99535 − 2.09686I
u = 0.932488 − 0.483370I
a = 0.96761 − 1.60037I
b = −0.206915 + 0.805921I
1.59893 − 1.80276I 4.99535 + 2.09686I
u = 0.932840
a = 0.687051
b = −0.498290
1.77401 4.83650
u = 0.764755 + 0.774203I
a = 0.171446 − 0.325902I
b = 0.784319 + 0.533336I
−3.51376 − 2.47052I −3.49276 + 4.45848I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.764755 − 0.774203I
a = 0.171446 + 0.325902I
b = 0.784319 − 0.533336I
−3.51376 + 2.47052I −3.49276 − 4.45848I
u = −0.437237 + 0.783767I
a = 0.49146 + 1.67035I
b = −1.037150 − 0.927401I
4.93859 − 5.35756I −1.01874 + 4.42089I
u = −0.437237 − 0.783767I
a = 0.49146 − 1.67035I
b = −1.037150 + 0.927401I
4.93859 + 5.35756I −1.01874 − 4.42089I
u = 1.156340 + 0.047910I
a = −2.12651 + 3.13266I
b = 1.12099 − 0.93923I
10.42970 + 7.39157I 4.47957 − 4.57784I
u = 1.156340 − 0.047910I
a = −2.12651 − 3.13266I
b = 1.12099 + 0.93923I
10.42970 − 7.39157I 4.47957 + 4.57784I
u = −0.970077 + 0.698318I
a = 0.166009 + 0.595943I
b = −0.620681 + 0.170359I
−2.58593 − 4.79128I −0.37722 + 2.00234I
u = −0.970077 − 0.698318I
a = 0.166009 − 0.595943I
b = −0.620681 − 0.170359I
−2.58593 + 4.79128I −0.37722 − 2.00234I
u = 0.951621 + 0.731482I
a = −0.63483 − 1.61897I
b = −0.831342 + 0.569410I
−2.94773 + 8.15802I −2.49516 − 9.64578I
u = 0.951621 − 0.731482I
a = −0.63483 + 1.61897I
b = −0.831342 − 0.569410I
−2.94773 − 8.15802I −2.49516 + 9.64578I
u = −1.076120 + 0.616232I
a = −2.32949 + 1.21588I
b = 1.02897 − 0.98641I
6.80687 + 0.12880I 1.81794 + 0.42247I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.076120 − 0.616232I
a = −2.32949 − 1.21588I
b = 1.02897 + 0.98641I
6.80687 − 0.12880I 1.81794 − 0.42247I
u = −1.066850 + 0.683933I
a = −0.18246 − 3.26046I
b = 1.16937 + 0.87177I
5.6578 − 14.4091I 0.10967 + 8.76133I
u = −1.066850 − 0.683933I
a = −0.18246 + 3.26046I
b = 1.16937 − 0.87177I
5.6578 + 14.4091I 0.10967 − 8.76133I
u = 0.060646 + 0.510945I
a = 0.334239 + 0.498112I
b = 0.490067 − 0.520637I
−0.268317 + 1.373590I −2.13600 − 4.81420I
u = 0.060646 − 0.510945I
a = 0.334239 − 0.498112I
b = 0.490067 + 0.520637I
−0.268317 − 1.373590I −2.13600 + 4.81420I
7
II. I
u
2
= h−36u
11
a + 71u
11
+ · · · + 286a − 731, −2u
11
a + 2u
10
a + · · · − 4a −
1, u
12
− 2u
10
+ · · · + 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
6
=
a
0.0599002au
11
− 0.118136u
11
+ ··· − 0.475874a + 1.21631
a
10
=
u
−u
3
+ u
a
2
=
−0.118136au
11
− 0.128120u
11
+ ··· + 1.21631a + 1.62895
0.0682196au
11
+ 0.0599002u
11
+ ··· − 0.153078a − 1.47587
a
1
=
−0.0499168au
11
− 0.0682196u
11
+ ··· + 1.06323a + 0.153078
0.0682196au
11
+ 0.0599002u
11
+ ··· − 0.153078a − 1.47587
a
5
=
−u
10
+ u
9
+ u
8
− u
7
− u
6
+ 3u
5
+ u
4
− u
3
+ 2u + 2
−u
9
+ u
7
− u
6
− 3u
5
+ u
3
− u
2
− 2u − 1
a
8
=
−u
3
u
5
− u
3
+ u
a
11
=
u
5
+ u
−u
7
+ u
5
− 2u
3
+ u
a
7
=
−u
5
− u
u
5
− u
3
+ u
a
12
=
−0.118136au
11
− 0.128120u
11
+ ··· + 1.21631a − 0.371048
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
11
− 8u
9
+ 4u
8
+ 12u
7
− 4u
6
− 8u
5
+ 8u
4
+ 4u
3
− 4u
2
− 4u + 2
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
24
+ 8u
23
+ ··· + 268u + 49
c
2
, c
5
, c
6
c
12
u
24
+ 2u
23
+ ··· + 4u − 7
c
3
, c
9
(u
12
− 2u
10
+ u
9
+ 4u
8
− u
7
− 3u
6
+ 3u
5
+ 3u
4
− u
3
− u
2
+ 2u + 1)
2
c
4
(u
12
− 8u
11
+ ··· − 48u − 23)
2
c
7
(u
12
+ 2u
11
+ ··· + 4u + 1)
2
c
8
, c
10
(u
12
− 4u
11
+ ··· − 6u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
24
+ 16y
23
+ ··· + 54988y + 2401
c
2
, c
5
, c
6
c
12
y
24
− 8y
23
+ ··· − 268y + 49
c
3
, c
9
(y
12
− 4y
11
+ ··· − 6y + 1)
2
c
4
(y
12
− 28y
11
+ ··· − 9802y + 529)
2
c
7
(y
12
− 16y
11
+ ··· − 6y + 1)
2
c
8
, c
10
(y
12
+ 8y
11
+ ··· − 14y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.511432 + 0.812623I
a = 0.67786 + 1.48575I
b = −0.900728 − 1.001250I
5.38423 − 1.70959I −0.128193 + 0.167200I
u = 0.511432 + 0.812623I
a = 0.55283 − 1.54744I
b = −0.756837 + 1.060930I
5.38423 − 1.70959I −0.128193 + 0.167200I
u = 0.511432 − 0.812623I
a = 0.67786 − 1.48575I
b = −0.900728 + 1.001250I
5.38423 + 1.70959I −0.128193 − 0.167200I
u = 0.511432 − 0.812623I
a = 0.55283 + 1.54744I
b = −0.756837 − 1.060930I
5.38423 + 1.70959I −0.128193 − 0.167200I
u = 0.850204 + 0.630914I
a = −0.132727 − 0.669979I
b = 1.145980 + 0.247522I
−5.05906 + 2.46907I −5.52253 − 3.95252I
u = 0.850204 + 0.630914I
a = 0.07414 − 2.86500I
b = −1.068390 + 0.305673I
−5.05906 + 2.46907I −5.52253 − 3.95252I
u = 0.850204 − 0.630914I
a = −0.132727 + 0.669979I
b = 1.145980 − 0.247522I
−5.05906 − 2.46907I −5.52253 + 3.95252I
u = 0.850204 − 0.630914I
a = 0.07414 + 2.86500I
b = −1.068390 − 0.305673I
−5.05906 − 2.46907I −5.52253 + 3.95252I
u = −0.635020 + 0.640255I
a = −0.226456 + 0.011257I
b = 1.204970 − 0.052489I
−3.08210 + 0.49850I −1.36863 − 1.38008I
u = −0.635020 + 0.640255I
a = 1.55856 − 1.03377I
b = −0.457992 + 0.354536I
−3.08210 + 0.49850I −1.36863 − 1.38008I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.635020 − 0.640255I
a = −0.226456 − 0.011257I
b = 1.204970 + 0.052489I
−3.08210 − 0.49850I −1.36863 + 1.38008I
u = −0.635020 − 0.640255I
a = 1.55856 + 1.03377I
b = −0.457992 − 0.354536I
−3.08210 − 0.49850I −1.36863 + 1.38008I
u = −1.16193
a = −1.91107 + 3.18977I
b = 0.855561 − 1.093600I
11.2998 5.66710
u = −1.16193
a = −1.91107 − 3.18977I
b = 0.855561 + 1.093600I
11.2998 5.66710
u = −0.985497 + 0.634576I
a = −0.67437 − 1.64764I
b = 0.301152 + 0.483288I
−2.05779 − 5.52285I 0.56374 + 6.48307I
u = −0.985497 + 0.634576I
a = 0.79418 + 1.81824I
b = −1.207840 − 0.138399I
−2.05779 − 5.52285I 0.56374 + 6.48307I
u = −0.985497 − 0.634576I
a = −0.67437 + 1.64764I
b = 0.301152 − 0.483288I
−2.05779 + 5.52285I 0.56374 − 6.48307I
u = −0.985497 − 0.634576I
a = 0.79418 − 1.81824I
b = −1.207840 + 0.138399I
−2.05779 + 5.52285I 0.56374 − 6.48307I
u = 1.075030 + 0.655125I
a = −2.21955 − 1.41327I
b = 0.739507 + 1.114900I
7.05914 + 7.20360I 2.08749 − 4.71657I
u = 1.075030 + 0.655125I
a = −0.12063 + 3.16354I
b = 0.949962 − 1.026010I
7.05914 + 7.20360I 2.08749 − 4.71657I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.075030 − 0.655125I
a = −2.21955 + 1.41327I
b = 0.739507 − 1.114900I
7.05914 − 7.20360I 2.08749 + 4.71657I
u = 1.075030 − 0.655125I
a = −0.12063 − 3.16354I
b = 0.949962 + 1.026010I
7.05914 − 7.20360I 2.08749 + 4.71657I
u = −0.470358
a = −0.00729607
b = 1.13611
−2.62918 3.06920
u = −0.470358
a = 4.26177
b = −0.746787
−2.62918 3.06920
13
III. I
u
3
= hb + 1, −u
3
+ 2u
2
+ 2a + u − 2, u
4
− u
2
+ 2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
6
=
1
2
u
3
− u
2
−
1
2
u + 1
−1
a
10
=
u
−u
3
+ u
a
2
=
1
2
u
3
− u
2
−
1
2
u + 2
−1
a
1
=
1
2
u
3
− u
2
−
1
2
u + 1
−1
a
5
=
−1
0
a
8
=
−u
3
−u
a
11
=
u
3
− u
u
a
7
=
−u
3
+ u
−u
a
12
=
3
2
u
3
− u
2
−
3
2
u + 1
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 4
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
11
c
12
(u − 1)
4
c
2
, c
6
(u + 1)
4
c
3
, c
4
, c
7
c
9
u
4
− u
2
+ 2
c
8
(u
2
+ u + 2)
2
c
10
(u
2
− u + 2)
2
15
(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)
4
c
3
, c
4
, c
7
c
9
(y
2
− y + 2)
2
c
8
, c
10
(y
2
+ 3y + 4)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.978318 + 0.676097I
a = −0.191776 − 0.844803I
b = −1.00000
−4.11234 + 5.33349I −6.00000 − 5.29150I
u = 0.978318 − 0.676097I
a = −0.191776 + 0.844803I
b = −1.00000
−4.11234 − 5.33349I −6.00000 + 5.29150I
u = −0.978318 + 0.676097I
a = 1.19178 + 1.80095I
b = −1.00000
−4.11234 − 5.33349I −6.00000 + 5.29150I
u = −0.978318 − 0.676097I
a = 1.19178 − 1.80095I
b = −1.00000
−4.11234 + 5.33349I −6.00000 − 5.29150I
17
IV. I
u
4
= hb − 1, a − u, u
4
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
6
=
u
1
a
10
=
u
−u
3
+ u
a
2
=
−u + 1
−1
a
1
=
−u
−1
a
5
=
1
0
a
8
=
−u
3
−u
3
a
11
=
0
−u
3
a
7
=
0
−u
3
a
12
=
−u
−u
3
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
11
(u − 1)
4
c
3
, c
4
, c
7
c
9
u
4
+ 1
c
5
, c
12
(u + 1)
4
c
8
, c
10
(u
2
+ 1)
2
19
(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)
4
c
3
, c
4
, c
7
c
9
(y
2
+ 1)
2
c
8
, c
10
(y + 1)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707107 + 0.707107I
a = 0.707107 + 0.707107I
b = 1.00000
−4.93480 −8.00000
u = 0.707107 − 0.707107I
a = 0.707107 − 0.707107I
b = 1.00000
−4.93480 −8.00000
u = −0.707107 + 0.707107I
a = −0.707107 + 0.707107I
b = 1.00000
−4.93480 −8.00000
u = −0.707107 − 0.707107I
a = −0.707107 − 0.707107I
b = 1.00000
−4.93480 −8.00000
21
V. I
u
5
= hb, a + 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
1
a
4
=
1
−1
a
6
=
−1
0
a
10
=
1
0
a
2
=
1
0
a
1
=
1
0
a
5
=
−1
0
a
8
=
−1
1
a
11
=
2
−1
a
7
=
−2
1
a
12
=
3
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
c
3
, c
6
, c
7
c
8
, c
9
, c
10
c
12
u − 1
c
4
, c
11
u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
c
3
, c
4
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 0
1.64493 6.00000
25
VI. I
u
6
= hb + 1, a − 2, u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
1
a
4
=
1
−1
a
6
=
2
−1
a
10
=
1
0
a
2
=
3
−1
a
1
=
2
−1
a
5
=
−1
0
a
8
=
−1
1
a
11
=
2
−1
a
7
=
−2
1
a
12
=
2
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u + 1
c
2
, c
3
, c
5
c
7
, c
8
, c
9
c
10
u − 1
c
6
, c
11
, c
12
u
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
, c
9
, c
10
y − 1
c
6
, c
11
, c
12
y
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 2.00000
b = −1.00000
1.64493 6.00000
29
VII. I
u
7
= hb + 1, a − 3, u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
1
a
4
=
1
−1
a
6
=
3
−1
a
10
=
1
0
a
2
=
4
−1
a
1
=
3
−1
a
5
=
−1
0
a
8
=
−1
1
a
11
=
2
−1
a
7
=
−2
1
a
12
=
5
−2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
10
, c
11
, c
12
u − 1
c
2
, c
4
, c
6
c
7
, c
8
, c
9
u + 1
31
(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
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 3.00000
b = −1.00000
0 0
33
VIII. I
u
8
= hb + 1, a − 1, u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
−1
a
4
=
1
−1
a
6
=
1
−1
a
10
=
−1
0
a
2
=
2
−1
a
1
=
1
−1
a
5
=
−1
0
a
8
=
1
−1
a
11
=
−2
1
a
7
=
2
−1
a
12
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
7
, c
9
, c
10
c
11
, c
12
u − 1
c
2
, c
3
, c
6
c
8
u + 1
35
(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
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = −1.00000
0 0
37
IX. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
−1
0
a
4
=
1
0
a
6
=
0
1
a
10
=
−1
0
a
2
=
1
−1
a
1
=
0
−1
a
5
=
1
0
a
8
=
−1
0
a
11
=
−1
0
a
7
=
−1
0
a
12
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
38
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
11
u − 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
u
c
5
, c
12
u + 1
39
(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
c
3
, c
4
, c
7
c
8
, c
9
, c
10
y
40
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
41
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
u(u − 1)
11
(u + 1)(u
24
+ 8u
23
+ ··· + 268u + 49)
· (u
25
+ 5u
24
+ ··· + 11u + 1)
c
2
, c
6
u(u − 1)
6
(u + 1)
6
(u
24
+ 2u
23
+ ··· + 4u − 7)(u
25
+ u
24
+ ··· + u − 1)
c
3
, c
9
u(u − 1)
3
(u + 1)(u
4
+ 1)(u
4
− u
2
+ 2)
· (u
12
− 2u
10
+ u
9
+ 4u
8
− u
7
− 3u
6
+ 3u
5
+ 3u
4
− u
3
− u
2
+ 2u + 1)
2
· (u
25
+ 3u
24
+ ··· − 4u − 2)
c
4
u(u − 1)(u + 1)
3
(u
4
+ 1)(u
4
− u
2
+ 2)(u
12
− 8u
11
+ ··· − 48u − 23)
2
· (u
25
+ 21u
24
+ ··· + 13332u + 2962)
c
5
, c
12
u(u − 1)
7
(u + 1)
5
(u
24
+ 2u
23
+ ··· + 4u − 7)(u
25
+ u
24
+ ··· + u − 1)
c
7
u(u − 1)
3
(u + 1)(u
4
+ 1)(u
4
− u
2
+ 2)(u
12
+ 2u
11
+ ··· + 4u + 1)
2
· (u
25
− 3u
24
+ ··· − 92u − 26)
c
8
u(u − 1)
2
(u + 1)
2
(u
2
+ 1)
2
(u
2
+ u + 2)
2
· ((u
12
− 4u
11
+ ··· − 6u + 1)
2
)(u
25
− 9u
24
+ ··· − 8u − 4)
c
10
u(u − 1)
4
(u
2
+ 1)
2
(u
2
− u + 2)
2
(u
12
− 4u
11
+ ··· − 6u + 1)
2
· (u
25
− 9u
24
+ ··· − 8u − 4)
42
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
y(y − 1)
12
(y
24
+ 16y
23
+ ··· + 54988y + 2401)
· (y
25
+ 43y
24
+ ··· + 11y − 1)
c
2
, c
5
, c
6
c
12
y(y − 1)
12
(y
24
− 8y
23
+ ··· − 268y + 49)(y
25
− 5y
24
+ ··· + 11y − 1)
c
3
, c
9
y(y − 1)
4
(y
2
+ 1)
2
(y
2
− y + 2)
2
(y
12
− 4y
11
+ ··· − 6y + 1)
2
· (y
25
− 9y
24
+ ··· − 8y − 4)
c
4
y(y − 1)
4
(y
2
+ 1)
2
(y
2
− y + 2)
2
· (y
12
− 28y
11
+ ··· − 9802y + 529)
2
· (y
25
− 33y
24
+ ··· − 42476552y − 8773444)
c
7
y(y − 1)
4
(y
2
+ 1)
2
(y
2
− y + 2)
2
(y
12
− 16y
11
+ ··· − 6y + 1)
2
· (y
25
− 21y
24
+ ··· − 4952y − 676)
c
8
, c
10
y(y − 1)
4
(y + 1)
4
(y
2
+ 3y + 4)
2
(y
12
+ 8y
11
+ ··· − 14y + 1)
2
· (y
25
+ 15y
24
+ ··· + 320y − 16)
43
