12a
0248
(K12a
0248
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 9 2 11 12 5 4 1 8
Solving Sequence
3,6
2 7
4,11
8 1 12 9 5 10
c
2
c
6
c
3
c
7
c
1
c
11
c
8
c
5
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hu
20
+ u
19
+ ··· − 3u
2
+ 2b, u
20
+ u
19
+ ··· + 2a − 1, u
22
+ u
21
+ ··· + u + 1i
I
u
2
= h3.68754 × 10
30
u
61
+ 8.39103 × 10
30
u
60
+ ··· + 2.19146 × 10
31
b − 4.54412 × 10
30
,
5.62366 × 10
30
u
61
+ 9.32012 × 10
29
u
60
+ ··· + 6.57438 × 10
31
a + 1.25939 × 10
32
, u
62
+ 2u
61
+ ··· + 7u + 3i
I
u
3
= h−au + b − u, a
2
− 2u, u
2
− u + 1i
I
u
4
= hb + u, a, u
2
+ u + 1i
I
u
5
= h−au + b + 1, a
2
− 2u, u
2
− u + 1i
I
u
6
= hb + 1, a, u
2
+ u + 1i
* 6 irreducible components of dim
C
= 0, with total 96 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
20
+u
19
+· · ·−3u
2
+2b, u
20
+u
19
+· · ·+2a − 1, u
22
+u
21
+· · ·+u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
11
=
−
1
2
u
20
−
1
2
u
19
+ ··· −
1
2
u +
1
2
−
1
2
u
20
−
1
2
u
19
+ ··· −
1
2
u
3
+
3
2
u
2
a
8
=
1
2
u
21
+
1
2
u
20
+ ··· +
1
2
u
4
−
5
2
u
3
−
1
2
u
19
−
1
2
u
18
+ ··· −
1
2
u
2
+
1
2
u
a
1
=
u
2
+ 1
u
2
a
12
=
−
1
2
u
20
−
1
2
u
19
+ ··· −
1
2
u +
1
2
−
1
2
u
20
−
1
2
u
19
+ ··· −
1
2
u
3
+
3
2
u
2
a
9
=
−
1
2
u
19
−
1
2
u
18
+ ··· −
1
2
u
2
+
1
2
u
−
1
2
u
21
−
1
2
u
20
+ ··· −
1
2
u
2
+
1
2
u
a
5
=
−
1
2
u
20
− u
19
+ ··· − 2u −
1
2
−u
21
−
3
2
u
20
+ ··· − 2u
2
−
1
2
u
a
10
=
−
1
2
u
20
−
1
2
u
19
+ ··· −
1
2
u +
1
2
−
1
2
u
20
−
1
2
u
19
+ ··· +
1
2
u +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 5u
21
+ u
20
+ 29u
19
+ u
18
+ 79u
17
− 5u
16
+ 115u
15
− 19u
14
+
79u
13
− 18u
12
− 5u
11
− 30u
9
+ 8u
8
+ 15u
7
− 18u
6
+ 37u
5
− 17u
4
+ 11u
3
+ 1
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
22
+ 13u
21
+ ··· + 3u + 1
c
2
, c
6
, c
8
c
12
u
22
− u
21
+ ··· − u + 1
c
3
, c
7
u
22
+ u
21
+ ··· + u + 1
c
4
, c
5
, c
9
c
10
u
22
− 5u
21
+ ··· − 24u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
22
− 3y
21
+ ··· + 11y + 1
c
2
, c
6
, c
8
c
12
y
22
+ 13y
21
+ ··· + 3y + 1
c
3
, c
7
y
22
− 19y
21
+ ··· + 3y + 1
c
4
, c
5
, c
9
c
10
y
22
+ 25y
21
+ ··· − 32y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.277173 + 1.020170I
a = −1.65615 − 0.40699I
b = 0.13433 − 1.51680I
−7.08694 + 3.87705I −7.21377 − 4.81561I
u = 0.277173 − 1.020170I
a = −1.65615 + 0.40699I
b = 0.13433 + 1.51680I
−7.08694 − 3.87705I −7.21377 + 4.81561I
u = −0.121456 + 0.889759I
a = −1.029430 − 0.242749I
b = −0.505192 + 0.384473I
−2.07127 − 1.48890I −2.67809 + 4.69847I
u = −0.121456 − 0.889759I
a = −1.029430 + 0.242749I
b = −0.505192 − 0.384473I
−2.07127 + 1.48890I −2.67809 − 4.69847I
u = −0.848934 + 0.255974I
a = 1.72949 − 0.07214I
b = 1.176080 − 0.436448I
−8.20167 + 4.95433I 1.91829 − 2.01188I
u = −0.848934 − 0.255974I
a = 1.72949 + 0.07214I
b = 1.176080 + 0.436448I
−8.20167 − 4.95433I 1.91829 + 2.01188I
u = 0.403077 + 1.151660I
a = −0.87654 − 1.38792I
b = 1.59601 − 1.51481I
−7.80702 + 4.05683I −5.44929 − 3.62162I
u = 0.403077 − 1.151660I
a = −0.87654 + 1.38792I
b = 1.59601 + 1.51481I
−7.80702 − 4.05683I −5.44929 + 3.62162I
u = 0.716845 + 0.261797I
a = 1.67749 + 0.17960I
b = 0.911783 + 0.513874I
−0.28086 − 2.78084I 4.54791 + 3.72037I
u = 0.716845 − 0.261797I
a = 1.67749 − 0.17960I
b = 0.911783 − 0.513874I
−0.28086 + 2.78084I 4.54791 − 3.72037I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498272 + 1.142550I
a = −0.43520 + 1.93340I
b = 2.28341 + 1.52363I
−3.73649 − 7.94900I −0.13573 + 6.16396I
u = −0.498272 − 1.142550I
a = −0.43520 − 1.93340I
b = 2.28341 − 1.52363I
−3.73649 + 7.94900I −0.13573 − 6.16396I
u = 0.444842 + 0.593309I
a = 1.42127 + 1.52607I
b = −0.44921 + 1.51322I
−4.25955 + 2.40332I 2.42276 − 1.87700I
u = 0.444842 − 0.593309I
a = 1.42127 − 1.52607I
b = −0.44921 − 1.51322I
−4.25955 − 2.40332I 2.42276 + 1.87700I
u = 0.551692 + 1.163780I
a = −0.01034 − 1.91326I
b = 2.50735 − 1.20167I
−5.50564 + 12.55900I −1.64021 − 10.10675I
u = 0.551692 − 1.163780I
a = −0.01034 + 1.91326I
b = 2.50735 + 1.20167I
−5.50564 − 12.55900I −1.64021 + 10.10675I
u = −0.335392 + 1.264210I
a = −0.530073 + 0.859819I
b = 1.47236 + 0.87987I
−17.5375 − 2.7555I −7.01676 + 2.91273I
u = −0.335392 − 1.264210I
a = −0.530073 − 0.859819I
b = 1.47236 − 0.87987I
−17.5375 + 2.7555I −7.01676 − 2.91273I
u = −0.591533 + 1.189200I
a = 0.24537 + 1.77352I
b = 2.54369 + 0.94767I
−13.6900 − 15.6170I −3.36409 + 8.79372I
u = −0.591533 − 1.189200I
a = 0.24537 − 1.77352I
b = 2.54369 − 0.94767I
−13.6900 + 15.6170I −3.36409 − 8.79372I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498042 + 0.364034I
a = 1.46412 − 0.51940I
b = 0.329394 − 0.747695I
1.089740 − 0.536721I 8.60899 + 3.28109I
u = −0.498042 − 0.364034I
a = 1.46412 + 0.51940I
b = 0.329394 + 0.747695I
1.089740 + 0.536721I 8.60899 − 3.28109I
7
II.
I
u
2
= h3.69 × 10
30
u
61
+ 8.39 × 10
30
u
60
+ · · · + 2.19 × 10
31
b − 4.54 × 10
30
, 5.62 ×
10
30
u
61
+9.32×10
29
u
60
+· · ·+6.57×10
31
a+1.26×10
32
, u
62
+2u
61
+· · ·+7u+3i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
11
=
−0.0855391u
61
− 0.0141764u
60
+ ··· − 4.70351u − 1.91561
−0.168269u
61
− 0.382897u
60
+ ··· − 2.55324u + 0.207356
a
8
=
−0.784652u
61
− 1.03466u
60
+ ··· − 6.06002u − 3.97213
−0.416695u
61
+ 0.167342u
60
+ ··· + 4.79125u + 3.54242
a
1
=
u
2
+ 1
u
2
a
12
=
−0.0402708u
61
+ 0.447531u
60
+ ··· − 3.91890u − 2.58902
−0.267323u
61
− 0.161926u
60
+ ··· − 2.65084u + 0.351084
a
9
=
−0.291785u
61
− 0.157841u
60
+ ··· − 2.92917u − 3.12929
0.0849651u
61
+ 0.650458u
60
+ ··· + 0.142039u + 0.688054
a
5
=
−0.890090u
61
− 2.38676u
60
+ ··· − 9.65587u − 6.58484
0.381623u
61
− 0.451639u
60
+ ··· + 1.38007u + 0.627994
a
10
=
−0.223944u
61
+ 0.335268u
60
+ ··· − 2.74033u − 3.36849
−0.480269u
61
− 0.308145u
60
+ ··· − 1.68366u − 0.00366767
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.13514u
61
+ 3.90356u
60
+ ··· + 2.88438u − 1.52833
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
62
+ 30u
61
+ ··· + 35u + 9
c
2
, c
6
, c
8
c
12
u
62
− 2u
61
+ ··· − 7u + 3
c
3
, c
7
u
62
+ 2u
61
+ ··· − 10747u + 14583
c
4
, c
5
, c
9
c
10
(u
31
+ 2u
30
+ ··· − 8u − 2)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
62
+ 6y
61
+ ··· − 1009y + 81
c
2
, c
6
, c
8
c
12
y
62
+ 30y
61
+ ··· + 35y + 9
c
3
, c
7
y
62
− 18y
61
+ ··· + 711358091y + 212663889
c
4
, c
5
, c
9
c
10
(y
31
+ 38y
30
+ ··· − 48y −4)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.666104 + 0.730543I
a = 0.087322 + 0.584354I
b = 0.496094 − 0.738057I
−0.36232 − 5.51796I 0.77837 + 9.61169I
u = −0.666104 − 0.730543I
a = 0.087322 − 0.584354I
b = 0.496094 + 0.738057I
−0.36232 + 5.51796I 0.77837 − 9.61169I
u = 0.686447 + 0.784394I
a = 0.440237 + 0.732627I
b = −0.108205 + 0.403174I
−5.20347 + 2.59275I 2.06256 − 3.16265I
u = 0.686447 − 0.784394I
a = 0.440237 − 0.732627I
b = −0.108205 − 0.403174I
−5.20347 − 2.59275I 2.06256 + 3.16265I
u = −0.896489 + 0.288317I
a = −2.09267 − 0.04312I
b = −1.76964 + 0.85544I
−10.9647 + 10.1676I −0.91392 − 5.40901I
u = −0.896489 − 0.288317I
a = −2.09267 + 0.04312I
b = −1.76964 − 0.85544I
−10.9647 − 10.1676I −0.91392 + 5.40901I
u = −0.629178 + 0.873889I
a = −0.199672 − 0.056127I
b = −1.082620 − 0.085481I
−0.779034 + 0.507247I 0. − 2.93446I
u = −0.629178 − 0.873889I
a = −0.199672 + 0.056127I
b = −1.082620 + 0.085481I
−0.779034 − 0.507247I 0. + 2.93446I
u = 0.449825 + 0.996232I
a = −0.050283 − 0.198043I
b = −1.082620 − 0.085481I
−0.779034 + 0.507247I 0
u = 0.449825 − 0.996232I
a = −0.050283 + 0.198043I
b = −1.082620 + 0.085481I
−0.779034 − 0.507247I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.890494 + 0.168471I
a = −1.321460 − 0.466064I
b = −1.36135 − 0.59633I
−12.95390 + 1.38125I −3.10767 + 0.27219I
u = −0.890494 − 0.168471I
a = −1.321460 + 0.466064I
b = −1.36135 + 0.59633I
−12.95390 − 1.38125I −3.10767 − 0.27219I
u = 0.788781 + 0.767503I
a = 0.238484 − 0.701341I
b = 0.558659 + 0.646395I
−7.97068 + 6.77480I 0. − 6.34396I
u = 0.788781 − 0.767503I
a = 0.238484 + 0.701341I
b = 0.558659 − 0.646395I
−7.97068 − 6.77480I 0. + 6.34396I
u = −0.563357 + 0.949810I
a = 0.400448 − 0.334162I
b = 0.360204 − 0.897228I
0.38775 − 3.17615I 0
u = −0.563357 − 0.949810I
a = 0.400448 + 0.334162I
b = 0.360204 + 0.897228I
0.38775 + 3.17615I 0
u = 0.550433 + 0.959763I
a = 1.297360 + 0.482083I
b = 0.29971 + 1.71948I
−5.29982 + 1.79874I 0
u = 0.550433 − 0.959763I
a = 1.297360 − 0.482083I
b = 0.29971 − 1.71948I
−5.29982 − 1.79874I 0
u = −0.586824 + 0.636146I
a = 0.495132 − 0.651002I
b = −0.374983 − 0.161852I
1.31051 − 1.39768I 6.56379 + 5.41262I
u = −0.586824 − 0.636146I
a = 0.495132 + 0.651002I
b = −0.374983 + 0.161852I
1.31051 + 1.39768I 6.56379 − 5.41262I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.491654 + 1.034130I
a = 0.074800 + 0.504612I
b = 0.496094 + 0.738057I
−0.36232 + 5.51796I 0
u = 0.491654 − 1.034130I
a = 0.074800 − 0.504612I
b = 0.496094 − 0.738057I
−0.36232 − 5.51796I 0
u = 0.801270 + 0.256679I
a = −2.23504 − 0.16817I
b = −1.66877 − 0.97408I
−2.82013 − 7.52476I 1.18698 + 6.99451I
u = 0.801270 − 0.256679I
a = −2.23504 + 0.16817I
b = −1.66877 + 0.97408I
−2.82013 + 7.52476I 1.18698 − 6.99451I
u = 0.323535 + 1.114360I
a = 0.075800 + 1.078080I
b = −1.27158 + 0.73117I
−4.23586 + 0.27259I 0
u = 0.323535 − 1.114360I
a = 0.075800 − 1.078080I
b = −1.27158 − 0.73117I
−4.23586 − 0.27259I 0
u = 0.750659 + 0.887428I
a = −0.358620 + 0.042820I
b = −1.162170 + 0.126258I
−8.32783 − 1.04707I 0
u = 0.750659 − 0.887428I
a = −0.358620 − 0.042820I
b = −1.162170 − 0.126258I
−8.32783 + 1.04707I 0
u = −0.472572 + 1.082310I
a = 0.148446 − 1.393170I
b = −1.41819 − 1.05546I
−0.99698 − 3.48995I 0
u = −0.472572 − 1.082310I
a = 0.148446 + 1.393170I
b = −1.41819 + 1.05546I
−0.99698 + 3.48995I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.387583 + 1.137140I
a = 0.60373 + 1.77130I
b = 1.90030
−4.52090 0
u = −0.387583 − 1.137140I
a = 0.60373 − 1.77130I
b = 1.90030
−4.52090 0
u = −0.426409 + 1.129220I
a = −0.131838 + 0.321832I
b = −1.162170 + 0.126258I
−8.32783 − 1.04707I 0
u = −0.426409 − 1.129220I
a = −0.131838 − 0.321832I
b = −1.162170 − 0.126258I
−8.32783 + 1.04707I 0
u = 0.291515 + 1.180250I
a = 0.23307 − 1.67452I
b = 1.65227 − 0.33136I
−7.28291 − 4.17154I 0
u = 0.291515 − 1.180250I
a = 0.23307 + 1.67452I
b = 1.65227 + 0.33136I
−7.28291 + 4.17154I 0
u = −0.475171 + 1.135050I
a = 0.049532 − 0.660701I
b = 0.558659 − 0.646395I
−7.97068 − 6.77480I 0
u = −0.475171 − 1.135050I
a = 0.049532 + 0.660701I
b = 0.558659 + 0.646395I
−7.97068 + 6.77480I 0
u = 0.418242 + 0.627505I
a = −0.559898 − 0.519466I
b = 0.360204 + 0.897228I
0.38775 + 3.17615I 4.19909 + 0.89025I
u = 0.418242 − 0.627505I
a = −0.559898 + 0.519466I
b = 0.360204 − 0.897228I
0.38775 − 3.17615I 4.19909 − 0.89025I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.530235 + 1.136730I
a = −0.07716 + 1.50150I
b = −1.66877 + 0.97408I
−2.82013 + 7.52476I 0
u = 0.530235 − 1.136730I
a = −0.07716 − 1.50150I
b = −1.66877 − 0.97408I
−2.82013 − 7.52476I 0
u = 0.477297 + 1.164540I
a = 0.77266 − 1.43879I
b = 1.65227 + 0.33136I
−7.28291 + 4.17154I 0
u = 0.477297 − 1.164540I
a = 0.77266 + 1.43879I
b = 1.65227 − 0.33136I
−7.28291 − 4.17154I 0
u = −0.278446 + 1.228190I
a = −0.071389 − 1.005860I
b = −1.36135 − 0.59633I
−12.95390 + 1.38125I 0
u = −0.278446 − 1.228190I
a = −0.071389 + 1.005860I
b = −1.36135 + 0.59633I
−12.95390 − 1.38125I 0
u = 0.722560 + 0.106633I
a = −1.50741 + 0.82209I
b = −1.27158 + 0.73117I
−4.23586 + 0.27259I −1.68227 + 0.33399I
u = 0.722560 − 0.106633I
a = −1.50741 − 0.82209I
b = −1.27158 − 0.73117I
−4.23586 − 0.27259I −1.68227 − 0.33399I
u = −0.240118 + 1.264390I
a = 0.15678 + 1.45730I
b = 1.40042 + 0.34149I
−16.1317 + 6.5577I 0
u = −0.240118 − 1.264390I
a = 0.15678 − 1.45730I
b = 1.40042 − 0.34149I
−16.1317 − 6.5577I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.566003 + 1.180140I
a = −0.23494 − 1.48755I
b = −1.76964 − 0.85544I
−10.9647 − 10.1676I 0
u = −0.566003 − 1.180140I
a = −0.23494 + 1.48755I
b = −1.76964 + 0.85544I
−10.9647 + 10.1676I 0
u = −0.664612 + 0.170734I
a = −2.32627 + 0.63475I
b = −1.41819 + 1.05546I
−0.99698 + 3.48995I 4.01270 − 2.89115I
u = −0.664612 − 0.170734I
a = −2.32627 − 0.63475I
b = −1.41819 − 1.05546I
−0.99698 − 3.48995I 4.01270 + 2.89115I
u = 0.501484 + 0.456925I
a = 0.826582 + 0.636737I
b = −0.374983 − 0.161852I
1.31051 − 1.39768I 6.56379 + 5.41262I
u = 0.501484 − 0.456925I
a = 0.826582 − 0.636737I
b = −0.374983 + 0.161852I
1.31051 + 1.39768I 6.56379 − 5.41262I
u = −0.536448 + 1.217100I
a = 0.67450 + 1.24755I
b = 1.40042 − 0.34149I
−16.1317 − 6.5577I 0
u = −0.536448 − 1.217100I
a = 0.67450 − 1.24755I
b = 1.40042 + 0.34149I
−16.1317 + 6.5577I 0
u = 0.078963 + 0.630242I
a = −2.31047 − 0.68841I
b = 0.29971 − 1.71948I
−5.29982 − 1.79874I −2.21614 + 3.31862I
u = 0.078963 − 0.630242I
a = −2.31047 + 0.68841I
b = 0.29971 + 1.71948I
−5.29982 + 1.79874I −2.21614 − 3.31862I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.583093 + 0.120029I
a = 0.73556 − 1.30329I
b = −0.108205 + 0.403174I
−5.20347 + 2.59275I 2.06256 − 3.16265I
u = −0.583093 − 0.120029I
a = 0.73556 + 1.30329I
b = −0.108205 − 0.403174I
−5.20347 − 2.59275I 2.06256 + 3.16265I
17
III. I
u
3
= h−au + b − u, a
2
− 2u, u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u − 1
a
7
=
u
u − 1
a
4
=
0
−u
a
11
=
a
au + u
a
8
=
au − a + u
−a + u − 2
a
1
=
u
u − 1
a
12
=
a + 1
au + 2u
a
9
=
−a
−au − u
a
5
=
−2u + 2
−au + a + u + 2
a
10
=
a
2au − a + u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u + 4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
c
11
(u
2
− u + 1)
2
c
3
, c
6
, c
7
c
12
(u
2
+ u + 1)
2
c
4
, c
5
, c
9
c
10
(u
2
+ 2)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
c
11
, c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
9
c
10
(y + 2)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.224740 + 0.707110I
b = 0.50000 + 2.28024I
−4.93480 + 4.05977I 0. − 6.92820I
u = 0.500000 + 0.866025I
a = −1.224740 − 0.707110I
b = 0.500000 − 0.548188I
−4.93480 + 4.05977I 0. − 6.92820I
u = 0.500000 − 0.866025I
a = 1.224740 − 0.707110I
b = 0.50000 − 2.28024I
−4.93480 − 4.05977I 0. + 6.92820I
u = 0.500000 − 0.866025I
a = −1.224740 + 0.707110I
b = 0.500000 + 0.548188I
−4.93480 − 4.05977I 0. + 6.92820I
21
IV. I
u
4
= hb + u, a, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u − 1
a
7
=
u
u + 1
a
4
=
0
u
a
11
=
0
−u
a
8
=
u
u + 2
a
1
=
−u
−u − 1
a
12
=
1
−2u
a
9
=
0
−u
a
5
=
0
u
a
10
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u + 4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
11
, c
12
u
2
− u + 1
c
2
, c
8
u
2
+ u + 1
c
4
, c
5
, c
9
c
10
u
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
c
11
, c
12
y
2
+ y + 1
c
4
, c
5
, c
9
c
10
y
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0
b = 0.500000 − 0.866025I
− 4.05977I 0. + 6.92820I
u = −0.500000 − 0.866025I
a = 0
b = 0.500000 + 0.866025I
4.05977I 0. − 6.92820I
25
V. I
u
5
= h−au + b + 1, a
2
− 2u, u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u − 1
a
7
=
u
u − 1
a
4
=
0
−u
a
11
=
a
au − 1
a
8
=
−au + u
−au + a + 2u − 1
a
1
=
u
u − 1
a
12
=
a + u − 1
au − 2
a
9
=
−a
−au + 1
a
5
=
−2u + 2
au + u + 2
a
10
=
a
2au − a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
c
11
(u
2
− u + 1)
2
c
3
, c
6
, c
7
c
12
(u
2
+ u + 1)
2
c
4
, c
5
, c
9
c
10
(u
2
+ 2)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
c
11
, c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
9
c
10
(y + 2)
4
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.224740 + 0.707110I
b = −1.00000 + 1.41421I
−4.93480 0
u = 0.500000 + 0.866025I
a = −1.224740 − 0.707110I
b = −1.00000 − 1.41421I
−4.93480 0
u = 0.500000 − 0.866025I
a = 1.224740 − 0.707110I
b = −1.00000 − 1.41421I
−4.93480 0
u = 0.500000 − 0.866025I
a = −1.224740 + 0.707110I
b = −1.00000 + 1.41421I
−4.93480 0
29
VI. I
u
6
= hb + 1, a, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u − 1
a
7
=
u
u + 1
a
4
=
0
u
a
11
=
0
−1
a
8
=
u
2u + 1
a
1
=
−u
−u − 1
a
12
=
−u − 1
−2
a
9
=
0
−1
a
5
=
0
u
a
10
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
11
, c
12
u
2
− u + 1
c
2
, c
8
u
2
+ u + 1
c
4
, c
5
, c
9
c
10
u
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
c
11
, c
12
y
2
+ y + 1
c
4
, c
5
, c
9
c
10
y
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0
b = −1.00000
0 6.00000
u = −0.500000 − 0.866025I
a = 0
b = −1.00000
0 6.00000
33
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
((u
2
− u + 1)
6
)(u
22
+ 13u
21
+ ··· + 3u + 1)(u
62
+ 30u
61
+ ··· + 35u + 9)
c
2
, c
8
((u
2
− u + 1)
4
)(u
2
+ u + 1)
2
(u
22
− u
21
+ ··· − u + 1)
· (u
62
− 2u
61
+ ··· − 7u + 3)
c
3
, c
7
((u
2
− u + 1)
2
)(u
2
+ u + 1)
4
(u
22
+ u
21
+ ··· + u + 1)
· (u
62
+ 2u
61
+ ··· − 10747u + 14583)
c
4
, c
5
, c
9
c
10
u
4
(u
2
+ 2)
4
(u
22
− 5u
21
+ ··· − 24u + 4)(u
31
+ 2u
30
+ ··· − 8u − 2)
2
c
6
, c
12
((u
2
− u + 1)
2
)(u
2
+ u + 1)
4
(u
22
− u
21
+ ··· − u + 1)
· (u
62
− 2u
61
+ ··· − 7u + 3)
34
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y
2
+ y + 1)
6
)(y
22
− 3y
21
+ ··· + 11y + 1)
· (y
62
+ 6y
61
+ ··· − 1009y + 81)
c
2
, c
6
, c
8
c
12
((y
2
+ y + 1)
6
)(y
22
+ 13y
21
+ ··· + 3y + 1)(y
62
+ 30y
61
+ ··· + 35y + 9)
c
3
, c
7
((y
2
+ y + 1)
6
)(y
22
− 19y
21
+ ··· + 3y + 1)
· (y
62
− 18y
61
+ ··· + 711358091y + 212663889)
c
4
, c
5
, c
9
c
10
y
4
(y + 2)
8
(y
22
+ 25y
21
+ ··· − 32y + 16)
· (y
31
+ 38y
30
+ ··· − 48y −4)
2
35
