12a
0182
(K12a
0182
)
A knot diagram
1
Linearized knot diagam
3 5 9 6 2 12 10 11 4 8 1 7
Solving Sequence
3,9
4
5,10
2 6
1,11
8 7 12
c
3
c
9
c
2
c
5
c
1
c
8
c
7
c
12
c
4
, c
6
, c
10
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.01638 × 10
144
u
70
+ 3.79783 × 10
144
u
69
+ ··· + 2.19432 × 10
148
d + 4.74337 × 10
147
,
− 1.52787 × 10
144
u
70
+ 2.07626 × 10
144
u
69
+ ··· + 3.13474 × 10
147
c − 1.26268 × 10
147
,
2.08280 × 10
163
u
70
− 6.54445 × 10
163
u
69
+ ··· + 3.56067 × 10
166
b − 1.75912 × 10
166
,
2.20933 × 10
163
u
70
− 4.97335 × 10
163
u
69
+ ··· + 1.01733 × 10
166
a − 9.57968 × 10
164
,
u
71
− 2u
70
+ ··· + 1536u
2
− 512i
I
u
2
= hc
2
u + u
2
c + d − c,
u
8
c + u
8
− 3u
6
c + u
7
− u
5
c − 2u
6
+ 4u
4
c − 3u
5
+ 2u
3
c + u
4
+ c
3
− u
2
c + 3u
3
− 2cu + 2u
2
− c − 1,
u
8
− 2u
6
+ 2u
4
+ b, −u
6
+ u
4
+ a − 1, u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
I
v
1
= ha, d − v + 1, av + c − v, b + v, v
2
− v + 1i
I
v
2
= ha, d, c − v, b − v, v
2
+ v + 1i
I
v
3
= hc, d + 1, b, a − 1, v − 1i
I
v
4
= ha, da − cb − d − b − 1, dv + 1, cv − ba − bv + b − a + 1, b
2
+ b + 1i
* 5 irreducible components of dim
C
= 0, with total 103 representations.
* 1 irreducible components of dim
C
= 1
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
=
h1.02 × 10
144
u
70
+ 3.80 × 10
144
u
69
+ · · · + 2.19 × 10
148
d + 4.74 × 10
147
, −1.53 ×
10
144
u
70
+2.08×10
144
u
69
+· · · + 3.13×10
147
c−1.26×10
147
, 2.08×10
163
u
70
−
6.54 × 10
163
u
69
+ · · · + 3.56 × 10
166
b − 1.76 × 10
166
, 2.21 × 10
163
u
70
− 4.97 ×
10
163
u
69
+ · · · + 1.02 × 10
166
a − 9.58 × 10
164
, u
71
− 2u
70
+ · · · + 1536u
2
− 512i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
5
=
−0.00217169u
70
+ 0.00488861u
69
+ ··· − 2.25991u + 0.0941645
−0.000584947u
70
+ 0.00183798u
69
+ ··· − 0.979894u + 0.494041
a
10
=
u
−u
3
+ u
a
2
=
0.000125704u
70
+ 0.00219339u
69
+ ··· − 0.129419u + 0.703347
0.000888998u
70
− 0.00320644u
69
+ ··· + 2.30414u − 0.769289
a
6
=
0.000125704u
70
+ 0.00219339u
69
+ ··· − 0.129419u + 0.703347
−0.00231995u
70
+ 0.00405624u
69
+ ··· − 2.36850u − 0.482448
a
1
=
0.00101470u
70
− 0.00101305u
69
+ ··· + 2.17472u − 0.0659421
0.000888998u
70
− 0.00320644u
69
+ ··· + 2.30414u − 0.769289
a
11
=
0.000487399u
70
− 0.000662337u
69
+ ··· + 1.64247u + 0.402802
−0.0000463186u
70
− 0.000173075u
69
+ ··· + 0.648446u − 0.216166
a
8
=
−0.000515659u
70
+ 0.000632921u
69
+ ··· − 0.744479u − 0.458988
0.0000317918u
70
+ 0.0000611450u
69
+ ··· + 1.16201u + 0.147793
a
7
=
−0.000533717u
70
+ 0.000489262u
69
+ ··· − 0.994027u − 0.618968
0.000164426u
70
− 0.000246208u
69
+ ··· + 0.921710u + 0.0798584
a
12
=
0.00194846u
70
− 0.00138153u
69
+ ··· + 2.53194u + 0.453579
0.000595399u
70
− 0.00245201u
69
+ ··· + 1.96648u − 0.834037
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.000644196u
70
+ 0.0111115u
69
+ ··· − 0.863041u + 15.1191
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
71
+ 24u
70
+ ··· − 40u − 16
c
2
, c
5
u
71
+ 2u
70
+ ··· − 5u
2
− 4
c
3
, c
9
u
71
− 2u
70
+ ··· + 1536u
2
− 512
c
6
, c
12
u
71
− 8u
70
+ ··· + 56u − 16
c
7
, c
8
, c
10
u
71
+ 8u
70
+ ··· + 56u − 16
c
11
u
71
+ 30u
70
+ ··· + 4640u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
71
+ 48y
70
+ ··· − 6880y − 256
c
2
, c
5
y
71
+ 24y
70
+ ··· − 40y − 16
c
3
, c
9
y
71
− 30y
70
+ ··· + 1572864y − 262144
c
6
, c
12
y
71
− 30y
70
+ ··· + 4640y − 256
c
7
, c
8
, c
10
y
71
− 70y
70
+ ··· − 1504y − 256
c
11
y
71
+ 30y
70
+ ··· + 5022208y − 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.372595 + 0.922213I
a = 0.706869 + 0.294839I
b = −0.705480 + 0.710846I
c = −0.470907 + 0.554383I
d = −1.70042 + 0.50968I
−0.206074 + 1.106620I 1.82615 − 2.10157I
u = −0.372595 − 0.922213I
a = 0.706869 − 0.294839I
b = −0.705480 − 0.710846I
c = −0.470907 − 0.554383I
d = −1.70042 − 0.50968I
−0.206074 − 1.106620I 1.82615 + 2.10157I
u = 0.661751 + 0.731261I
a = 1.05387 − 1.06299I
b = 0.033676 − 0.991675I
c = 0.475791 + 0.487011I
d = 1.339240 − 0.225092I
−5.31233 − 1.23150I −6.16629 + 0.79467I
u = 0.661751 − 0.731261I
a = 1.05387 + 1.06299I
b = 0.033676 + 0.991675I
c = 0.475791 − 0.487011I
d = 1.339240 + 0.225092I
−5.31233 + 1.23150I −6.16629 − 0.79467I
u = 0.216094 + 0.961248I
a = 0.490833 + 0.220678I
b = 0.626372 − 0.146182I
c = 0.190153 − 1.314880I
d = −0.304165 − 0.812210I
2.60149 − 2.06138I 6.60052 + 3.22142I
u = 0.216094 − 0.961248I
a = 0.490833 − 0.220678I
b = 0.626372 + 0.146182I
c = 0.190153 + 1.314880I
d = −0.304165 + 0.812210I
2.60149 + 2.06138I 6.60052 − 3.22142I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.510340 + 0.919175I
a = 0.97241 + 1.52837I
b = 0.167182 + 1.050320I
c = −0.387643 − 1.176070I
d = 0.698084 − 0.628537I
−1.22762 + 4.53498I −0.48837 − 4.83158I
u = −0.510340 − 0.919175I
a = 0.97241 − 1.52837I
b = 0.167182 − 1.050320I
c = −0.387643 + 1.176070I
d = 0.698084 + 0.628537I
−1.22762 − 4.53498I −0.48837 + 4.83158I
u = 0.843761 + 0.417994I
a = −3.24462 + 0.27087I
b = 0.648309 + 0.950753I
c = 0.537281 + 0.453998I
d = 0.703145 − 0.615016I
−1.74336 + 3.95563I 0.57229 − 6.63484I
u = 0.843761 − 0.417994I
a = −3.24462 − 0.27087I
b = 0.648309 − 0.950753I
c = 0.537281 − 0.453998I
d = 0.703145 + 0.615016I
−1.74336 − 3.95563I 0.57229 + 6.63484I
u = −0.980094 + 0.401535I
a = 0.780465 + 0.104472I
b = −0.675884 + 0.258339I
c = −0.548184 + 0.485014I
d = −0.641289 − 0.881527I
0.13020 − 4.00402I 4.41276 + 6.69495I
u = −0.980094 − 0.401535I
a = 0.780465 − 0.104472I
b = −0.675884 − 0.258339I
c = −0.548184 − 0.485014I
d = −0.641289 + 0.881527I
0.13020 + 4.00402I 4.41276 − 6.69495I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.482781 + 0.984718I
a = 0.632388 + 0.401253I
b = −0.681961 + 0.973056I
c = 0.486783 + 0.532736I
d = 1.88522 + 0.25805I
−0.99233 − 6.45679I 0.34368 + 6.97496I
u = 0.482781 − 0.984718I
a = 0.632388 − 0.401253I
b = −0.681961 − 0.973056I
c = 0.486783 − 0.532736I
d = 1.88522 − 0.25805I
−0.99233 + 6.45679I 0.34368 − 6.97496I
u = 0.777198 + 0.427799I
a = 0.661548 + 0.487935I
b = −0.527615 + 1.024960I
c = 0.525019 + 0.439223I
d = 0.729049 − 0.488658I
−1.94652 − 0.34051I −0.37051 − 3.03065I
u = 0.777198 − 0.427799I
a = 0.661548 − 0.487935I
b = −0.527615 − 1.024960I
c = 0.525019 − 0.439223I
d = 0.729049 + 0.488658I
−1.94652 + 0.34051I −0.37051 + 3.03065I
u = 1.127060 + 0.152551I
a = 0.639024 + 0.570894I
b = −0.435782 + 1.114890I
c = −1.214770 + 0.100113I
d = −1.35450 + 0.44354I
4.50468 − 2.47836I 7.49354 + 3.38416I
u = 1.127060 − 0.152551I
a = 0.639024 − 0.570894I
b = −0.435782 − 1.114890I
c = −1.214770 − 0.100113I
d = −1.35450 − 0.44354I
4.50468 + 2.47836I 7.49354 − 3.38416I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.982347 + 0.611518I
a = 0.755795 − 0.846393I
b = −0.132131 − 1.098790I
c = 0.515465 + 0.490470I
d = 1.08458 − 0.93082I
−4.29573 + 6.37313I −3.00781 − 7.19219I
u = 0.982347 − 0.611518I
a = 0.755795 + 0.846393I
b = −0.132131 + 1.098790I
c = 0.515465 − 0.490470I
d = 1.08458 + 0.93082I
−4.29573 − 6.37313I −3.00781 + 7.19219I
u = 1.173990 + 0.222972I
a = −2.07252 − 0.44952I
b = 0.744384 + 0.914398I
c = 0.606381 − 0.672488I
d = −0.633879 + 0.879788I
5.09577 + 1.83902I 8.24819 + 0.I
u = 1.173990 − 0.222972I
a = −2.07252 + 0.44952I
b = 0.744384 − 0.914398I
c = 0.606381 + 0.672488I
d = −0.633879 − 0.879788I
5.09577 − 1.83902I 8.24819 + 0.I
u = −1.203430 + 0.094057I
a = −1.52309 − 0.96637I
b = 0.774513 + 0.827694I
c = −0.596615 − 0.625599I
d = 0.431350 + 1.041490I
5.36659 + 3.89584I 8.41567 − 5.55146I
u = −1.203430 − 0.094057I
a = −1.52309 + 0.96637I
b = 0.774513 − 0.827694I
c = −0.596615 + 0.625599I
d = 0.431350 − 1.041490I
5.36659 − 3.89584I 8.41567 + 5.55146I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.117530 + 0.478181I
a = 0.690211 − 0.765567I
b = −0.209298 − 1.133130I
c = −1.116800 + 0.271956I
d = −1.28841 + 1.30589I
3.15531 + 5.12152I 0
u = 1.117530 − 0.478181I
a = 0.690211 + 0.765567I
b = −0.209298 + 1.133130I
c = −1.116800 − 0.271956I
d = −1.28841 − 1.30589I
3.15531 − 5.12152I 0
u = −1.137650 + 0.460214I
a = 0.609632 − 0.520416I
b = −0.523715 − 1.123490I
c = 1.116170 + 0.256986I
d = 1.24509 + 1.25727I
3.19656 − 2.55854I 0
u = −1.137650 − 0.460214I
a = 0.609632 + 0.520416I
b = −0.523715 + 1.123490I
c = 1.116170 − 0.256986I
d = 1.24509 − 1.25727I
3.19656 + 2.55854I 0
u = −0.725491 + 0.260568I
a = −0.74999 − 2.93714I
b = 0.621787 + 0.746410I
c = −0.573783 + 0.383951I
d = −0.438809 − 0.376035I
−1.09934 + 1.05821I 3.09814 + 1.72718I
u = −0.725491 − 0.260568I
a = −0.74999 + 2.93714I
b = 0.621787 − 0.746410I
c = −0.573783 − 0.383951I
d = −0.438809 + 0.376035I
−1.09934 − 1.05821I 3.09814 − 1.72718I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.247645 + 1.226350I
a = 0.653789 + 0.300056I
b = −0.795711 + 0.784067I
c = −0.133830 − 1.140380I
d = 0.422479 − 1.218340I
6.94619 − 1.12108I 0
u = −0.247645 − 1.226350I
a = 0.653789 − 0.300056I
b = −0.795711 − 0.784067I
c = −0.133830 + 1.140380I
d = 0.422479 + 1.218340I
6.94619 + 1.12108I 0
u = 0.464983 + 0.581438I
a = 1.72522 − 0.64973I
b = 0.139048 − 0.768176I
c = 0.71852 − 1.33569I
d = −0.442687 − 0.257326I
1.011140 − 0.938516I 3.66296 − 0.79830I
u = 0.464983 − 0.581438I
a = 1.72522 + 0.64973I
b = 0.139048 + 0.768176I
c = 0.71852 + 1.33569I
d = −0.442687 + 0.257326I
1.011140 + 0.938516I 3.66296 + 0.79830I
u = 0.368570 + 1.210560I
a = 0.618935 + 0.372180I
b = −0.745652 + 0.954700I
c = 0.194177 − 1.117100I
d = −0.623618 − 1.150760I
6.42018 − 4.68044I 0
u = 0.368570 − 1.210560I
a = 0.618935 − 0.372180I
b = −0.745652 − 0.954700I
c = 0.194177 + 1.117100I
d = −0.623618 + 1.150760I
6.42018 + 4.68044I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.248660 + 0.306382I
a = 0.734113 + 0.059783I
b = −0.802776 + 0.158635I
c = 1.116690 + 0.156605I
d = 0.994223 + 0.843737I
7.51654 − 1.91781I 0
u = −1.248660 − 0.306382I
a = 0.734113 − 0.059783I
b = −0.802776 − 0.158635I
c = 1.116690 − 0.156605I
d = 0.994223 − 0.843737I
7.51654 + 1.91781I 0
u = 0.504947 + 1.215580I
a = 0.662564 − 0.264148I
b = −0.825179 − 0.702952I
c = 0.245007 − 1.071700I
d = −0.859773 − 1.094450I
5.42990 − 4.32973I 0
u = 0.504947 − 1.215580I
a = 0.662564 + 0.264148I
b = −0.825179 + 0.702952I
c = 0.245007 + 1.071700I
d = −0.859773 + 1.094450I
5.42990 + 4.32973I 0
u = −1.152900 + 0.667545I
a = 0.653927 + 0.849988I
b = −0.143613 + 1.176100I
c = 1.028980 + 0.314229I
d = 1.17468 + 1.72508I
0.80414 − 10.42400I 0
u = −1.152900 − 0.667545I
a = 0.653927 − 0.849988I
b = −0.143613 − 1.176100I
c = 1.028980 − 0.314229I
d = 1.17468 − 1.72508I
0.80414 + 10.42400I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.185800 + 0.609579I
a = −0.604647 − 0.948689I
b = 0.833000 + 0.664986I
c = −0.515530 + 0.509861I
d = −1.03285 − 1.38981I
2.33908 − 6.73341I 0
u = −1.185800 − 0.609579I
a = −0.604647 + 0.948689I
b = 0.833000 − 0.664986I
c = −0.515530 − 0.509861I
d = −1.03285 + 1.38981I
2.33908 + 6.73341I 0
u = −0.593784 + 1.208600I
a = 0.602225 − 0.393473I
b = −0.733361 − 1.011480I
c = −0.274626 − 1.042820I
d = 1.00911 − 1.02929I
4.48821 + 10.17210I 0
u = −0.593784 − 1.208600I
a = 0.602225 + 0.393473I
b = −0.733361 + 1.011480I
c = −0.274626 + 1.042820I
d = 1.00911 + 1.02929I
4.48821 − 10.17210I 0
u = 1.233000 + 0.545251I
a = 0.716779 − 0.101507I
b = −0.834377 − 0.273084I
c = −1.052540 + 0.252051I
d = −1.00331 + 1.44383I
5.82408 + 7.48275I 0
u = 1.233000 − 0.545251I
a = 0.716779 + 0.101507I
b = −0.834377 + 0.273084I
c = −1.052540 − 0.252051I
d = −1.00331 − 1.44383I
5.82408 − 7.48275I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.176438 + 0.617781I
a = −1.24181 − 5.67569I
b = 0.472468 − 0.965679I
c = −0.38103 − 1.75179I
d = 0.176185 − 0.407221I
0.42738 − 1.60074I 0.77404 + 2.18898I
u = −0.176438 − 0.617781I
a = −1.24181 + 5.67569I
b = 0.472468 + 0.965679I
c = −0.38103 + 1.75179I
d = 0.176185 + 0.407221I
0.42738 + 1.60074I 0.77404 − 2.18898I
u = 1.181300 + 0.680585I
a = −1.94797 + 0.51901I
b = 0.722487 + 1.031630I
c = 0.510240 + 0.507622I
d = 1.20020 − 1.39980I
1.22414 + 12.55690I 0
u = 1.181300 − 0.680585I
a = −1.94797 − 0.51901I
b = 0.722487 − 1.031630I
c = 0.510240 − 0.507622I
d = 1.20020 + 1.39980I
1.22414 − 12.55690I 0
u = 0.010891 + 0.626888I
a = 0.717451 − 0.379980I
b = −0.596253 − 0.833536I
c = −0.145864 + 0.996178I
d = −0.36117 + 2.00147I
0.65592 + 2.35939I 1.51759 − 4.85897I
u = 0.010891 − 0.626888I
a = 0.717451 + 0.379980I
b = −0.596253 + 0.833536I
c = −0.145864 − 0.996178I
d = −0.36117 − 2.00147I
0.65592 − 2.35939I 1.51759 + 4.85897I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.617428 + 0.085193I
a = 0.771703 + 0.515946I
b = −0.399151 + 0.927946I
c = −0.667996 + 0.208298I
d = −0.215095 − 0.146010I
−0.93328 − 2.67780I 3.99337 + 7.95500I
u = −0.617428 − 0.085193I
a = 0.771703 − 0.515946I
b = −0.399151 − 0.927946I
c = −0.667996 − 0.208298I
d = −0.215095 + 0.146010I
−0.93328 + 2.67780I 3.99337 − 7.95500I
u = 0.591164
a = 0.929806
b = −0.315087
c = 1.20948
d = −0.0779789
1.02886 10.5160
u = −0.282782 + 0.492299I
a = 1.070690 − 0.124673I
b = 0.198227 + 0.270585I
c = −0.298696 + 0.445240I
d = −0.632940 + 0.412834I
−1.67984 + 0.60130I −3.90300 − 0.33160I
u = −0.282782 − 0.492299I
a = 1.070690 + 0.124673I
b = 0.198227 − 0.270585I
c = −0.298696 − 0.445240I
d = −0.632940 − 0.412834I
−1.67984 − 0.60130I −3.90300 + 0.33160I
u = −1.33133 + 0.61244I
a = −0.691353 − 0.789833I
b = 0.877454 + 0.689350I
c = 1.004370 + 0.240216I
d = 0.77088 + 1.60236I
10.54930 − 5.35435I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.33133 − 0.61244I
a = −0.691353 + 0.789833I
b = 0.877454 − 0.689350I
c = 1.004370 − 0.240216I
d = 0.77088 − 1.60236I
10.54930 + 5.35435I 0
u = 1.29995 + 0.68416I
a = −1.77475 + 0.42337I
b = 0.751329 + 1.038160I
c = −0.990397 + 0.266490I
d = −0.85024 + 1.76626I
9.4739 + 11.4004I 0
u = 1.29995 − 0.68416I
a = −1.77475 − 0.42337I
b = 0.751329 − 1.038160I
c = −0.990397 − 0.266490I
d = −0.85024 − 1.76626I
9.4739 − 11.4004I 0
u = 1.27239 + 0.75883I
a = −0.528127 + 0.758818I
b = 0.887462 − 0.636245I
c = −0.972392 + 0.290048I
d = −0.92205 + 1.92929I
7.95427 + 11.37060I 0
u = 1.27239 − 0.75883I
a = −0.528127 − 0.758818I
b = 0.887462 + 0.636245I
c = −0.972392 − 0.290048I
d = −0.92205 − 1.92929I
7.95427 − 11.37060I 0
u = −1.24401 + 0.80606I
a = −1.73933 − 0.62055I
b = 0.732124 − 1.065030I
c = 0.961782 + 0.307183I
d = 0.99186 + 2.02574I
6.6365 − 17.3722I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.24401 − 0.80606I
a = −1.73933 + 0.62055I
b = 0.732124 + 1.065030I
c = 0.961782 − 0.307183I
d = 0.99186 − 2.02574I
6.6365 + 17.3722I 0
u = −1.51788 + 0.06429I
a = −1.289590 − 0.499691I
b = 0.858480 + 0.864860I
c = 1.033780 + 0.023696I
d = 0.276083 + 0.176660I
13.78050 − 0.08878I 0
u = −1.51788 − 0.06429I
a = −1.289590 + 0.499691I
b = 0.858480 − 0.864860I
c = 1.033780 − 0.023696I
d = 0.276083 − 0.176660I
13.78050 + 0.08878I 0
u = 1.51414 + 0.16464I
a = −1.47755 − 0.28880I
b = 0.837181 + 0.923149I
c = −1.029750 + 0.060361I
d = −0.287259 + 0.451271I
13.6007 + 6.3599I 0
u = 1.51414 − 0.16464I
a = −1.47755 + 0.28880I
b = 0.837181 − 0.923149I
c = −1.029750 − 0.060361I
d = −0.287259 − 0.451271I
13.6007 − 6.3599I 0
16
II. I
u
2
= hc
2
u + u
2
c + d − c, u
8
c + u
8
+ · · · − c − 1, u
8
− 2u
6
+ 2u
4
+
b, −u
6
+ u
4
+ a − 1, u
9
+ u
8
+ · · · − u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
5
=
u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
10
=
u
−u
3
+ u
a
2
=
u
3
−u
3
+ u
a
6
=
u
3
−u
5
+ u
3
− u
a
1
=
u
−u
3
+ u
a
11
=
c
−c
2
u − u
2
c + c
a
8
=
−c
2
u
u
3
c
2
− c
2
u + c
a
7
=
−c
2
u − u
2
c
u
3
c
2
+ u
4
c − c
2
u − u
2
c + c
a
12
=
u
3
c
2
+ c
−u
5
c
2
+ u
3
c
2
− c
2
u − u
2
c + c
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
7
− 8u
5
− 4u
4
+ 8u
3
+ 4u
2
+ 4u + 2
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
3
c
2
, c
5
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
3
c
3
, c
9
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
3
c
6
, c
7
, c
8
c
10
, c
12
u
27
− 9u
25
+ ··· − u + 1
c
11
u
27
+ 18u
26
+ ··· + 5u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
3
c
2
, c
5
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
3
c
3
, c
9
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
3
c
6
, c
7
, c
8
c
10
, c
12
y
27
− 18y
26
+ ··· + 5y − 1
c
11
y
27
− 18y
26
+ ··· − 15y − 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 + 0.510351I
a = 0.917974 + 0.753965I
b = −0.140343 + 0.966856I
c = −0.719765 − 0.954592I
d = 0.673261 + 0.061997I
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = −0.772920 + 0.510351I
a = 0.917974 + 0.753965I
b = −0.140343 + 0.966856I
c = −0.508051 + 0.453456I
d = −0.889180 − 0.483066I
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = −0.772920 + 0.510351I
a = 0.917974 + 0.753965I
b = −0.140343 + 0.966856I
c = 1.227820 + 0.501136I
d = 2.01788 + 1.61089I
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = −0.772920 − 0.510351I
a = 0.917974 − 0.753965I
b = −0.140343 − 0.966856I
c = −0.719765 + 0.954592I
d = 0.673261 − 0.061997I
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = −0.772920 − 0.510351I
a = 0.917974 − 0.753965I
b = −0.140343 − 0.966856I
c = −0.508051 − 0.453456I
d = −0.889180 + 0.483066I
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = −0.772920 − 0.510351I
a = 0.917974 − 0.753965I
b = −0.140343 − 0.966856I
c = 1.227820 − 0.501136I
d = 2.01788 − 1.61089I
−1.78344 + 2.09337I −0.51499 − 4.16283I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.825933
a = 0.852096
b = −0.512358
c = 0.753259 + 0.486083I
d = −0.034073 − 0.450330I
1.19845 8.65230
u = 0.825933
a = 0.852096
b = −0.512358
c = 0.753259 − 0.486083I
d = −0.034073 + 0.450330I
1.19845 8.65230
u = 0.825933
a = 0.852096
b = −0.512358
c = −1.50652
d = −2.35336
1.19845 8.65230
u = 1.173910 + 0.391555I
a = −0.92292 + 1.10816I
b = 0.796005 − 0.733148I
c = 0.585219 − 0.735474I
d = −0.911760 + 0.715540I
4.37135 + 1.33617I 7.28409 − 0.70175I
u = 1.173910 + 0.391555I
a = −0.92292 + 1.10816I
b = 0.796005 − 0.733148I
c = −1.125820 + 0.215546I
d = −1.17222 + 1.07817I
4.37135 + 1.33617I 7.28409 − 0.70175I
u = 1.173910 + 0.391555I
a = −0.92292 + 1.10816I
b = 0.796005 − 0.733148I
c = 0.540604 + 0.519928I
d = 0.550840 − 1.282330I
4.37135 + 1.33617I 7.28409 − 0.70175I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.173910 − 0.391555I
a = −0.92292 − 1.10816I
b = 0.796005 + 0.733148I
c = 0.585219 + 0.735474I
d = −0.911760 − 0.715540I
4.37135 − 1.33617I 7.28409 + 0.70175I
u = 1.173910 − 0.391555I
a = −0.92292 − 1.10816I
b = 0.796005 + 0.733148I
c = −1.125820 − 0.215546I
d = −1.17222 − 1.07817I
4.37135 − 1.33617I 7.28409 + 0.70175I
u = 1.173910 − 0.391555I
a = −0.92292 − 1.10816I
b = 0.796005 + 0.733148I
c = 0.540604 − 0.519928I
d = 0.550840 + 1.282330I
4.37135 − 1.33617I 7.28409 + 0.70175I
u = −0.141484 + 0.739668I
a = 0.688816 − 0.385922I
b = −0.628449 − 0.875112I
c = 0.588998 + 0.928874I
d = 1.44140 + 2.07815I
0.61694 + 2.45442I 2.32792 − 2.91298I
u = −0.141484 + 0.739668I
a = 0.688816 − 0.385922I
b = −0.628449 − 0.875112I
c = −0.370252 + 0.657000I
d = −1.10445 + 1.07485I
0.61694 + 2.45442I 2.32792 − 2.91298I
u = −0.141484 + 0.739668I
a = 0.688816 − 0.385922I
b = −0.628449 − 0.875112I
c = −0.21875 − 1.58587I
d = 0.162007 − 0.544526I
0.61694 + 2.45442I 2.32792 − 2.91298I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.141484 − 0.739668I
a = 0.688816 + 0.385922I
b = −0.628449 + 0.875112I
c = 0.588998 − 0.928874I
d = 1.44140 − 2.07815I
0.61694 − 2.45442I 2.32792 + 2.91298I
u = −0.141484 − 0.739668I
a = 0.688816 + 0.385922I
b = −0.628449 + 0.875112I
c = −0.370252 − 0.657000I
d = −1.10445 − 1.07485I
0.61694 − 2.45442I 2.32792 + 2.91298I
u = −0.141484 − 0.739668I
a = 0.688816 + 0.385922I
b = −0.628449 + 0.875112I
c = −0.21875 + 1.58587I
d = 0.162007 + 0.544526I
0.61694 − 2.45442I 2.32792 + 2.91298I
u = −1.172470 + 0.500383I
a = −2.10992 − 0.19571I
b = 0.728966 − 0.986295I
c = −0.561253 − 0.771469I
d = 1.079830 + 0.592867I
3.59813 − 7.08493I 5.57680 + 5.91335I
u = −1.172470 + 0.500383I
a = −2.10992 − 0.19571I
b = 0.728966 − 0.986295I
c = 1.088090 + 0.258687I
d = 1.15257 + 1.34568I
3.59813 − 7.08493I 5.57680 + 5.91335I
u = −1.172470 + 0.500383I
a = −2.10992 − 0.19571I
b = 0.728966 − 0.986295I
c = −0.526836 + 0.512782I
d = −0.78942 − 1.32272I
3.59813 − 7.08493I 5.57680 + 5.91335I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.172470 − 0.500383I
a = −2.10992 + 0.19571I
b = 0.728966 + 0.986295I
c = −0.561253 + 0.771469I
d = 1.079830 − 0.592867I
3.59813 + 7.08493I 5.57680 − 5.91335I
u = −1.172470 − 0.500383I
a = −2.10992 + 0.19571I
b = 0.728966 + 0.986295I
c = 1.088090 − 0.258687I
d = 1.15257 − 1.34568I
3.59813 + 7.08493I 5.57680 − 5.91335I
u = −1.172470 − 0.500383I
a = −2.10992 + 0.19571I
b = 0.728966 + 0.986295I
c = −0.526836 − 0.512782I
d = −0.78942 + 1.32272I
3.59813 + 7.08493I 5.57680 − 5.91335I
24
III. I
v
1
= ha, d − v + 1, av + c − v, b + v, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
0
−v
a
10
=
v
0
a
2
=
1
v − 1
a
6
=
−v
−v + 1
a
1
=
v
v − 1
a
11
=
v
v − 1
a
8
=
0
−v + 1
a
7
=
−v
−v + 1
a
12
=
v
v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v + 11
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
, c
6
, c
9
c
11
, c
12
u
2
c
7
, c
8
(u + 1)
2
c
10
(u − 1)
2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
y
2
+ y + 1
c
3
, c
6
, c
9
c
11
, c
12
y
2
c
7
, c
8
, c
10
(y − 1)
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −0.500000 − 0.866025I
c = 0.500000 + 0.866025I
d = −0.500000 + 0.866025I
1.64493 + 2.02988I 9.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 + 0.866025I
c = 0.500000 − 0.866025I
d = −0.500000 − 0.866025I
1.64493 − 2.02988I 9.00000 + 3.46410I
28
IV. I
v
2
= ha, d, c − v, b − v, v
2
+ v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
0
v
a
10
=
v
0
a
2
=
1
−v − 1
a
6
=
v
v + 1
a
1
=
−v
−v − 1
a
11
=
v
0
a
8
=
v
0
a
7
=
v
0
a
12
=
0
−v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 1
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
, c
7
, c
8
c
9
, c
10
u
2
c
6
, c
11
(u − 1)
2
c
12
(u + 1)
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
y
2
+ y + 1
c
3
, c
7
, c
8
c
9
, c
10
y
2
c
6
, c
11
, c
12
(y − 1)
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = −0.500000 + 0.866025I
c = −0.500000 + 0.866025I
d = 0
−1.64493 − 2.02988I −3.00000 + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −0.500000 − 0.866025I
c = −0.500000 − 0.866025I
d = 0
−1.64493 + 2.02988I −3.00000 − 3.46410I
32
V. I
v
3
= hc, d + 1, b, a − 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
1
0
a
4
=
1
0
a
5
=
1
0
a
10
=
1
0
a
2
=
1
0
a
6
=
1
0
a
1
=
1
0
a
11
=
0
−1
a
8
=
1
1
a
7
=
0
1
a
12
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
u
c
6
, c
7
, c
8
u + 1
c
10
, c
11
, c
12
u − 1
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
y
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y − 1
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 1.00000
b = 0
c = 0
d = −1.00000
0 0
36
VI. I
v
4
= ha, da − cb − d − b − 1, dv + 1, cv − ba − bv + b − a + 1, b
2
+ b + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
0
b
a
10
=
v
0
a
2
=
1
−b − 1
a
6
=
b
b + 1
a
1
=
−b
−b − 1
a
11
=
c
−cb − b − 1
a
8
=
−c + v
cb + b + 1
a
7
=
−c
cb + b + 1
a
12
=
c − b
−cb − 2b − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = c
2
b + c
2
− v
2
+ 2c + 3b + 4
(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.
37
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
2.02988I 0.00174 + 3.27049I
38
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u(u
2
− u + 1)
2
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
3
· (u
71
+ 24u
70
+ ··· − 40u − 16)
c
2
u(u
2
+ u + 1)
2
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
3
· (u
71
+ 2u
70
+ ··· − 5u
2
− 4)
c
3
, c
9
u
5
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
3
· (u
71
− 2u
70
+ ··· + 1536u
2
− 512)
c
5
u(u
2
− u + 1)
2
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
3
· (u
71
+ 2u
70
+ ··· − 5u
2
− 4)
c
6
u
2
(u − 1)
2
(u + 1)(u
27
− 9u
25
+ ··· − u + 1)(u
71
− 8u
70
+ ··· + 56u − 16)
c
7
, c
8
u
2
(u + 1)
3
(u
27
− 9u
25
+ ··· − u + 1)(u
71
+ 8u
70
+ ··· + 56u − 16)
c
10
u
2
(u − 1)
3
(u
27
− 9u
25
+ ··· − u + 1)(u
71
+ 8u
70
+ ··· + 56u − 16)
c
11
u
2
(u − 1)
3
(u
27
+ 18u
26
+ ··· + 5u + 1)
· (u
71
+ 30u
70
+ ··· + 4640u + 256)
c
12
u
2
(u − 1)(u + 1)
2
(u
27
− 9u
25
+ ··· − u + 1)(u
71
− 8u
70
+ ··· + 56u − 16)
39
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y(y
2
+ y + 1)
2
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
3
· (y
71
+ 48y
70
+ ··· − 6880y − 256)
c
2
, c
5
y(y
2
+ y + 1)
2
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
3
· (y
71
+ 24y
70
+ ··· − 40y − 16)
c
3
, c
9
y
5
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
3
· (y
71
− 30y
70
+ ··· + 1572864y − 262144)
c
6
, c
12
y
2
(y − 1)
3
(y
27
− 18y
26
+ ··· + 5y − 1)
· (y
71
− 30y
70
+ ··· + 4640y − 256)
c
7
, c
8
, c
10
y
2
(y − 1)
3
(y
27
− 18y
26
+ ··· + 5y − 1)
· (y
71
− 70y
70
+ ··· − 1504y − 256)
c
11
y
2
(y − 1)
3
(y
27
− 18y
26
+ ··· − 15y − 1)
· (y
71
+ 30y
70
+ ··· + 5022208y − 65536)
40
