12n
0222
(K12n
0222
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 11 12 10 3 7 9 1 6
Solving Sequence
3,9 4,5,11
6 2 1 8 10 7 12
c
3
c
5
c
2
c
1
c
8
c
10
c
7
c
12
c
4
, c
6
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.12031 × 10
34
u
30
− 2.31311 × 10
35
u
29
+ ··· + 1.08242 × 10
37
d − 4.05250 × 10
35
,
− 3.25140 × 10
35
u
30
− 1.04293 × 10
36
u
29
+ ··· + 2.16483 × 10
37
c − 2.49953 × 10
37
,
− 6.96435 × 10
33
u
30
+ 1.25405 × 10
34
u
29
+ ··· + 1.08242 × 10
37
b − 4.63583 × 10
36
,
9.28423 × 10
34
u
30
+ 2.43126 × 10
35
u
29
+ ··· + 2.16483 × 10
37
a − 1.72516 × 10
37
, u
31
+ 3u
30
+ ··· + 64u + 32i
I
u
2
= h114533971308u
22
a − 295693377683u
22
+ ··· + 309089289992a − 1727678279402,
− 106328835549u
22
a − 37415285413u
22
+ ··· − 881316945982a − 268636021714,
− 38636161249u
22
a + 6684998365u
22
+ ··· + 212657671098a − 31359529106,
709294494705u
22
a − 467986206381u
22
+ ··· + 1120177291630a + 112735730394,
u
23
− u
22
+ ··· + 8u + 4i
I
v
1
= ha, d, c − v, b − 1, v
2
− v + 1i
I
v
2
= hc, d + v − 1, b, a − 1, v
2
− v + 1i
I
v
3
= ha, d + 1, c + a, b − 1, v + 1i
I
v
4
= ha, a
2
d + c
2
v − 2ca − cv + a + v, dv − 1, c
2
v
2
− 2cav − v
2
c + a
2
+ av + v
2
, b − 1i
* 5 irreducible components of dim
C
= 0, with total 82 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
= h−4.12 × 10
34
u
30
− 2.31 × 10
35
u
29
+ · · · + 1.08 × 10
37
d − 4.05 ×
10
35
, −3.25×10
35
u
30
−1.04×10
36
u
29
+· · ·+2.16×10
37
c−2.50×10
37
, −6.96×
10
33
u
30
+ 1.25 × 10
34
u
29
+ · · · + 1.08 × 10
37
b − 4.64 × 10
36
, 9.28 × 10
34
u
30
+
2.43 × 10
35
u
29
+ · · · + 2.16 × 10
37
a − 1.73 × 10
37
, u
31
+ 3u
30
+ · · · + 64u + 32i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
−0.00428866u
30
− 0.0112307u
29
+ ··· − 0.0728208u + 0.796905
0.000643408u
30
− 0.00115856u
29
+ ··· − 0.160798u + 0.428286
a
11
=
0.0150192u
30
+ 0.0481763u
29
+ ··· + 0.421287u + 1.15461
0.00380659u
30
+ 0.0213699u
29
+ ··· + 0.391169u + 0.0374394
a
6
=
0.0281261u
30
+ 0.0745920u
29
+ ··· − 0.311221u + 1.89333
−0.000510466u
30
− 0.00677158u
29
+ ··· − 0.959619u + 0.547953
a
2
=
−0.00428866u
30
− 0.0112307u
29
+ ··· − 0.0728208u + 0.796905
0.00311868u
30
+ 0.0115274u
29
+ ··· + 0.193379u − 0.480614
a
1
=
−0.00116998u
30
+ 0.000296647u
29
+ ··· + 0.120558u + 0.316290
0.00311868u
30
+ 0.0115274u
29
+ ··· + 0.193379u − 0.480614
a
8
=
u
u
a
10
=
0.0150192u
30
+ 0.0481763u
29
+ ··· + 0.421287u + 1.15461
0.00163526u
30
+ 0.00866787u
29
+ ··· + 1.07138u + 0.137237
a
7
=
−0.0133839u
30
− 0.0395084u
29
+ ··· + 0.650092u − 1.01737
0.00163526u
30
+ 0.00866787u
29
+ ··· + 1.07138u + 0.137237
a
12
=
0.0125773u
30
+ 0.0545128u
29
+ ··· + 1.19403u + 1.13915
−0.00454622u
30
+ 0.00263169u
29
+ ··· − 0.487370u − 0.916371
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0330834u
30
− 0.0743041u
29
+ ··· − 9.35750u − 13.8824
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
31
+ 11u
30
+ ··· + 21u + 1
c
2
, c
4
, c
7
c
9
u
31
− 5u
30
+ ··· − 3u + 1
c
3
, c
8
u
31
+ 3u
30
+ ··· + 64u + 32
c
5
u
31
+ u
30
+ ··· + 128u + 548
c
6
, c
12
u
31
− u
30
+ ··· + 8u + 4
c
11
u
31
− 15u
30
+ ··· + 120u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
31
+ 29y
30
+ ··· + 61y − 1
c
2
, c
4
, c
7
c
9
y
31
− 11y
30
+ ··· + 21y − 1
c
3
, c
8
y
31
+ 15y
30
+ ··· + 1024y − 1024
c
5
y
31
− 9y
30
+ ··· + 4451896y − 300304
c
6
, c
12
y
31
+ 15y
30
+ ··· + 120y − 16
c
11
y
31
+ 3y
30
+ ··· + 25888y − 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.753219 + 0.379837I
a = 0.685053 − 0.287784I
b = 0.240774 + 0.521238I
c = 0.092235 − 0.379751I
d = 0.881620 − 0.064438I
1.42006 − 1.96537I −1.93692 + 5.44006I
u = 0.753219 − 0.379837I
a = 0.685053 + 0.287784I
b = 0.240774 − 0.521238I
c = 0.092235 + 0.379751I
d = 0.881620 + 0.064438I
1.42006 + 1.96537I −1.93692 − 5.44006I
u = −0.337564 + 1.132290I
a = 0.17117 − 1.61585I
b = −0.935169 + 0.612003I
c = 1.049310 + 0.128753I
d = 0.644525 − 0.213262I
−0.45247 + 2.02679I −7.73031 − 3.42583I
u = −0.337564 − 1.132290I
a = 0.17117 + 1.61585I
b = −0.935169 − 0.612003I
c = 1.049310 − 0.128753I
d = 0.644525 + 0.213262I
−0.45247 − 2.02679I −7.73031 + 3.42583I
u = 1.121020 + 0.424146I
a = 0.460731 + 0.138106I
b = 0.991521 − 0.596969I
c = −0.139555 + 1.108810I
d = −0.74679 + 1.41149I
−1.55877 + 4.66712I −11.51750 − 4.56967I
u = 1.121020 − 0.424146I
a = 0.460731 − 0.138106I
b = 0.991521 + 0.596969I
c = −0.139555 − 1.108810I
d = −0.74679 − 1.41149I
−1.55877 − 4.66712I −11.51750 + 4.56967I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.698083 + 0.364692I
a = 0.498679 + 0.078631I
b = 0.956651 − 0.308522I
c = −0.575750 + 1.146380I
d = −0.468258 + 0.349784I
−3.68376 + 3.19069I −14.6846 − 5.1485I
u = 0.698083 − 0.364692I
a = 0.498679 − 0.078631I
b = 0.956651 + 0.308522I
c = −0.575750 − 1.146380I
d = −0.468258 − 0.349784I
−3.68376 − 3.19069I −14.6846 + 5.1485I
u = −1.235540 + 0.189024I
a = 0.472913 − 0.179552I
b = 0.848142 + 0.701686I
c = 0.035497 + 0.968785I
d = −0.04493 + 1.73894I
2.56816 − 1.34649I −5.38369 + 2.07194I
u = −1.235540 − 0.189024I
a = 0.472913 + 0.179552I
b = 0.848142 − 0.701686I
c = 0.035497 − 0.968785I
d = −0.04493 − 1.73894I
2.56816 + 1.34649I −5.38369 − 2.07194I
u = 0.464557 + 1.163760I
a = −0.05406 + 1.60814I
b = −1.020880 − 0.621136I
c = −1.134180 + 0.111276I
d = −0.725633 − 0.668879I
−1.15318 − 7.72517I −9.61403 + 8.29170I
u = 0.464557 − 1.163760I
a = −0.05406 − 1.60814I
b = −1.020880 + 0.621136I
c = −1.134180 − 0.111276I
d = −0.725633 + 0.668879I
−1.15318 + 7.72517I −9.61403 − 8.29170I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.253240 + 0.506936I
a = 0.439439 − 0.143874I
b = 1.055310 + 0.672917I
c = 0.059221 + 1.157240I
d = 1.07042 + 1.84800I
1.12377 − 9.51847I −8.01541 + 7.69926I
u = −1.253240 − 0.506936I
a = 0.439439 + 0.143874I
b = 1.055310 − 0.672917I
c = 0.059221 − 1.157240I
d = 1.07042 − 1.84800I
1.12377 + 9.51847I −8.01541 − 7.69926I
u = 0.223678 + 1.371700I
a = 0.413752 − 0.939419I
b = −0.607334 + 0.891545I
c = 0.818360 − 0.177114I
d = −0.009021 + 1.183990I
4.93468 + 0.57606I −5.79676 − 1.97891I
u = 0.223678 − 1.371700I
a = 0.413752 + 0.939419I
b = −0.607334 − 0.891545I
c = 0.818360 + 0.177114I
d = −0.009021 − 1.183990I
4.93468 − 0.57606I −5.79676 + 1.97891I
u = −0.591801
a = 0.699591
b = 0.429406
c = 0.311574
d = −0.304897
−0.834149 −11.9720
u = −0.540907 + 0.236782I
a = 0.518602 − 0.047373I
b = 0.912302 + 0.174686I
c = 1.02746 + 1.03902I
d = 0.239860 + 0.130978I
−3.12062 + 1.49349I −14.4230 − 1.8126I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.540907 − 0.236782I
a = 0.518602 + 0.047373I
b = 0.912302 − 0.174686I
c = 1.02746 − 1.03902I
d = 0.239860 − 0.130978I
−3.12062 − 1.49349I −14.4230 + 1.8126I
u = 0.067118 + 0.557682I
a = 1.45537 − 0.23813I
b = −0.330807 + 0.109496I
c = 0.107319 + 0.187646I
d = 0.183545 + 0.746172I
−0.46111 + 2.29513I −1.47827 − 3.85950I
u = 0.067118 − 0.557682I
a = 1.45537 + 0.23813I
b = −0.330807 − 0.109496I
c = 0.107319 − 0.187646I
d = 0.183545 − 0.746172I
−0.46111 − 2.29513I −1.47827 + 3.85950I
u = 0.71578 + 1.28059I
a = −0.37486 + 1.39000I
b = −1.180860 − 0.670647I
c = −1.256580 + 0.035321I
d = −0.69622 − 1.82856I
1.16605 − 11.32090I −10.43454 + 6.71502I
u = 0.71578 − 1.28059I
a = −0.37486 − 1.39000I
b = −1.180860 + 0.670647I
c = −1.256580 − 0.035321I
d = −0.69622 + 1.82856I
1.16605 + 11.32090I −10.43454 − 6.71502I
u = −0.39077 + 1.46203I
a = 0.382686 + 0.821951I
b = −0.534475 − 0.999877I
c = −0.804151 − 0.273493I
d = −0.06766 + 1.69998I
8.24554 + 4.31764I −2.71892 − 1.88458I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.39077 − 1.46203I
a = 0.382686 − 0.821951I
b = −0.534475 + 0.999877I
c = −0.804151 + 0.273493I
d = −0.06766 − 1.69998I
8.24554 − 4.31764I −2.71892 + 1.88458I
u = −0.79393 + 1.30401I
a = −0.444220 − 1.327190I
b = −1.226790 + 0.677567I
c = 1.286380 + 0.018874I
d = 0.74586 − 2.20933I
3.7041 + 16.8176I −8.02968 − 10.05725I
u = −0.79393 − 1.30401I
a = −0.444220 + 1.327190I
b = −1.226790 − 0.677567I
c = 1.286380 − 0.018874I
d = 0.74586 + 2.20933I
3.7041 − 16.8176I −8.02968 + 10.05725I
u = −0.62073 + 1.40356I
a = −0.237422 − 1.289560I
b = −1.138090 + 0.750034I
c = 1.210460 − 0.013304I
d = 0.01599 − 1.62087I
6.51517 + 8.00123I −4.81025 − 4.92455I
u = −0.62073 − 1.40356I
a = −0.237422 + 1.289560I
b = −1.138090 − 0.750034I
c = 1.210460 + 0.013304I
d = 0.01599 + 1.62087I
6.51517 − 8.00123I −4.81025 + 4.92455I
u = −0.07489 + 1.53753I
a = 0.262372 + 0.979829I
b = −0.744999 − 0.952303I
c = −0.931800 − 0.183463I
d = 0.629132 + 0.977280I
9.13328 − 4.81435I −2.44035 + 4.85668I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07489 − 1.53753I
a = 0.262372 − 0.979829I
b = −0.744999 + 0.952303I
c = −0.931800 + 0.183463I
d = 0.629132 − 0.977280I
9.13328 + 4.81435I −2.44035 − 4.85668I
10
II.
I
u
2
= h1.15×10
11
au
22
−2.96×10
11
u
22
+· · ·+3.09×10
11
a−1.73×10
12
, −1.06×
10
11
au
22
− 3.74 × 10
10
u
22
+ · · · − 8.81 × 10
11
a − 2.69 × 10
11
, −3.86 ×
10
10
au
22
+ 6.68 × 10
9
u
22
+ · · · + 2.13 × 10
11
a − 3.14 × 10
10
, 7.09 × 10
11
au
22
−
4.68 × 10
11
u
22
+ · · · + 1.12 × 10
12
a + 1.13 × 10
11
, u
23
− u
22
+ · · · + 8u + 4i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
a
0.134392au
22
− 0.0232531u
22
+ ··· − 0.739709a + 0.109081
a
11
=
0.184927au
22
+ 0.0650727u
22
+ ··· + 1.53279a + 0.467212
−0.199198au
22
+ 0.514270u
22
+ ··· − 0.537569a + 3.00478
a
6
=
0.0536818au
22
− 0.109233u
22
+ ··· + 1.15888a − 1.35137
0.147105au
22
− 0.215441u
22
+ ··· − 2.41722a − 0.588197
a
2
=
a
−0.134392au
22
+ 0.0232531u
22
+ ··· + 0.739709a − 0.109081
a
1
=
−0.134392au
22
+ 0.0232531u
22
+ ··· + 1.73971a − 0.109081
−0.134392au
22
+ 0.0232531u
22
+ ··· + 0.739709a − 0.109081
a
8
=
u
u
a
10
=
0.184927au
22
+ 0.0650727u
22
+ ··· + 1.53279a + 0.467212
0.315073u
22
− 0.449465u
21
+ ··· + 3.96032u + 2.46721
a
7
=
−0.184927au
22
+ 0.250000u
22
+ ··· − 1.53279a + 2
0.315073u
22
− 0.449465u
21
+ ··· + 3.96032u + 2.46721
a
12
=
−0.0514525au
22
+ 0.220414u
22
+ ··· + 1.82586a + 0.884563
−0.655758au
22
+ 0.669612u
22
+ ··· − 0.373694a + 3.42213
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
173371509589
143744120962
u
22
+
241902270957
143744120962
u
21
+ ··· +
379864412243
143744120962
u −
545150434432
71872060481
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
46
+ 23u
45
+ ··· + 288u + 256
c
2
, c
4
, c
7
c
9
u
46
− 3u
45
+ ··· − 56u + 16
c
3
, c
8
(u
23
− u
22
+ ··· + 8u + 4)
2
c
5
(u
23
+ 2u
22
+ ··· + 18u + 9)
2
c
6
, c
12
(u
23
− 2u
22
+ ··· − 2u + 1)
2
c
11
(u
23
− 12u
22
+ ··· − 2u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
46
− 3y
45
+ ··· − 2449920y + 65536
c
2
, c
4
, c
7
c
9
y
46
− 23y
45
+ ··· − 288y + 256
c
3
, c
8
(y
23
+ 15y
22
+ ··· − 40y − 16)
2
c
5
(y
23
− 12y
22
+ ··· − 450y − 81)
2
c
6
, c
12
(y
23
+ 12y
22
+ ··· − 2y − 1)
2
c
11
(y
23
+ 24y
21
+ ··· + 10y − 1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.969482
a = 0.546696 + 0.177229I
b = 0.655217 − 0.536590I
c = 0.145831 + 0.725301I
d = −0.392946 + 0.853527I
−0.502753 −9.67610
u = −0.969482
a = 0.546696 − 0.177229I
b = 0.655217 + 0.536590I
c = 0.145831 − 0.725301I
d = −0.392946 − 0.853527I
−0.502753 −9.67610
u = 0.308169 + 0.985429I
a = 0.430219 + 0.027076I
b = 1.315230 − 0.145711I
c = −1.015110 + 0.244961I
d = −1.008850 + 0.100976I
−2.62555 − 2.00215I −10.76412 + 3.62705I
u = 0.308169 + 0.985429I
a = 0.35592 + 1.88659I
b = −0.903437 − 0.511840I
c = −0.13961 + 1.69019I
d = −0.798336 − 1.133280I
−2.62555 − 2.00215I −10.76412 + 3.62705I
u = 0.308169 − 0.985429I
a = 0.430219 − 0.027076I
b = 1.315230 + 0.145711I
c = −1.015110 − 0.244961I
d = −1.008850 − 0.100976I
−2.62555 + 2.00215I −10.76412 − 3.62705I
u = 0.308169 − 0.985429I
a = 0.35592 − 1.88659I
b = −0.903437 + 0.511840I
c = −0.13961 − 1.69019I
d = −0.798336 + 1.133280I
−2.62555 + 2.00215I −10.76412 − 3.62705I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.107498 + 1.054050I
a = 0.716893 + 1.112390I
b = −0.590662 − 0.635162I
c = 0.855712 + 0.135596I
d = 0.567042 + 0.449517I
0.12065 + 2.74438I −5.99863 − 3.42075I
u = −0.107498 + 1.054050I
a = 0.60269 − 1.46286I
b = −0.759232 + 0.584397I
c = −0.709753 + 0.020633I
d = −0.464556 + 0.774218I
0.12065 + 2.74438I −5.99863 − 3.42075I
u = −0.107498 − 1.054050I
a = 0.716893 − 1.112390I
b = −0.590662 + 0.635162I
c = 0.855712 − 0.135596I
d = 0.567042 − 0.449517I
0.12065 − 2.74438I −5.99863 + 3.42075I
u = −0.107498 − 1.054050I
a = 0.60269 + 1.46286I
b = −0.759232 − 0.584397I
c = −0.709753 − 0.020633I
d = −0.464556 − 0.774218I
0.12065 − 2.74438I −5.99863 + 3.42075I
u = −0.000983 + 1.149400I
a = 0.547631 − 1.231120I
b = −0.698366 + 0.678096I
c = 0.00032 + 1.69379I
d = 0.00309 − 1.75784I
0.86138 − 1.33135I −4.84050 + 0.67575I
u = −0.000983 + 1.149400I
a = 0.417486 − 0.000081I
b = 1.395290 + 0.000467I
c = 0.824032 + 0.023570I
d = 0.325917 + 0.597656I
0.86138 − 1.33135I −4.84050 + 0.67575I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.000983 − 1.149400I
a = 0.547631 + 1.231120I
b = −0.698366 − 0.678096I
c = 0.00032 − 1.69379I
d = 0.00309 + 1.75784I
0.86138 + 1.33135I −4.84050 − 0.67575I
u = −0.000983 − 1.149400I
a = 0.417486 + 0.000081I
b = 1.395290 − 0.000467I
c = 0.824032 − 0.023570I
d = 0.325917 − 0.597656I
0.86138 + 1.33135I −4.84050 − 0.67575I
u = 1.222080 + 0.199525I
a = 0.508002 − 0.253270I
b = 0.576609 + 0.786036I
c = −0.046249 + 0.972025I
d = 0.00251 + 1.70085I
2.55344 + 3.99588I −5.39099 − 3.49800I
u = 1.222080 + 0.199525I
a = 0.473795 + 0.176635I
b = 0.853067 − 0.690841I
c = 0.109495 − 0.759619I
d = 1.20097 − 1.25900I
2.55344 + 3.99588I −5.39099 − 3.49800I
u = 1.222080 − 0.199525I
a = 0.508002 + 0.253270I
b = 0.576609 − 0.786036I
c = −0.046249 − 0.972025I
d = 0.00251 − 1.70085I
2.55344 − 3.99588I −5.39099 + 3.49800I
u = 1.222080 − 0.199525I
a = 0.473795 − 0.176635I
b = 0.853067 + 0.690841I
c = 0.109495 + 0.759619I
d = 1.20097 + 1.25900I
2.55344 − 3.99588I −5.39099 + 3.49800I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.383777 + 1.192290I
a = 0.06728 − 1.54278I
b = −0.971785 + 0.646950I
c = 0.08568 + 1.62327I
d = 1.25576 − 1.64401I
0.03073 + 6.47771I −7.22220 − 6.52194I
u = −0.383777 + 1.192290I
a = 0.411691 − 0.031373I
b = 1.41498 + 0.18404I
c = 1.084230 + 0.092026I
d = 0.516239 − 0.437185I
0.03073 + 6.47771I −7.22220 − 6.52194I
u = −0.383777 − 1.192290I
a = 0.06728 + 1.54278I
b = −0.971785 − 0.646950I
c = 0.08568 − 1.62327I
d = 1.25576 + 1.64401I
0.03073 − 6.47771I −7.22220 + 6.52194I
u = −0.383777 − 1.192290I
a = 0.411691 + 0.031373I
b = 1.41498 − 0.18404I
c = 1.084230 − 0.092026I
d = 0.516239 + 0.437185I
0.03073 − 6.47771I −7.22220 + 6.52194I
u = 0.494865 + 0.507562I
a = 0.478200 + 0.048575I
b = 1.069820 − 0.210247I
c = −1.52565 + 0.64156I
d = −3.09128 + 0.72732I
−4.00909 − 1.37448I −14.7018 + 4.3512I
u = 0.494865 + 0.507562I
a = −1.22900 + 4.29549I
b = −1.061570 − 0.215187I
c = −0.62919 + 1.55437I
d = −0.560840 − 0.069102I
−4.00909 − 1.37448I −14.7018 + 4.3512I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.494865 − 0.507562I
a = 0.478200 − 0.048575I
b = 1.069820 + 0.210247I
c = −1.52565 − 0.64156I
d = −3.09128 − 0.72732I
−4.00909 + 1.37448I −14.7018 − 4.3512I
u = 0.494865 − 0.507562I
a = −1.22900 − 4.29549I
b = −1.061570 + 0.215187I
c = −0.62919 − 1.55437I
d = −0.560840 + 0.069102I
−4.00909 + 1.37448I −14.7018 − 4.3512I
u = −0.441227 + 0.551458I
a = 0.894756 + 0.404298I
b = −0.071873 − 0.419376I
c = 0.57801 + 1.66032I
d = 0.559533 − 0.183511I
−1.18777 − 0.88878I −5.60709 − 0.92577I
u = −0.441227 + 0.551458I
a = 0.472778 − 0.042452I
b = 1.098240 + 0.188408I
c = −0.217661 − 0.135410I
d = −0.659821 + 0.435772I
−1.18777 − 0.88878I −5.60709 − 0.92577I
u = −0.441227 − 0.551458I
a = 0.894756 − 0.404298I
b = −0.071873 + 0.419376I
c = 0.57801 − 1.66032I
d = 0.559533 + 0.183511I
−1.18777 + 0.88878I −5.60709 + 0.92577I
u = −0.441227 − 0.551458I
a = 0.472778 + 0.042452I
b = 1.098240 − 0.188408I
c = −0.217661 + 0.135410I
d = −0.659821 − 0.435772I
−1.18777 + 0.88878I −5.60709 + 0.92577I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.598699 + 0.195967I
a = 0.530888 − 0.055930I
b = 0.862960 + 0.196265I
c = 2.04319 + 0.35996I
d = 4.54195 + 0.43654I
−3.01275 − 2.59653I −13.46303 + 3.78636I
u = −0.598699 + 0.195967I
a = −5.34285 − 3.08636I
b = −1.140340 + 0.081067I
c = 0.898106 + 0.859760I
d = 0.182289 + 0.201936I
−3.01275 − 2.59653I −13.46303 + 3.78636I
u = −0.598699 − 0.195967I
a = 0.530888 + 0.055930I
b = 0.862960 − 0.196265I
c = 2.04319 − 0.35996I
d = 4.54195 − 0.43654I
−3.01275 + 2.59653I −13.46303 − 3.78636I
u = −0.598699 − 0.195967I
a = −5.34285 + 3.08636I
b = −1.140340 − 0.081067I
c = 0.898106 − 0.859760I
d = 0.182289 − 0.201936I
−3.01275 + 2.59653I −13.46303 − 3.78636I
u = −0.51611 + 1.32552I
a = 0.461233 + 0.756174I
b = −0.412094 − 0.963850I
c = 1.162240 + 0.022087I
d = 0.201349 − 1.083730I
3.51902 + 5.35900I −7.50458 − 3.06793I
u = −0.51611 + 1.32552I
a = −0.132196 − 1.384640I
b = −1.068330 + 0.715684I
c = −0.714060 − 0.294716I
d = −0.57921 + 1.63741I
3.51902 + 5.35900I −7.50458 − 3.06793I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.51611 − 1.32552I
a = 0.461233 − 0.756174I
b = −0.412094 + 0.963850I
c = 1.162240 − 0.022087I
d = 0.201349 + 1.083730I
3.51902 − 5.35900I −7.50458 + 3.06793I
u = −0.51611 − 1.32552I
a = −0.132196 + 1.384640I
b = −1.068330 − 0.715684I
c = −0.714060 + 0.294716I
d = −0.57921 − 1.63741I
3.51902 − 5.35900I −7.50458 + 3.06793I
u = 0.63403 + 1.38420I
a = 0.425486 − 0.700704I
b = −0.366859 + 1.042680I
c = −1.216340 − 0.005176I
d = −0.11894 − 1.65112I
6.36348 − 10.62070I −4.97373 + 6.45650I
u = 0.63403 + 1.38420I
a = −0.254465 + 1.306340I
b = −1.143660 − 0.737515I
c = 0.717396 − 0.359583I
d = 0.78471 + 1.94831I
6.36348 − 10.62070I −4.97373 + 6.45650I
u = 0.63403 − 1.38420I
a = 0.425486 + 0.700704I
b = −0.366859 − 1.042680I
c = −1.216340 + 0.005176I
d = −0.11894 + 1.65112I
6.36348 + 10.62070I −4.97373 − 6.45650I
u = 0.63403 − 1.38420I
a = −0.254465 − 1.306340I
b = −1.143660 + 0.737515I
c = 0.717396 + 0.359583I
d = 0.78471 − 1.94831I
6.36348 + 10.62070I −4.97373 − 6.45650I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.37388 + 1.47842I
a = 0.371907 − 0.829286I
b = −0.549766 + 1.003940I
c = −1.105830 − 0.059862I
d = 0.536481 − 0.654741I
8.32991 − 1.64388I −2.69530 + 0.40272I
u = 0.37388 + 1.47842I
a = −0.005040 + 1.210940I
b = −1.003440 − 0.825793I
c = 0.815223 − 0.271139I
d = −0.00306 + 1.69575I
8.32991 − 1.64388I −2.69530 + 0.40272I
u = 0.37388 − 1.47842I
a = 0.371907 + 0.829286I
b = −0.549766 − 1.003940I
c = −1.105830 + 0.059862I
d = 0.536481 + 0.654741I
8.32991 + 1.64388I −2.69530 − 0.40272I
u = 0.37388 − 1.47842I
a = −0.005040 − 1.210940I
b = −1.003440 + 0.825793I
c = 0.815223 + 0.271139I
d = −0.00306 − 1.69575I
8.32991 + 1.64388I −2.69530 − 0.40272I
21
III. I
v
1
= ha, d, c − v, b − 1, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
0
1
a
11
=
v
0
a
6
=
v − 1
1
a
2
=
1
−1
a
1
=
0
−1
a
8
=
v
0
a
10
=
v
0
a
7
=
v
0
a
12
=
v
−v
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 7
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
7
, c
8
c
9
, c
10
u
2
c
4
(u + 1)
2
c
5
, c
11
, c
12
u
2
+ u + 1
c
6
u
2
− u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
7
, c
8
c
9
, c
10
y
2
c
5
, c
6
, c
11
c
12
y
2
+ y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = 1.00000
c = 0.500000 + 0.866025I
d = 0
−1.64493 + 2.02988I −9.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 1.00000
c = 0.500000 − 0.866025I
d = 0
−1.64493 − 2.02988I −9.00000 + 3.46410I
25
IV. I
v
2
= hc, d + v − 1, b, a − 1, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
1
0
a
11
=
0
−v + 1
a
6
=
1
v
a
2
=
1
0
a
1
=
1
0
a
8
=
v
0
a
10
=
v
−v + 1
a
7
=
0
v − 1
a
12
=
−v + 1
−v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 11
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
u
2
c
5
, c
12
u
2
− u + 1
c
6
, c
11
u
2
+ u + 1
c
7
(u − 1)
2
c
9
, c
10
(u + 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
y
2
c
5
, c
6
, c
11
c
12
y
2
+ y + 1
c
7
, c
9
, c
10
(y − 1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 1.00000
b = 0
c = 0
d = 0.500000 − 0.866025I
−1.64493 − 2.02988I −9.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 1.00000
b = 0
c = 0
d = 0.500000 + 0.866025I
−1.64493 + 2.02988I −9.00000 − 3.46410I
29
V. I
v
3
= ha, d + 1, c + a, b − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
−1
0
a
4
=
1
0
a
5
=
0
1
a
11
=
0
−1
a
6
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
8
=
−1
0
a
10
=
−1
−1
a
7
=
0
1
a
12
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u − 1
c
3
, c
5
, c
6
c
8
, c
11
, c
12
u
c
4
, c
9
, c
10
u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
9
, c
10
y − 1
c
3
, c
5
, c
6
c
8
, c
11
, c
12
y
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
c = 0
d = −1.00000
−3.28987 −12.0000
33
VI.
I
v
4
= ha, c
2
v − cv + · · · − 2ca + a, dv − 1, c
2
v
2
− v
2
c + · · · + a
2
+ av, b − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
0
1
a
11
=
c
d
a
6
=
c − 1
dc + 1
a
2
=
1
−1
a
1
=
0
−1
a
8
=
v
0
a
10
=
c + v
d
a
7
=
−c
−d
a
12
=
c
d − c
(ii) Obstruction class = −1
(iii) Cusp Shapes = d
2
+ v
2
− 4c − 12
(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.
34
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
−3.28987 − 2.02988I −12.31314 − 3.47908I
35
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 1)
3
(u
31
+ 11u
30
+ ··· + 21u + 1)
· (u
46
+ 23u
45
+ ··· + 288u + 256)
c
2
, c
7
u
2
(u − 1)
3
(u
31
− 5u
30
+ ··· − 3u + 1)(u
46
− 3u
45
+ ··· − 56u + 16)
c
3
, c
8
u
5
(u
23
− u
22
+ ··· + 8u + 4)
2
(u
31
+ 3u
30
+ ··· + 64u + 32)
c
4
, c
9
u
2
(u + 1)
3
(u
31
− 5u
30
+ ··· − 3u + 1)(u
46
− 3u
45
+ ··· − 56u + 16)
c
5
u(u
2
− u + 1)(u
2
+ u + 1)(u
23
+ 2u
22
+ ··· + 18u + 9)
2
· (u
31
+ u
30
+ ··· + 128u + 548)
c
6
, c
12
u(u
2
− u + 1)(u
2
+ u + 1)(u
23
− 2u
22
+ ··· − 2u + 1)
2
· (u
31
− u
30
+ ··· + 8u + 4)
c
10
u
2
(u + 1)
3
(u
31
+ 11u
30
+ ··· + 21u + 1)
· (u
46
+ 23u
45
+ ··· + 288u + 256)
c
11
u(u
2
+ u + 1)
2
(u
23
− 12u
22
+ ··· − 2u + 1)
2
· (u
31
− 15u
30
+ ··· + 120u + 16)
36
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
2
(y − 1)
3
(y
31
+ 29y
30
+ ··· + 61y − 1)
· (y
46
− 3y
45
+ ··· − 2449920y + 65536)
c
2
, c
4
, c
7
c
9
y
2
(y − 1)
3
(y
31
− 11y
30
+ ··· + 21y − 1)
· (y
46
− 23y
45
+ ··· − 288y + 256)
c
3
, c
8
y
5
(y
23
+ 15y
22
+ ··· − 40y − 16)
2
· (y
31
+ 15y
30
+ ··· + 1024y − 1024)
c
5
y(y
2
+ y + 1)
2
(y
23
− 12y
22
+ ··· − 450y − 81)
2
· (y
31
− 9y
30
+ ··· + 4451896y − 300304)
c
6
, c
12
y(y
2
+ y + 1)
2
(y
23
+ 12y
22
+ ··· − 2y − 1)
2
· (y
31
+ 15y
30
+ ··· + 120y − 16)
c
11
y(y
2
+ y + 1)
2
(y
23
+ 24y
21
+ ··· + 10y − 1)
2
· (y
31
+ 3y
30
+ ··· + 25888y − 256)
37
