12n
0682
(K12n
0682
)
A knot diagram
1
Linearized knot diagam
4 5 7 2 11 3 10 11 1 8 5 9
Solving Sequence
1,4
2
5,9
10 12 11 6 8 7 3
c
1
c
4
c
9
c
12
c
11
c
5
c
8
c
7
c
3
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
12
+ 2u
11
− 4u
10
− 8u
9
+ 6u
8
+ 9u
7
− 6u
6
+ u
5
+ 5u
4
− 6u
3
− 2u
2
+ 2b + 3u,
3u
12
+ 9u
11
− 22u
9
− 16u
8
+ 5u
7
+ 5u
6
+ 11u
5
+ 20u
4
+ 9u
3
− 2u
2
+ 2a − 3u − 1,
u
13
+ 3u
12
− u
11
− 10u
10
− 4u
9
+ 9u
8
+ 3u
7
+ 8u
5
− 7u
3
− u
2
+ u − 1i
I
u
2
= h2.01428 × 10
42
u
43
+ 5.41774 × 10
42
u
42
+ ··· + 7.34448 × 10
41
b − 8.38901 × 10
41
,
8.61708 × 10
41
u
43
+ 1.60924 × 10
42
u
42
+ ··· + 7.34448 × 10
41
a − 4.49822 × 10
43
, u
44
+ 4u
43
+ ··· + 116u − 1i
I
u
3
= hb, −3u
2
+ a − 5u − 4, u
3
+ u
2
− 1i
I
u
4
= h−4a
2
+ 23b − 33a − 3, a
3
+ 8a
2
+ 3a + 7, u − 1i
I
u
5
= hb + u, a + u, u
2
+ u − 1i
I
u
6
= hb − u − 1, a + 2, u
2
+ u − 1i
* 6 irreducible components of dim
C
= 0, with total 67 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
12
+2u
11
+· · ·+ 2b+3u, 3u
12
+9u
11
+· · ·+ 2a−1, u
13
+3u
12
+· · ·+ u−1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
−
3
2
u
12
−
9
2
u
11
+ ··· +
3
2
u +
1
2
−
1
2
u
12
− u
11
+ ··· + u
2
−
3
2
u
a
10
=
−u
12
−
7
2
u
11
+ ··· + 3u +
1
2
−
1
2
u
12
− u
11
+ ··· + u
2
−
3
2
u
a
12
=
−
1
2
u
12
− 2u
11
+ ··· +
3
2
u + 1
u
3
− u
a
11
=
−u
11
− 2u
10
+ 2u
9
+ 6u
8
+ u
7
− 3u
6
− 2u
5
− 3u
4
− 3u
3
+ 2u + 1
1
2
u
12
+
1
2
u
11
+ ··· −
1
2
u −
1
2
a
6
=
1
2
u
12
− 3u
10
+ ··· +
3
2
u − 1
3
2
u
12
+
7
2
u
11
+ ··· +
7
2
u −
3
2
a
8
=
−
1
2
u
12
−
5
2
u
11
+ ··· +
1
2
u +
1
2
1
2
u
12
+
1
2
u
11
+ ··· −
1
2
u −
1
2
a
7
=
1
2
u
11
+ u
10
+ ··· − u +
3
2
−u
11
− u
10
+ 4u
9
+ 3u
8
− 6u
7
− u
6
+ 3u
5
− 4u
4
+ u
3
+ 3u
2
− u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −3u
12
−18u
11
−24u
10
+ 32u
9
+ 80u
8
+ 9u
7
−34u
6
+ 5u
5
−47u
4
−70u
3
+ 6u
2
+ 11u −18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
, c
10
u
13
− 3u
12
− u
11
+ 10u
10
− 4u
9
− 9u
8
+ 3u
7
+ 8u
5
− 7u
3
+ u
2
+ u + 1
c
3
, c
6
, c
9
c
12
u
13
+ u
12
+ ··· + 5u + 1
c
5
, c
11
u
13
+ 5u
12
+ ··· − 8u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
, c
10
y
13
− 11y
12
+ ··· − y −1
c
3
, c
6
, c
9
c
12
y
13
− 3y
12
+ ··· + 7y −1
c
5
, c
11
y
13
− 5y
12
+ ··· + 96y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.920255
a = −7.53293
b = −0.375392
−2.84609 −65.8580
u = 0.217488 + 0.883339I
a = 0.447419 − 0.357015I
b = 1.079610 + 0.670263I
2.14237 − 5.68500I −7.77978 + 6.07128I
u = 0.217488 − 0.883339I
a = 0.447419 + 0.357015I
b = 1.079610 − 0.670263I
2.14237 + 5.68500I −7.77978 − 6.07128I
u = −0.795282 + 0.405757I
a = −0.416083 + 0.498754I
b = −0.175698 + 0.846144I
1.52283 + 3.56370I −3.66796 − 8.41026I
u = −0.795282 − 0.405757I
a = −0.416083 − 0.498754I
b = −0.175698 − 0.846144I
1.52283 − 3.56370I −3.66796 + 8.41026I
u = 1.266340 + 0.164860I
a = −1.095680 + 0.368409I
b = −0.352007 + 0.886032I
−3.86762 − 1.80054I −11.65148 + 0.61379I
u = 1.266340 − 0.164860I
a = −1.095680 − 0.368409I
b = −0.352007 − 0.886032I
−3.86762 + 1.80054I −11.65148 − 0.61379I
u = −1.38670 + 0.37744I
a = 1.155750 + 0.361386I
b = 1.132190 − 0.771142I
−10.71940 + 7.71547I −15.7360 − 5.7316I
u = −1.38670 − 0.37744I
a = 1.155750 − 0.361386I
b = 1.132190 + 0.771142I
−10.71940 − 7.71547I −15.7360 + 5.7316I
u = 0.240304 + 0.377267I
a = 1.36715 + 1.11084I
b = −0.640664 − 0.285334I
−0.98403 − 1.11558I −8.69395 + 6.01211I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.240304 − 0.377267I
a = 1.36715 − 1.11084I
b = −0.640664 + 0.285334I
−0.98403 + 1.11558I −8.69395 − 6.01211I
u = −1.50228 + 0.43298I
a = −1.69209 − 0.37137I
b = −1.35574 + 0.89152I
−8.8777 + 15.5620I −14.5417 − 7.8795I
u = −1.50228 − 0.43298I
a = −1.69209 + 0.37137I
b = −1.35574 − 0.89152I
−8.8777 − 15.5620I −14.5417 + 7.8795I
6
II. I
u
2
=
h2.01×10
42
u
43
+5.42×10
42
u
42
+· · ·+7.34×10
41
b−8.39×10
41
, 8.62×10
41
u
43
+
1.61 × 10
42
u
42
+ · · · + 7.34 × 10
41
a − 4.50 × 10
43
, u
44
+ 4u
43
+ · · · + 116u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
−1.17327u
43
− 2.19108u
42
+ ··· − 439.275u + 61.2463
−2.74257u
43
− 7.37661u
42
+ ··· − 201.685u + 1.14222
a
10
=
1.56930u
43
+ 5.18553u
42
+ ··· − 237.590u + 60.1040
−2.74257u
43
− 7.37661u
42
+ ··· − 201.685u + 1.14222
a
12
=
3.61816u
43
+ 9.27065u
42
+ ··· + 182.489u + 32.8026
4.49904u
43
+ 11.8002u
42
+ ··· + 312.338u − 3.00702
a
11
=
1.96942u
43
+ 5.25944u
42
+ ··· + 65.5876u + 33.8026
2.07745u
43
+ 5.75738u
42
+ ··· + 127.873u − 1.42316
a
6
=
1.07148u
43
+ 2.89399u
42
+ ··· + 59.4605u + 9.96375
1.37364u
43
+ 3.38028u
42
+ ··· + 86.1371u − 0.830453
a
8
=
1.70871u
43
+ 4.01744u
42
+ ··· + 60.7021u + 31.6372
2.07745u
43
+ 5.75738u
42
+ ··· + 127.873u − 1.42316
a
7
=
1.78926u
43
+ 4.62600u
42
+ ··· + 163.701u − 11.9689
−1.22781u
43
− 2.74973u
42
+ ··· − 70.8975u + 0.701920
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.60530u
43
− 11.0854u
42
+ ··· + 553.011u − 13.5461
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
, c
10
u
44
− 4u
43
+ ··· − 116u − 1
c
3
, c
6
, c
9
c
12
u
44
+ 3u
43
+ ··· − 44u + 8
c
5
, c
11
(u
22
− u
21
+ ··· − 9u − 2)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
, c
10
y
44
− 40y
43
+ ··· − 12428y + 1
c
3
, c
6
, c
9
c
12
y
44
− 21y
43
+ ··· − 7760y + 64
c
5
, c
11
(y
22
− 15y
21
+ ··· − 113y + 4)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.090540 + 0.022158I
a = −3.21063 − 2.07089I
b = −0.729158 − 0.031613I
−2.83824 + 0.14755I −2.77483 − 4.21375I
u = 1.090540 − 0.022158I
a = −3.21063 + 2.07089I
b = −0.729158 + 0.031613I
−2.83824 − 0.14755I −2.77483 + 4.21375I
u = 0.109119 + 0.888646I
a = −0.410159 − 0.255099I
b = 1.061150 + 0.336334I
−5.93215 − 3.14286I −14.6418 + 3.7109I
u = 0.109119 − 0.888646I
a = −0.410159 + 0.255099I
b = 1.061150 − 0.336334I
−5.93215 + 3.14286I −14.6418 − 3.7109I
u = 0.344224 + 1.065750I
a = −0.392445 + 0.502444I
b = −1.174950 − 0.756583I
−3.01557 − 10.18830I −12.15400 + 6.99410I
u = 0.344224 − 1.065750I
a = −0.392445 − 0.502444I
b = −1.174950 + 0.756583I
−3.01557 + 10.18830I −12.15400 − 6.99410I
u = −1.134110 + 0.122816I
a = −0.077142 + 0.931712I
b = 0.03859 + 1.46465I
1.18895 + 3.23778I −15.5021 − 9.5411I
u = −1.134110 − 0.122816I
a = −0.077142 − 0.931712I
b = 0.03859 − 1.46465I
1.18895 − 3.23778I −15.5021 + 9.5411I
u = 1.036890 + 0.519128I
a = 0.495432 − 0.747200I
b = 0.705965 − 0.517769I
−0.357526 + 0.716312I −8.85937 − 2.91987I
u = 1.036890 − 0.519128I
a = 0.495432 + 0.747200I
b = 0.705965 + 0.517769I
−0.357526 − 0.716312I −8.85937 + 2.91987I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.748799 + 0.898808I
a = −0.318628 − 0.160414I
b = −0.598618 + 0.291695I
1.18895 + 3.23778I −15.5021 − 9.5411I
u = −0.748799 − 0.898808I
a = −0.318628 + 0.160414I
b = −0.598618 − 0.291695I
1.18895 − 3.23778I −15.5021 + 9.5411I
u = 0.238284 + 0.726491I
a = −0.590561 − 1.081680I
b = −0.583355 + 1.078870I
−1.09298 − 3.55787I −9.79859 + 4.38747I
u = 0.238284 − 0.726491I
a = −0.590561 + 1.081680I
b = −0.583355 − 1.078870I
−1.09298 + 3.55787I −9.79859 − 4.38747I
u = 0.736176
a = 0.801410
b = 0.0947175
−1.10346 −8.70720
u = −0.164222 + 0.700108I
a = 0.889479 + 0.479637I
b = 0.576121 − 0.856265I
3.71629 −3.80483 + 0.I
u = −0.164222 − 0.700108I
a = 0.889479 − 0.479637I
b = 0.576121 + 0.856265I
3.71629 −3.80483 + 0.I
u = 1.243520 + 0.352072I
a = 0.852793 − 1.120250I
b = 1.274130 + 0.140265I
−9.47192 − 1.36166I 0
u = 1.243520 − 0.352072I
a = 0.852793 + 1.120250I
b = 1.274130 − 0.140265I
−9.47192 + 1.36166I 0
u = 0.643688 + 0.282110I
a = −2.22845 + 4.03294I
b = −0.062262 − 0.456825I
−2.83824 − 0.14755I −2.77483 + 4.21375I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.643688 − 0.282110I
a = −2.22845 − 4.03294I
b = −0.062262 + 0.456825I
−2.83824 + 0.14755I −2.77483 − 4.21375I
u = 1.047760 + 0.864022I
a = −0.255518 + 0.521043I
b = −1.055110 + 0.486781I
−5.02280 + 3.68716I 0
u = 1.047760 − 0.864022I
a = −0.255518 − 0.521043I
b = −1.055110 − 0.486781I
−5.02280 − 3.68716I 0
u = −1.351490 + 0.160264I
a = −1.139470 − 0.246938I
b = −0.991832 + 0.785748I
−5.93215 + 3.14286I 0
u = −1.351490 − 0.160264I
a = −1.139470 + 0.246938I
b = −0.991832 − 0.785748I
−5.93215 − 3.14286I 0
u = −1.347140 + 0.234013I
a = −2.04959 − 0.19598I
b = −1.55821 + 0.42887I
−5.02280 + 3.68716I 0
u = −1.347140 − 0.234013I
a = −2.04959 + 0.19598I
b = −1.55821 − 0.42887I
−5.02280 − 3.68716I 0
u = 1.358520 + 0.282419I
a = 1.96744 − 0.07093I
b = 0.937408 + 0.526012I
−1.09298 − 3.55787I 0
u = 1.358520 − 0.282419I
a = 1.96744 + 0.07093I
b = 0.937408 − 0.526012I
−1.09298 + 3.55787I 0
u = 0.117503 + 0.569726I
a = −0.457122 − 0.216490I
b = −1.007210 − 0.504052I
−0.357526 − 0.716312I −8.85937 + 2.91987I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.117503 − 0.569726I
a = −0.457122 + 0.216490I
b = −1.007210 + 0.504052I
−0.357526 + 0.716312I −8.85937 − 2.91987I
u = −1.42436
a = 2.09618
b = 2.01618
−16.0009 0
u = −1.39535 + 0.29610I
a = −0.197837 − 0.800968I
b = −0.58639 − 1.50954I
−6.28468 + 7.27868I 0
u = −1.39535 − 0.29610I
a = −0.197837 + 0.800968I
b = −0.58639 + 1.50954I
−6.28468 − 7.27868I 0
u = −1.40825 + 0.36939I
a = 1.88459 + 0.34782I
b = 1.39293 − 0.68109I
−3.01557 + 10.18830I 0
u = −1.40825 − 0.36939I
a = 1.88459 − 0.34782I
b = 1.39293 + 0.68109I
−3.01557 − 10.18830I 0
u = −1.45462 + 0.06689I
a = 0.830038 − 0.316230I
b = 0.720926 + 0.858306I
−9.47192 + 1.36166I 0
u = −1.45462 − 0.06689I
a = 0.830038 + 0.316230I
b = 0.720926 − 0.858306I
−9.47192 − 1.36166I 0
u = 0.521744
a = −2.11947
b = 1.64818
−9.78452 30.1490
u = 1.57069 + 0.28000I
a = −1.52006 + 0.01103I
b = −1.152160 − 0.610789I
−6.28468 − 7.27868I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57069 − 0.28000I
a = −1.52006 − 0.01103I
b = −1.152160 + 0.610789I
−6.28468 + 7.27868I 0
u = −1.63226
a = 1.82053
b = 0.616211
−9.78452 0
u = −1.80378
a = −1.14737
b = −1.21054
−16.0009 0
u = 0.00897213
a = 57.4044
b = −0.580690
−1.10346 −8.70720
14
III. I
u
3
= hb, −3u
2
+ a − 5u − 4, u
3
+ u
2
− 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
u
2
+ u − 1
a
9
=
3u
2
+ 5u + 4
0
a
10
=
3u
2
+ 5u + 4
0
a
12
=
1
0
a
11
=
u
−2u
2
− u + 2
a
6
=
−2u + 1
5u
2
+ 2u − 4
a
8
=
3u
2
+ 4u + 4
2u
2
+ u − 2
a
7
=
−u
2u
2
+ u − 2
a
3
=
−u
2
+ 1
u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 21u
2
+ 45u + 27
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
3
+ u
2
− 1
c
3
u
3
− u
2
+ 2u − 1
c
4
u
3
− u
2
+ 1
c
5
u
3
− 3u
2
+ 2u + 1
c
6
u
3
+ u
2
+ 2u + 1
c
7
, c
8
(u − 1)
3
c
9
, c
12
u
3
c
10
(u + 1)
3
c
11
u
3
+ 3u
2
+ 2u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
3
− y
2
+ 2y −1
c
3
, c
6
y
3
+ 3y
2
+ 2y −1
c
5
, c
11
y
3
− 5y
2
+ 10y −1
c
7
, c
8
, c
10
(y −1)
3
c
9
, c
12
y
3
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.258045 − 0.197115I
b = 0
1.37919 + 2.82812I −7.96807 + 6.06881I
u = −0.877439 − 0.744862I
a = 0.258045 + 0.197115I
b = 0
1.37919 − 2.82812I −7.96807 − 6.06881I
u = 0.754878
a = 9.48391
b = 0
−2.75839 72.9360
18
IV. I
u
4
= h−4a
2
+ 23b − 33a − 3, a
3
+ 8a
2
+ 3a + 7, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
9
=
a
4
23
a
2
+
33
23
a +
3
23
a
10
=
−
4
23
a
2
−
10
23
a −
3
23
4
23
a
2
+
33
23
a +
3
23
a
12
=
−
1
23
a
2
+
9
23
a +
51
23
1
23
a
2
+
14
23
a +
41
23
a
11
=
−
2
23
a
2
−
5
23
a +
10
23
1
23
a
2
+
14
23
a +
41
23
a
6
=
0
5
23
a
2
+
47
23
a +
67
23
a
8
=
−
1
23
a
2
+
9
23
a +
5
23
1
23
a
2
+
14
23
a +
41
23
a
7
=
0
5
23
a
2
+
47
23
a +
67
23
a
3
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
51
23
a
2
+
162
23
a −
117
23
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
6
u
3
c
4
(u + 1)
3
c
5
u
3
+ 3u
2
+ 2u − 1
c
7
, c
8
u
3
+ u
2
− 1
c
9
u
3
− u
2
+ 2u − 1
c
10
u
3
− u
2
+ 1
c
11
u
3
− 3u
2
+ 2u + 1
c
12
u
3
+ u
2
+ 2u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
3
c
3
, c
6
y
3
c
5
, c
11
y
3
− 5y
2
+ 10y − 1
c
7
, c
8
, c
10
y
3
− y
2
+ 2y − 1
c
9
, c
12
y
3
+ 3y
2
+ 2y − 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.135484 + 0.941977I
b = −0.215080 + 1.307140I
1.37919 + 2.82812I −7.96807 + 6.06881I
u = 1.00000
a = −0.135484 − 0.941977I
b = −0.215080 − 1.307140I
1.37919 − 2.82812I −7.96807 − 6.06881I
u = 1.00000
a = −7.72903
b = −0.569840
−2.75839 72.9360
22
V. I
u
5
= hb + u, a + u, u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
−u + 1
a
5
=
−u
−u + 1
a
9
=
−u
−u
a
10
=
0
−u
a
12
=
u
u − 1
a
11
=
u
u − 1
a
6
=
−u
−u + 1
a
8
=
−1
u − 1
a
7
=
−1
0
a
3
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −20
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
u
2
+ u − 1
c
4
, c
6
, c
10
c
12
u
2
− u − 1
c
5
, c
11
u
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
c
8
, c
9
, c
10
c
12
y
2
− 3y + 1
c
5
, c
11
y
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −0.618034
b = −0.618034
−1.97392 −20.0000
u = −1.61803
a = 1.61803
b = 1.61803
−17.7653 −20.0000
26
VI. I
u
6
= hb − u − 1, a + 2, u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
−u + 1
a
5
=
−u
−u + 1
a
9
=
−2
u + 1
a
10
=
−u − 3
u + 1
a
12
=
2u + 3
−u − 2
a
11
=
2u + 3
−u − 2
a
6
=
−u
−u + 1
a
8
=
3u + 3
−u − 2
a
7
=
−1
0
a
3
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −65
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
u
2
+ u − 1
c
4
, c
6
, c
10
c
12
u
2
− u − 1
c
5
, c
11
u
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
c
8
, c
9
, c
10
c
12
y
2
− 3y + 1
c
5
, c
11
y
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −2.00000
b = 1.61803
−9.86960 −65.0000
u = −1.61803
a = −2.00000
b = −0.618034
−9.86960 −65.0000
30
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
(u − 1)
3
(u
2
+ u − 1)
2
(u
3
+ u
2
− 1)
· (u
13
− 3u
12
− u
11
+ 10u
10
− 4u
9
− 9u
8
+ 3u
7
+ 8u
5
− 7u
3
+ u
2
+ u + 1)
· (u
44
− 4u
43
+ ··· − 116u − 1)
c
3
, c
9
u
3
(u
2
+ u − 1)
2
(u
3
− u
2
+ 2u − 1)(u
13
+ u
12
+ ··· + 5u + 1)
· (u
44
+ 3u
43
+ ··· − 44u + 8)
c
4
, c
10
(u + 1)
3
(u
2
− u − 1)
2
(u
3
− u
2
+ 1)
· (u
13
− 3u
12
− u
11
+ 10u
10
− 4u
9
− 9u
8
+ 3u
7
+ 8u
5
− 7u
3
+ u
2
+ u + 1)
· (u
44
− 4u
43
+ ··· − 116u − 1)
c
5
, c
11
u
4
(u
3
− 3u
2
+ 2u + 1)(u
3
+ 3u
2
+ 2u − 1)(u
13
+ 5u
12
+ ··· − 8u − 4)
· (u
22
− u
21
+ ··· − 9u − 2)
2
c
6
, c
12
u
3
(u
2
− u − 1)
2
(u
3
+ u
2
+ 2u + 1)(u
13
+ u
12
+ ··· + 5u + 1)
· (u
44
+ 3u
43
+ ··· − 44u + 8)
31
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
, c
10
((y − 1)
3
)(y
2
− 3y + 1)
2
(y
3
− y
2
+ 2y − 1)(y
13
− 11y
12
+ ··· − y − 1)
· (y
44
− 40y
43
+ ··· − 12428y + 1)
c
3
, c
6
, c
9
c
12
y
3
(y
2
− 3y + 1)
2
(y
3
+ 3y
2
+ 2y − 1)(y
13
− 3y
12
+ ··· + 7y − 1)
· (y
44
− 21y
43
+ ··· − 7760y + 64)
c
5
, c
11
y
4
(y
3
− 5y
2
+ 10y − 1)
2
(y
13
− 5y
12
+ ··· + 96y − 16)
· (y
22
− 15y
21
+ ··· − 113y + 4)
2
32
