12a
0216
(K12a
0216
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 10 2 12 4 5 1 8 11
Solving Sequence
4,8
9 5 10
6,12
7 3 2 11 1
c
8
c
4
c
9
c
5
c
7
c
3
c
2
c
11
c
12
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.31230 × 10
33
u
63
− 9.21845 × 10
33
u
62
+ ··· + 2.52277 × 10
34
b − 5.95857 × 10
34
,
1.05553 × 10
34
u
63
− 2.85080 × 10
34
u
62
+ ··· + 2.52277 × 10
34
a − 9.65444 × 10
33
, u
64
− 4u
63
+ ··· + 32u + 16i
I
u
2
= h2b + 2a − u + 2, 2a
2
− 2au + 2a − u + 3, u
2
− 2i
I
u
3
= ha
4
u − 2a
4
+ 4a
3
u − 8a
3
+ 4a
2
u − 8a
2
− 7au + 25b − 11a − 14u − 2,
a
5
+ 2a
4
u + 2a
4
+ 3a
3
u + 6a
3
+ 8a
2
u + 10a
2
+ 7au + 13a − u − 1, u
2
+ u − 1i
I
u
4
= hau + b + 2a + u + 2, 2a
2
+ au + 2a − u + 3, u
2
− 2i
I
v
1
= ha, b − v −1, v
2
+ v + 1i
I
v
2
= ha, b
2
− b + 1, v −1i
* 6 irreducible components of dim
C
= 0, with total 86 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
=
h3.31×10
33
u
63
−9.22×10
33
u
62
+· · ·+2.52×10
34
b−5.96×10
34
, 1.06×10
34
u
63
−
2.85 × 10
34
u
62
+ · · · + 2.52 × 10
34
a − 9.65 × 10
33
, u
64
− 4u
63
+ · · · + 32u + 16i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
5
=
−u
−u
3
+ u
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
6
=
u
3
− 2u
u
5
− 3u
3
+ u
a
12
=
−0.418403u
63
+ 1.13003u
62
+ ··· + 7.82001u + 0.382692
−0.131296u
63
+ 0.365410u
62
+ ··· + 4.28462u + 2.36192
a
7
=
−0.342599u
63
+ 0.737839u
62
+ ··· + 11.5782u + 4.46198
−0.263432u
63
+ 0.630688u
62
+ ··· + 6.03905u + 1.99604
a
3
=
0.790350u
63
− 2.05902u
62
+ ··· − 18.5463u − 5.88736
0.362768u
63
− 0.965419u
62
+ ··· − 6.85471u − 2.61286
a
2
=
0.203141u
63
− 0.562340u
62
+ ··· − 3.81650u − 1.43156
0.409877u
63
− 1.08413u
62
+ ··· − 8.12806u − 2.97524
a
11
=
−0.549700u
63
+ 1.49544u
62
+ ··· + 12.1046u + 2.74461
−0.131296u
63
+ 0.365410u
62
+ ··· + 4.28462u + 2.36192
a
1
=
0.768798u
63
− 1.82001u
62
+ ··· − 19.8193u − 8.43548
0.735613u
63
− 1.86045u
62
+ ··· − 15.0301u − 5.18940
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.52449u
63
− 5.73943u
62
+ ··· − 69.7334u − 34.4634
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
64
+ 35u
63
+ ··· + 416u + 49
c
2
, c
6
u
64
− 3u
63
+ ··· − 16u + 7
c
3
u
64
+ 3u
63
+ ··· − 4558u + 763
c
4
, c
5
, c
8
c
9
u
64
+ 4u
63
+ ··· − 32u + 16
c
7
, c
11
u
64
+ 3u
63
+ ··· − 6u + 7
c
10
, c
12
u
64
− 19u
63
+ ··· − 608u + 49
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
64
− 5y
63
+ ··· − 30760y + 2401
c
2
, c
6
y
64
+ 35y
63
+ ··· + 416y + 49
c
3
y
64
− 45y
63
+ ··· + 15204664y + 582169
c
4
, c
5
, c
8
c
9
y
64
− 76y
63
+ ··· − 1024y + 256
c
7
, c
11
y
64
+ 19y
63
+ ··· + 608y + 49
c
10
, c
12
y
64
+ 59y
63
+ ··· + 133272y + 2401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.873442 + 0.450062I
a = 0.316313 + 0.070275I
b = −0.799432 + 0.773699I
−4.38307 − 0.99571I 0
u = 0.873442 − 0.450062I
a = 0.316313 − 0.070275I
b = −0.799432 − 0.773699I
−4.38307 + 0.99571I 0
u = −0.819111 + 0.526710I
a = −1.11929 − 1.64147I
b = −0.751905 + 0.969822I
−3.78557 + 6.83757I 0
u = −0.819111 − 0.526710I
a = −1.11929 + 1.64147I
b = −0.751905 − 0.969822I
−3.78557 − 6.83757I 0
u = 0.824871 + 0.622233I
a = −0.92431 + 1.81972I
b = −0.773002 − 1.004690I
−6.66344 − 11.86030I 0
u = 0.824871 − 0.622233I
a = −0.92431 − 1.81972I
b = −0.773002 + 1.004690I
−6.66344 + 11.86030I 0
u = −0.879555 + 0.575858I
a = 0.533241 + 0.042734I
b = −0.858792 − 0.753406I
−7.43975 + 5.78092I 0
u = −0.879555 − 0.575858I
a = 0.533241 − 0.042734I
b = −0.858792 + 0.753406I
−7.43975 − 5.78092I 0
u = 0.974065 + 0.497285I
a = −0.83168 + 1.35722I
b = −0.798463 − 0.924252I
−8.15312 − 3.18144I 0
u = 0.974065 − 0.497285I
a = −0.83168 − 1.35722I
b = −0.798463 + 0.924252I
−8.15312 + 3.18144I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.857795 + 0.198791I
a = −0.310940 + 0.261733I
b = 0.651190 − 0.065793I
−3.65580 + 3.51727I −12.68996 − 5.01598I
u = −0.857795 − 0.198791I
a = −0.310940 − 0.261733I
b = 0.651190 + 0.065793I
−3.65580 − 3.51727I −12.68996 + 5.01598I
u = −1.057340 + 0.437339I
a = 0.206911 + 0.270794I
b = −0.815263 − 0.853921I
−8.36696 − 2.85624I 0
u = −1.057340 − 0.437339I
a = 0.206911 − 0.270794I
b = −0.815263 + 0.853921I
−8.36696 + 2.85624I 0
u = 0.142496 + 0.804798I
a = −0.47916 + 1.62652I
b = 0.772417 − 0.938985I
−4.61047 + 7.11222I −7.85412 − 5.57393I
u = 0.142496 − 0.804798I
a = −0.47916 − 1.62652I
b = 0.772417 + 0.938985I
−4.61047 − 7.11222I −7.85412 + 5.57393I
u = −0.060512 + 0.798911I
a = −0.45707 + 1.46569I
b = 0.803492 − 0.827725I
−4.95457 − 1.19128I −8.68532 + 0.53231I
u = −0.060512 − 0.798911I
a = −0.45707 − 1.46569I
b = 0.803492 + 0.827725I
−4.95457 + 1.19128I −8.68532 − 0.53231I
u = 0.679164 + 0.384679I
a = 0.56201 − 2.37763I
b = 0.240421 + 1.058780I
−0.09688 − 6.48785I −5.34636 + 9.14112I
u = 0.679164 − 0.384679I
a = 0.56201 + 2.37763I
b = 0.240421 − 1.058780I
−0.09688 + 6.48785I −5.34636 − 9.14112I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.063045 + 0.685748I
a = −0.37731 − 1.58111I
b = 0.723329 + 0.880008I
−1.54119 − 2.76193I −3.74007 + 2.60897I
u = −0.063045 − 0.685748I
a = −0.37731 + 1.58111I
b = 0.723329 − 0.880008I
−1.54119 + 2.76193I −3.74007 − 2.60897I
u = −0.639376 + 0.195260I
a = −2.34545 − 0.43868I
b = −0.654214 + 0.889738I
−0.81009 + 5.04742I −8.02999 − 8.42703I
u = −0.639376 − 0.195260I
a = −2.34545 + 0.43868I
b = −0.654214 − 0.889738I
−0.81009 − 5.04742I −8.02999 + 8.42703I
u = −0.535329 + 0.395031I
a = 0.72597 + 2.21083I
b = 0.176464 − 0.974491I
1.96190 + 2.14353I −0.48240 − 5.32337I
u = −0.535329 − 0.395031I
a = 0.72597 − 2.21083I
b = 0.176464 + 0.974491I
1.96190 − 2.14353I −0.48240 + 5.32337I
u = −1.378940 + 0.142145I
a = −0.499258 − 0.680732I
b = −0.644422 + 0.661579I
−6.70970 + 3.00332I 0
u = −1.378940 − 0.142145I
a = −0.499258 + 0.680732I
b = −0.644422 − 0.661579I
−6.70970 − 3.00332I 0
u = −0.363836 + 0.462721I
a = 1.38698 + 2.18023I
b = −0.033354 − 0.884096I
2.47588 + 0.92435I 1.91401 − 4.19238I
u = −0.363836 − 0.462721I
a = 1.38698 − 2.18023I
b = −0.033354 + 0.884096I
2.47588 − 0.92435I 1.91401 + 4.19238I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42295 + 0.10139I
a = −0.310419 − 0.898915I
b = −0.574977 + 0.965428I
−5.75578 + 1.76368I 0
u = 1.42295 − 0.10139I
a = −0.310419 + 0.898915I
b = −0.574977 − 0.965428I
−5.75578 − 1.76368I 0
u = −1.43142 + 0.07936I
a = −1.220480 − 0.666038I
b = −0.061312 + 0.624389I
−4.32668 − 1.79922I 0
u = −1.43142 − 0.07936I
a = −1.220480 + 0.666038I
b = −0.061312 − 0.624389I
−4.32668 + 1.79922I 0
u = 0.378088 + 0.391436I
a = 0.149787 − 1.097520I
b = 0.493469 + 0.542722I
−1.13035 − 0.98038I −9.44439 + 5.04601I
u = 0.378088 − 0.391436I
a = 0.149787 + 1.097520I
b = 0.493469 − 0.542722I
−1.13035 + 0.98038I −9.44439 − 5.04601I
u = 1.45615 + 0.08976I
a = −1.01574 + 1.04774I
b = −0.145990 − 0.826005I
−3.41948 − 2.73930I 0
u = 1.45615 − 0.08976I
a = −1.01574 − 1.04774I
b = −0.145990 + 0.826005I
−3.41948 + 2.73930I 0
u = 0.269672 + 0.456052I
a = 2.17570 − 2.31816I
b = −0.187057 + 0.849183I
1.13367 + 3.50081I −0.27253 − 1.56313I
u = 0.269672 − 0.456052I
a = 2.17570 + 2.31816I
b = −0.187057 − 0.849183I
1.13367 − 3.50081I −0.27253 + 1.56313I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.345458 + 0.308634I
a = −0.16531 − 1.86311I
b = 0.537021 + 0.956459I
−0.00299 − 3.22788I −5.50185 − 1.31175I
u = −0.345458 − 0.308634I
a = −0.16531 + 1.86311I
b = 0.537021 − 0.956459I
−0.00299 + 3.22788I −5.50185 + 1.31175I
u = 0.162481 + 0.408835I
a = 1.44324 − 0.12966I
b = −0.318816 + 0.244523I
−0.51706 − 1.49158I −5.11534 + 4.83543I
u = 0.162481 − 0.408835I
a = 1.44324 + 0.12966I
b = −0.318816 − 0.244523I
−0.51706 + 1.49158I −5.11534 − 4.83543I
u = 1.57045 + 0.06947I
a = −0.56984 + 1.35554I
b = −0.279628 − 1.103440I
−5.18358 − 3.62251I 0
u = 1.57045 − 0.06947I
a = −0.56984 − 1.35554I
b = −0.279628 + 1.103440I
−5.18358 + 3.62251I 0
u = 1.61840 + 0.04481I
a = 1.367660 − 0.140722I
b = 0.774064 + 0.910389I
−8.72706 − 5.87646I 0
u = 1.61840 − 0.04481I
a = 1.367660 + 0.140722I
b = 0.774064 − 0.910389I
−8.72706 + 5.87646I 0
u = −1.61803 + 0.10068I
a = −0.52547 − 1.48304I
b = −0.253191 + 1.186100I
−8.02622 + 8.25020I 0
u = −1.61803 − 0.10068I
a = −0.52547 + 1.48304I
b = −0.253191 − 1.186100I
−8.02622 − 8.25020I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.65295 + 0.15535I
a = 1.21356 − 0.98307I
b = 0.785284 + 1.028100I
−12.2488 − 9.4695I 0
u = 1.65295 − 0.15535I
a = 1.21356 + 0.98307I
b = 0.785284 − 1.028100I
−12.2488 + 9.4695I 0
u = 1.65992 + 0.04982I
a = −0.142293 + 0.110211I
b = −0.885583 − 0.091250I
−12.43950 − 4.45006I 0
u = 1.65992 − 0.04982I
a = −0.142293 − 0.110211I
b = −0.885583 + 0.091250I
−12.43950 + 4.45006I 0
u = −1.65878 + 0.18881I
a = 1.14079 + 1.15178I
b = 0.784282 − 1.059400I
−15.1084 + 14.9979I 0
u = −1.65878 − 0.18881I
a = 1.14079 − 1.15178I
b = 0.784282 + 1.059400I
−15.1084 − 14.9979I 0
u = −1.66569 + 0.12660I
a = 0.219521 + 0.247710I
b = 0.899613 + 0.742060I
−13.14280 + 3.23432I 0
u = −1.66569 − 0.12660I
a = 0.219521 − 0.247710I
b = 0.899613 − 0.742060I
−13.14280 − 3.23432I 0
u = 1.67592 + 0.16565I
a = 0.056375 − 0.215125I
b = 0.934162 − 0.708886I
−16.2081 − 8.6708I 0
u = 1.67592 − 0.16565I
a = 0.056375 + 0.215125I
b = 0.934162 + 0.708886I
−16.2081 + 8.6708I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.69835 + 0.12447I
a = 0.974819 + 0.805892I
b = 0.834072 − 1.009660I
−17.4538 + 5.5952I 0
u = −1.69835 − 0.12447I
a = 0.974819 − 0.805892I
b = 0.834072 + 1.009660I
−17.4538 − 5.5952I 0
u = 1.71155 + 0.09018I
a = 0.321141 − 0.008755I
b = 0.926120 − 0.804268I
−18.1024 + 0.8823I 0
u = 1.71155 − 0.09018I
a = 0.321141 + 0.008755I
b = 0.926120 + 0.804268I
−18.1024 − 0.8823I 0
11
II. I
u
2
= h2b + 2a − u + 2, 2a
2
− 2au + 2a − u + 3, u
2
− 2i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
2
a
5
=
−u
−u
a
10
=
−1
0
a
6
=
0
−u
a
12
=
a
−a +
1
2
u − 1
a
7
=
1
2
au +
1
2
u −
1
2
−a +
1
2
u
a
3
=
1
2
au −
1
2
u + 1
a
2
=
1
2
au −
1
2
au + u
a
11
=
1
2
u − 1
−a +
1
2
u − 1
a
1
=
1
2
au +
1
2
u −
1
2
−a +
1
2
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8a − 4u − 4
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
11
c
12
(u
2
− u + 1)
2
c
3
, c
6
, c
7
c
10
(u
2
+ u + 1)
2
c
4
, c
5
, c
8
c
9
(u
2
− 2)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
10
c
11
, c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
8
c
9
(y −2)
4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = 0.207107 + 0.866025I
b = −0.500000 − 0.866025I
−4.93480 − 4.05977I −8.00000 + 6.92820I
u = 1.41421
a = 0.207107 − 0.866025I
b = −0.500000 + 0.866025I
−4.93480 + 4.05977I −8.00000 − 6.92820I
u = −1.41421
a = −1.20711 + 0.86603I
b = −0.500000 − 0.866025I
−4.93480 − 4.05977I −8.00000 + 6.92820I
u = −1.41421
a = −1.20711 − 0.86603I
b = −0.500000 + 0.866025I
−4.93480 + 4.05977I −8.00000 − 6.92820I
15
III. I
u
3
= ha
4
u + 4a
3
u + · · · − 11a − 2, 2a
4
u + 3a
3
u + · · · + 13a − 1, u
2
+ u − 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
−u + 1
a
5
=
−u
−u + 1
a
10
=
u
u
a
6
=
−1
0
a
12
=
a
−0.0400000a
4
u − 0.160000a
3
u + ··· + 0.440000a + 0.0800000
a
7
=
0.320000a
4
u + 0.280000a
3
u + ··· + 0.680000a + 0.960000
0.640000a
4
u − 0.440000a
3
u + ··· + 0.360000a − 0.0800000
a
3
=
−0.0400000a
4
u − 0.160000a
3
u + ··· + 1.44000a + 0.0800000
−0.0400000a
4
u − 0.160000a
3
u + ··· + 0.440000a + 0.0800000
a
2
=
a
−0.0400000a
4
u − 0.160000a
3
u + ··· + 0.440000a + 0.0800000
a
11
=
−0.0400000a
4
u − 0.160000a
3
u + ··· + 1.44000a + 0.0800000
−0.0400000a
4
u − 0.160000a
3
u + ··· + 0.440000a + 0.0800000
a
1
=
−1.04000a
4
u − 0.160000a
3
u + ··· − 1.36000a − 0.320000
−0.560000a
4
u − 0.240000a
3
u + ··· − 0.240000a − 0.0800000
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ 4u
9
+ 10u
8
+ 16u
7
+ 19u
6
+ 13u
5
+ 4u
4
− 5u
3
− 5u
2
− 3u + 1
c
2
, c
6
, c
7
c
11
u
10
+ 2u
8
+ 3u
6
− u
5
+ 2u
4
− u
3
+ u
2
− u − 1
c
3
u
10
+ 2u
8
+ 2u
7
− 3u
6
− 3u
5
− 8u
4
+ u
3
+ 9u
2
− 5u − 5
c
4
, c
5
, c
8
c
9
(u
2
− u − 1)
5
c
10
, c
12
u
10
− 4u
9
+ 10u
8
− 16u
7
+ 19u
6
− 13u
5
+ 4u
4
+ 5u
3
− 5u
2
+ 3u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
, c
12
y
10
+ 4y
9
+ ··· − 19y + 1
c
2
, c
6
, c
7
c
11
y
10
+ 4y
9
+ 10y
8
+ 16y
7
+ 19y
6
+ 13y
5
+ 4y
4
− 5y
3
− 5y
2
− 3y + 1
c
3
y
10
+ 4y
9
+ ··· − 115y + 25
c
4
, c
5
, c
8
c
9
(y
2
− 3y + 1)
5
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0.0866109
b = 0.481001
−0.986960 −10.0000
u = 0.618034
a = −1.73755 + 0.98693I
b = −0.643219 + 0.835211I
−0.986960 −10.0000
u = 0.618034
a = −1.73755 − 0.98693I
b = −0.643219 − 0.835211I
−0.986960 −10.0000
u = 0.618034
a = 0.07621 + 2.16163I
b = 0.402718 − 0.997003I
−0.986960 −10.0000
u = 0.618034
a = 0.07621 − 2.16163I
b = 0.402718 + 0.997003I
−0.986960 −10.0000
u = −1.61803
a = 1.122050 + 0.202875I
b = 0.786437 + 0.860119I
−8.88264 −10.0000
u = −1.61803
a = 1.122050 − 0.202875I
b = 0.786437 − 0.860119I
−8.88264 −10.0000
u = −1.61803
a = −0.380191 + 1.332290I
b = −0.388630 − 1.160270I
−8.88264 −10.0000
u = −1.61803
a = −0.380191 − 1.332290I
b = −0.388630 + 1.160270I
−8.88264 −10.0000
u = −1.61803
a = −0.247641
b = −0.795614
−8.88264 −10.0000
19
IV. I
u
4
= hau + b + 2a + u + 2, 2a
2
+ au + 2a − u + 3, u
2
− 2i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
2
a
5
=
−u
−u
a
10
=
−1
0
a
6
=
0
−u
a
12
=
a
−au − 2a − u − 2
a
7
=
−au − a −
1
2
u − 1
−au − 2a − u − 1
a
3
=
−au − a − u − 1
−au − 2a − 2
a
2
=
−au − a − u − 1
−3au − 4a − 2u − 4
a
11
=
−au − a − u − 2
−au − 2a − u − 2
a
1
=
−au − a −
1
2
u − 1
−au − 2a − u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
11
c
12
(u
2
− u + 1)
2
c
3
, c
6
, c
7
c
10
(u
2
+ u + 1)
2
c
4
, c
5
, c
8
c
9
(u
2
− 2)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
10
c
11
, c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
8
c
9
(y −2)
4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −0.853553 + 0.253653I
b = −0.500000 − 0.866025I
−4.93480 −8.00000
u = 1.41421
a = −0.853553 − 0.253653I
b = −0.500000 + 0.866025I
−4.93480 −8.00000
u = −1.41421
a = −0.14645 + 1.47840I
b = −0.500000 − 0.866025I
−4.93480 −8.00000
u = −1.41421
a = −0.14645 − 1.47840I
b = −0.500000 + 0.866025I
−4.93480 −8.00000
23
V. I
v
1
= ha, b − v − 1, v
2
+ v + 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
9
=
1
0
a
5
=
v
0
a
10
=
1
0
a
6
=
v
0
a
12
=
0
v + 1
a
7
=
1
−v
a
3
=
−1
−1
a
2
=
−v − 2
−1
a
11
=
v + 1
v + 1
a
1
=
−1
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8v − 2
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
12
u
2
− u + 1
c
2
, c
10
, c
11
u
2
+ u + 1
c
4
, c
5
, c
8
c
9
u
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
10
c
11
, c
12
y
2
+ y + 1
c
4
, c
5
, c
8
c
9
y
2
26
(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
− 4.05977I −6.00000 + 6.92820I
v = −0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
4.05977I −6.00000 − 6.92820I
27
VI. I
v
2
= ha, b
2
− b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
1
0
a
9
=
1
0
a
5
=
1
0
a
10
=
1
0
a
6
=
1
0
a
12
=
0
b
a
7
=
1
−b + 1
a
3
=
b
b
a
2
=
0
b
a
11
=
b
b
a
1
=
−1
b − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
12
u
2
− u + 1
c
2
, c
10
, c
11
u
2
+ u + 1
c
4
, c
5
, c
8
c
9
u
2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
10
c
11
, c
12
y
2
+ y + 1
c
4
, c
5
, c
8
c
9
y
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.500000 + 0.866025I
0 0
v = 1.00000
a = 0
b = 0.500000 − 0.866025I
0 0
31
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
6
· (u
10
+ 4u
9
+ 10u
8
+ 16u
7
+ 19u
6
+ 13u
5
+ 4u
4
− 5u
3
− 5u
2
− 3u + 1)
· (u
64
+ 35u
63
+ ··· + 416u + 49)
c
2
((u
2
− u + 1)
4
)(u
2
+ u + 1)
2
(u
10
+ 2u
8
+ ··· − u − 1)
· (u
64
− 3u
63
+ ··· − 16u + 7)
c
3
(u
2
− u + 1)
2
(u
2
+ u + 1)
4
· (u
10
+ 2u
8
+ 2u
7
− 3u
6
− 3u
5
− 8u
4
+ u
3
+ 9u
2
− 5u − 5)
· (u
64
+ 3u
63
+ ··· − 4558u + 763)
c
4
, c
5
, c
8
c
9
u
4
(u
2
− 2)
4
(u
2
− u − 1)
5
(u
64
+ 4u
63
+ ··· − 32u + 16)
c
6
((u
2
− u + 1)
2
)(u
2
+ u + 1)
4
(u
10
+ 2u
8
+ ··· − u − 1)
· (u
64
− 3u
63
+ ··· − 16u + 7)
c
7
((u
2
− u + 1)
2
)(u
2
+ u + 1)
4
(u
10
+ 2u
8
+ ··· − u − 1)
· (u
64
+ 3u
63
+ ··· − 6u + 7)
c
10
(u
2
+ u + 1)
6
· (u
10
− 4u
9
+ 10u
8
− 16u
7
+ 19u
6
− 13u
5
+ 4u
4
+ 5u
3
− 5u
2
+ 3u + 1)
· (u
64
− 19u
63
+ ··· − 608u + 49)
c
11
((u
2
− u + 1)
4
)(u
2
+ u + 1)
2
(u
10
+ 2u
8
+ ··· − u − 1)
· (u
64
+ 3u
63
+ ··· − 6u + 7)
c
12
(u
2
− u + 1)
6
· (u
10
− 4u
9
+ 10u
8
− 16u
7
+ 19u
6
− 13u
5
+ 4u
4
+ 5u
3
− 5u
2
+ 3u + 1)
· (u
64
− 19u
63
+ ··· − 608u + 49)
32
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
10
+ 4y
9
+ ··· − 19y + 1)
· (y
64
− 5y
63
+ ··· − 30760y + 2401)
c
2
, c
6
(y
2
+ y + 1)
6
· (y
10
+ 4y
9
+ 10y
8
+ 16y
7
+ 19y
6
+ 13y
5
+ 4y
4
− 5y
3
− 5y
2
− 3y + 1)
· (y
64
+ 35y
63
+ ··· + 416y + 49)
c
3
((y
2
+ y + 1)
6
)(y
10
+ 4y
9
+ ··· − 115y + 25)
· (y
64
− 45y
63
+ ··· + 15204664y + 582169)
c
4
, c
5
, c
8
c
9
y
4
(y − 2)
8
(y
2
− 3y + 1)
5
(y
64
− 76y
63
+ ··· − 1024y + 256)
c
7
, c
11
(y
2
+ y + 1)
6
· (y
10
+ 4y
9
+ 10y
8
+ 16y
7
+ 19y
6
+ 13y
5
+ 4y
4
− 5y
3
− 5y
2
− 3y + 1)
· (y
64
+ 19y
63
+ ··· + 608y + 49)
c
10
, c
12
((y
2
+ y + 1)
6
)(y
10
+ 4y
9
+ ··· − 19y + 1)
· (y
64
+ 59y
63
+ ··· + 133272y + 2401)
33
