12n
0224
(K12n
0224
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 11 9 3 6 8 12 5 10
Solving Sequence
3,7
4
5,8
2
1,10
9 6 12 11
c
3
c
7
c
2
c
1
c
9
c
6
c
12
c
11
c
4
, c
5
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h9.65958 × 10
65
u
40
+ 1.97140 × 10
66
u
39
+ ··· + 1.18987 × 10
68
d − 9.62857 × 10
67
,
1.07299 × 10
66
u
40
+ 1.97354 × 10
66
u
39
+ ··· + 1.18987 × 10
68
c + 6.68255 × 10
67
,
− 1.37658 × 10
65
u
40
− 4.47424 × 10
65
u
39
+ ··· + 1.06596 × 10
68
b − 6.96533 × 10
67
,
5.90486 × 10
65
u
40
+ 1.83524 × 10
66
u
39
+ ··· + 4.26385 × 10
68
a − 3.18493 × 10
67
,
u
41
+ 2u
40
+ ··· − 512u
2
− 512i
I
u
2
= hu
3
a
2
+ 5u
3
a + 2a
2
u − 4u
2
a − 4u
3
+ 11au + 4u
2
+ d − 8a − 10u + 8,
u
3
a
2
+ 3u
3
a + a
2
u − 2u
2
a − 2u
3
+ 4au + 2u
2
+ c − 4a − 4u + 4, −a
2
u
2
+ b + 2a − 2,
4u
3
a
2
− 2a
2
u
2
− 6u
3
a + a
3
+ 10a
2
u + 3u
2
a + 2u
3
− 2a
2
− 15au − u
2
+ 3a + 5u − 1, u
4
− u
3
+ 3u
2
− 2u + 1i
I
v
1
= hc, d − v − 1, b, a − 1, v
2
+ v + 1i
I
v
2
= ha, d, c − v, b − 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 58 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
= h9.66 × 10
65
u
40
+ 1.97× 10
66
u
39
+ · · · + 1.19 × 10
68
d −9.63 × 10
67
, 1.07 ×
10
66
u
40
+ 1.97 × 10
66
u
39
+ · · · + 1.19 × 10
68
c + 6.68 × 10
67
, −1.38 × 10
65
u
40
−
4.47 × 10
65
u
39
+ · · · + 1.07 × 10
68
b − 6.97 × 10
67
, 5.90 × 10
65
u
40
+ 1.84 ×
10
66
u
39
+ · · · + 4.26 × 10
68
a − 3.18 × 10
67
, u
41
+ 2u
40
+ · · · − 512u
2
− 512i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
5
=
−0.00138487u
40
− 0.00430419u
39
+ ··· − 1.07263u + 0.0746961
0.00129140u
40
+ 0.00419737u
39
+ ··· + 1.25599u + 0.653432
a
8
=
u
u
a
2
=
−0.00138487u
40
− 0.00430419u
39
+ ··· − 1.07263u + 0.0746961
−0.000383620u
40
− 0.00160154u
39
+ ··· − 0.546942u + 0.132211
a
1
=
−0.00176849u
40
− 0.00590573u
39
+ ··· − 1.61957u + 0.206907
−0.000383620u
40
− 0.00160154u
39
+ ··· − 0.546942u + 0.132211
a
10
=
−0.00901765u
40
− 0.0165861u
39
+ ··· + 12.4282u − 0.561619
−0.00811817u
40
− 0.0165681u
39
+ ··· + 8.57387u + 0.809210
a
9
=
−0.00756180u
40
− 0.0140634u
39
+ ··· + 11.9677u + 0.350233
−0.00666231u
40
− 0.0140454u
39
+ ··· + 8.11334u + 1.72106
a
6
=
0.000899485u
40
+ 0.0000180094u
39
+ ··· − 3.85437u + 1.37083
−0.00666231u
40
− 0.0140454u
39
+ ··· + 8.11334u + 1.72106
a
12
=
−0.00898279u
40
− 0.0228872u
39
+ ··· + 6.35254u + 2.83155
−0.00602820u
40
− 0.0101798u
39
+ ··· + 8.49552u − 2.03570
a
11
=
−0.00761817u
40
− 0.0171648u
39
+ ··· + 9.71421u + 2.83352
−0.00515696u
40
− 0.00747593u
39
+ ··· + 7.91840u − 3.20299
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00750642u
40
+ 0.0137245u
39
+ ··· + 0.520985u + 10.6626
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
41
+ 50u
40
+ ··· + 8224u + 256
c
2
, c
4
u
41
− 8u
40
+ ··· − 8u − 16
c
3
, c
7
u
41
+ 2u
40
+ ··· − 512u
2
− 512
c
5
, c
11
u
41
− 2u
40
+ ··· + 16u − 4
c
6
, c
8
u
41
+ 8u
40
+ ··· − 8u − 16
c
9
u
41
− 10u
40
+ ··· + 2080u − 256
c
10
, c
12
u
41
− 12u
40
+ ··· + 344u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
41
− 110y
40
+ ··· + 25092608y − 65536
c
2
, c
4
y
41
− 50y
40
+ ··· + 8224y − 256
c
3
, c
7
y
41
+ 30y
40
+ ··· − 524288y − 262144
c
5
, c
11
y
41
+ 12y
40
+ ··· + 344y − 16
c
6
, c
8
y
41
− 10y
40
+ ··· + 2080y − 256
c
9
y
41
+ 50y
40
+ ··· − 663040y − 65536
c
10
, c
12
y
41
+ 36y
40
+ ··· + 135968y − 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.280189 + 0.954581I
a = 0.590964 − 0.259086I
b = 0.419345 + 0.622257I
c = 0.0474799 − 0.0430603I
d = 1.033380 + 0.229578I
1.60252 − 4.55290I 4.51064 + 8.08001I
u = −0.280189 − 0.954581I
a = 0.590964 + 0.259086I
b = 0.419345 − 0.622257I
c = 0.0474799 + 0.0430603I
d = 1.033380 − 0.229578I
1.60252 + 4.55290I 4.51064 − 8.08001I
u = −0.942111 + 0.024266I
a = 0.91333 − 1.27170I
b = −0.627424 + 0.518765I
c = −0.499993 + 0.079611I
d = −0.315261 + 0.806428I
−0.87865 + 4.07350I 1.48942 − 7.36111I
u = −0.942111 − 0.024266I
a = 0.91333 + 1.27170I
b = −0.627424 − 0.518765I
c = −0.499993 − 0.079611I
d = −0.315261 − 0.806428I
−0.87865 − 4.07350I 1.48942 + 7.36111I
u = −0.100000 + 0.892301I
a = 0.541244 + 0.141055I
b = 0.730090 − 0.450883I
c = 0.004841 + 0.674193I
d = −0.587647 + 0.795464I
−1.46086 + 1.42227I −3.88823 − 3.83998I
u = −0.100000 − 0.892301I
a = 0.541244 − 0.141055I
b = 0.730090 + 0.450883I
c = 0.004841 − 0.674193I
d = −0.587647 − 0.795464I
−1.46086 − 1.42227I −3.88823 + 3.83998I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.687957 + 0.421229I
a = 0.457946 + 0.040164I
b = 1.167000 − 0.190055I
c = −0.728909 + 0.390845I
d = −0.849961 + 0.066792I
−2.43397 + 0.55461I −3.61478 + 1.21885I
u = −0.687957 − 0.421229I
a = 0.457946 − 0.040164I
b = 1.167000 + 0.190055I
c = −0.728909 − 0.390845I
d = −0.849961 − 0.066792I
−2.43397 − 0.55461I −3.61478 − 1.21885I
u = −0.586118 + 0.499909I
a = 0.841488 − 0.427556I
b = −0.055470 + 0.479911I
c = 0.061137 − 1.346250I
d = 0.633993 + 0.071971I
3.14860 + 0.97270I 10.27133 − 0.16493I
u = −0.586118 − 0.499909I
a = 0.841488 + 0.427556I
b = −0.055470 − 0.479911I
c = 0.061137 + 1.346250I
d = 0.633993 − 0.071971I
3.14860 − 0.97270I 10.27133 + 0.16493I
u = 0.757570 + 0.057431I
a = 1.57773 − 1.54774I
b = −0.677009 + 0.316853I
c = 0.629935 + 0.107949I
d = 0.369651 − 0.357039I
−0.834104 − 1.057860I 1.84303 − 1.72199I
u = 0.757570 − 0.057431I
a = 1.57773 + 1.54774I
b = −0.677009 − 0.316853I
c = 0.629935 − 0.107949I
d = 0.369651 + 0.357039I
−0.834104 + 1.057860I 1.84303 + 1.72199I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.748122 + 0.099272I
a = 0.452596 − 0.009005I
b = 1.208600 + 0.043942I
c = 0.532023 − 0.239529I
d = 0.043520 + 0.421796I
−0.52179 − 2.81355I 3.88749 + 5.15717I
u = 0.748122 − 0.099272I
a = 0.452596 + 0.009005I
b = 1.208600 − 0.043942I
c = 0.532023 + 0.239529I
d = 0.043520 − 0.421796I
−0.52179 + 2.81355I 3.88749 − 5.15717I
u = −0.004283 + 0.652626I
a = 0.629363 − 0.061738I
b = 0.573765 + 0.154381I
c = −0.00038 − 2.68044I
d = 0.006876 − 0.589549I
0.70242 − 2.36927I −0.82941 + 4.59716I
u = −0.004283 − 0.652626I
a = 0.629363 + 0.061738I
b = 0.573765 − 0.154381I
c = −0.00038 + 2.68044I
d = 0.006876 + 0.589549I
0.70242 + 2.36927I −0.82941 − 4.59716I
u = −0.076846 + 0.625583I
a = 0.695357 − 0.090908I
b = 0.413943 + 0.184853I
c = 0.282886 + 0.791726I
d = 0.74226 + 1.57829I
0.85500 + 1.57570I 0.179374 + 0.776646I
u = −0.076846 − 0.625583I
a = 0.695357 + 0.090908I
b = 0.413943 − 0.184853I
c = 0.282886 − 0.791726I
d = 0.74226 − 1.57829I
0.85500 − 1.57570I 0.179374 − 0.776646I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.01326 + 1.47518I
a = −1.81673 + 0.02079I
b = −1.55037 − 0.00630I
c = 1.42698 + 0.86838I
d = 0.490726 + 0.727578I
−5.83509 − 1.34899I −0.977007 + 0.716014I
u = −0.01326 − 1.47518I
a = −1.81673 − 0.02079I
b = −1.55037 + 0.00630I
c = 1.42698 − 0.86838I
d = 0.490726 − 0.727578I
−5.83509 + 1.34899I −0.977007 − 0.716014I
u = 0.45410 + 1.44756I
a = −1.59641 − 0.64255I
b = −1.53907 + 0.21697I
c = 1.49469 − 0.92353I
d = 0.355963 − 0.961859I
−4.95290 + 7.65933I 2.00000 − 5.62562I
u = 0.45410 − 1.44756I
a = −1.59641 + 0.64255I
b = −1.53907 − 0.21697I
c = 1.49469 + 0.92353I
d = 0.355963 + 0.961859I
−4.95290 − 7.65933I 2.00000 + 5.62562I
u = 0.466919
a = 1.29906
b = −0.230214
c = 1.50297
d = −0.0988292
1.25610 8.53770
u = 0.35061 + 1.53639I
a = 0.443886 + 0.289097I
b = 0.581850 − 1.030240I
c = 1.88732 − 0.49585I
d = 0.784306 − 0.583648I
−6.34261 + 3.42138I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.35061 − 1.53639I
a = 0.443886 − 0.289097I
b = 0.581850 + 1.030240I
c = 1.88732 + 0.49585I
d = 0.784306 + 0.583648I
−6.34261 − 3.42138I 0
u = −0.51610 + 1.49655I
a = 0.446462 − 0.321741I
b = 0.474223 + 1.062390I
c = −1.68030 − 1.21373I
d = −0.511523 − 1.269150I
−5.66064 − 9.73522I 0. + 7.05049I
u = −0.51610 − 1.49655I
a = 0.446462 + 0.321741I
b = 0.474223 − 1.062390I
c = −1.68030 + 1.21373I
d = −0.511523 + 1.269150I
−5.66064 + 9.73522I 0. − 7.05049I
u = −1.62020 + 0.13077I
a = 0.381574 + 0.008996I
b = 1.61926 − 0.06175I
c = −0.47751 + 2.12520I
d = −0.63777 + 3.15512I
−8.89854 + 0.19005I 0
u = −1.62020 − 0.13077I
a = 0.381574 − 0.008996I
b = 1.61926 + 0.06175I
c = −0.47751 − 2.12520I
d = −0.63777 − 3.15512I
−8.89854 − 0.19005I 0
u = 1.59450 + 0.33027I
a = 0.382027 − 0.022906I
b = 1.60824 + 0.15639I
c = −0.39612 + 2.13768I
d = −0.28184 + 3.24036I
−8.54414 − 6.61454I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59450 − 0.33027I
a = 0.382027 + 0.022906I
b = 1.60824 − 0.15639I
c = −0.39612 − 2.13768I
d = −0.28184 − 3.24036I
−8.54414 + 6.61454I 0
u = −0.23388 + 1.65276I
a = −1.52839 + 0.26544I
b = −1.63512 − 0.11031I
c = −2.35058 + 0.06091I
d = −1.275640 − 0.091209I
−9.70458 − 3.47853I 0
u = −0.23388 − 1.65276I
a = −1.52839 − 0.26544I
b = −1.63512 + 0.11031I
c = −2.35058 − 0.06091I
d = −1.275640 + 0.091209I
−9.70458 + 3.47853I 0
u = 0.86658 + 1.51028I
a = −1.140130 − 0.820998I
b = −1.57759 + 0.41592I
c = 1.38502 − 2.89598I
d = 0.08526 − 2.95483I
−12.2320 + 15.1490I 0
u = 0.86658 − 1.51028I
a = −1.140130 + 0.820998I
b = −1.57759 − 0.41592I
c = 1.38502 + 2.89598I
d = 0.08526 + 2.95483I
−12.2320 − 15.1490I 0
u = −0.78943 + 1.61251I
a = −1.175700 + 0.706741I
b = −1.62479 − 0.37558I
c = −2.01798 − 2.64036I
d = −0.74497 − 2.73152I
−13.5026 − 8.6555I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.78943 − 1.61251I
a = −1.175700 − 0.706741I
b = −1.62479 + 0.37558I
c = −2.01798 + 2.64036I
d = −0.74497 + 2.73152I
−13.5026 + 8.6555I 0
u = −0.64330 + 1.72758I
a = −1.231740 + 0.552038I
b = −1.67606 − 0.30300I
c = 0.70493 + 3.45324I
d = −0.14309 + 3.02959I
−14.7932 − 7.9945I 0
u = −0.64330 − 1.72758I
a = −1.231740 − 0.552038I
b = −1.67606 + 0.30300I
c = 0.70493 − 3.45324I
d = −0.14309 − 3.02959I
−14.7932 + 7.9945I 0
u = 0.48873 + 1.82349I
a = −1.264400 − 0.401956I
b = −1.71830 + 0.22835I
c = −1.55696 + 3.30101I
d = −0.64880 + 2.90927I
−15.6167 + 1.2657I 0
u = 0.48873 − 1.82349I
a = −1.264400 + 0.401956I
b = −1.71830 − 0.22835I
c = −1.55696 − 3.30101I
d = −0.64880 − 2.90927I
−15.6167 − 1.2657I 0
11
II. I
u
2
= hu
3
a
2
+ 5u
3
a + · · · − 8a + 8, u
3
a
2
+ 3u
3
a + · · · − 4a + 4, −a
2
u
2
+
b + 2a − 2, 4u
3
a
2
− 6u
3
a + · · · + 3a − 1, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
5
=
a
a
2
u
2
− 2a + 2
a
8
=
u
u
a
2
=
a
−a
2
u
2
− u
2
a + 2a − 2
a
1
=
−a
2
u
2
− u
2
a + 3a − 2
−a
2
u
2
− u
2
a + 2a − 2
a
10
=
−u
3
a
2
− 3u
3
a − a
2
u + 2u
2
a + 2u
3
− 4au − 2u
2
+ 4a + 4u − 4
−u
3
a
2
− 5u
3
a − 2a
2
u + 4u
2
a + 4u
3
− 11au − 4u
2
+ 8a + 10u − 8
a
9
=
−2u
3
a − a
2
u + 2u
2
a + 2u
3
− 6au − 2u
2
+ 4a + 6u − 4
−4u
3
a − 2a
2
u + 4u
2
a + 4u
3
− 13au − 4u
2
+ 8a + 12u − 8
a
6
=
−2u
3
a − a
2
u + 2u
2
a + 2u
3
− 7au − 2u
2
+ 4a + 6u − 4
−4u
3
a − 2a
2
u + 4u
2
a + 4u
3
− 13au − 4u
2
+ 8a + 12u − 8
a
12
=
−u
3
a
2
+ a
2
u
2
− u
3
a − 2a
2
u + 4u
2
a + a
2
− 2au − 2u
2
+ 6a − 4
−u
3
a
2
− u
3
a − 2a
2
u + 3u
2
a + a
2
− 2au − 2u
2
+ 7a − 6
a
11
=
−u
3
a
2
+ a
2
u
2
− 2a
2
u + 3u
2
a + a
2
− 2u
2
+ 5a − 4
−2u
3
a
2
− 3u
3
a + ··· + 9a − 8
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 4u
2
− 12u + 6
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 8u
11
+ ··· − 10u + 1
c
2
, c
4
, c
6
c
8
u
12
− 4u
10
+ ··· + 2u + 1
c
3
, c
7
, c
10
c
12
(u
4
− u
3
+ 3u
2
− 2u + 1)
3
c
5
, c
11
(u
4
− u
3
+ u
2
+ 1)
3
c
9
u
12
− 8u
11
+ ··· + 10u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
12
− 8y
11
+ ··· − 78y + 1
c
2
, c
4
, c
6
c
8
y
12
− 8y
11
+ ··· + 10y + 1
c
3
, c
7
, c
10
c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
3
c
5
, c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
3
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = 0.837889 + 0.280931I
b = 0.072869 − 0.359716I
c = 0.394185 + 0.517164I
d = 0.577230 + 0.415041I
0.21101 + 1.41510I 1.82674 − 4.90874I
u = 0.395123 + 0.506844I
a = 0.492884 − 0.048733I
b = 1.009230 + 0.198659I
c = −1.39293 + 0.39378I
d = −2.82169 + 1.21168I
0.21101 + 1.41510I 1.82674 − 4.90874I
u = 0.395123 + 0.506844I
a = −2.51225 − 4.92832I
b = −1.082100 + 0.161058I
c = 0.20850 − 1.92463I
d = −0.459158 − 0.186039I
0.21101 + 1.41510I 1.82674 − 4.90874I
u = 0.395123 − 0.506844I
a = 0.837889 − 0.280931I
b = 0.072869 + 0.359716I
c = 0.394185 − 0.517164I
d = 0.577230 − 0.415041I
0.21101 − 1.41510I 1.82674 + 4.90874I
u = 0.395123 − 0.506844I
a = 0.492884 + 0.048733I
b = 1.009230 − 0.198659I
c = −1.39293 − 0.39378I
d = −2.82169 − 1.21168I
0.21101 − 1.41510I 1.82674 + 4.90874I
u = 0.395123 − 0.506844I
a = −2.51225 + 4.92832I
b = −1.082100 − 0.161058I
c = 0.20850 + 1.92463I
d = −0.459158 + 0.186039I
0.21101 − 1.41510I 1.82674 + 4.90874I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.10488 + 1.55249I
a = 0.439878 + 0.246240I
b = 0.730940 − 0.968963I
c = −1.56704 + 1.28737I
d = −0.641253 + 1.089290I
−6.79074 + 3.16396I −1.82674 − 2.56480I
u = 0.10488 + 1.55249I
a = 0.432622 − 0.214254I
b = 0.856215 + 0.919282I
c = 1.82916 + 0.51793I
d = 0.824626 + 0.377943I
−6.79074 + 3.16396I −1.82674 − 2.56480I
u = 0.10488 + 1.55249I
a = −1.69102 − 0.14308I
b = −1.58715 + 0.04968I
c = −0.47187 − 4.91028I
d = −0.47976 − 3.28982I
−6.79074 + 3.16396I −1.82674 − 2.56480I
u = 0.10488 − 1.55249I
a = 0.439878 − 0.246240I
b = 0.730940 + 0.968963I
c = −1.56704 − 1.28737I
d = −0.641253 − 1.089290I
−6.79074 − 3.16396I −1.82674 + 2.56480I
u = 0.10488 − 1.55249I
a = 0.432622 + 0.214254I
b = 0.856215 − 0.919282I
c = 1.82916 − 0.51793I
d = 0.824626 − 0.377943I
−6.79074 − 3.16396I −1.82674 + 2.56480I
u = 0.10488 − 1.55249I
a = −1.69102 + 0.14308I
b = −1.58715 − 0.04968I
c = −0.47187 + 4.91028I
d = −0.47976 + 3.28982I
−6.79074 − 3.16396I −1.82674 + 2.56480I
16
III. I
v
1
= hc, d − v − 1, b, a − 1, v
2
+ v + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
v
0
a
4
=
1
0
a
5
=
1
0
a
8
=
v
0
a
2
=
1
0
a
1
=
1
0
a
10
=
0
v + 1
a
9
=
v
v + 1
a
6
=
0
−v − 1
a
12
=
1
v
a
11
=
v + 1
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v + 7
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
u
2
c
5
, c
10
u
2
+ u + 1
c
6
(u + 1)
2
c
8
, c
9
(u − 1)
2
c
11
, c
12
u
2
− u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
y
2
c
5
, c
10
, c
11
c
12
y
2
+ y + 1
c
6
, c
8
, c
9
(y − 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−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
20
IV. I
v
2
= ha, d, c − v, b − 1, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
v
0
a
4
=
1
0
a
5
=
0
1
a
8
=
v
0
a
2
=
1
−1
a
1
=
0
−1
a
10
=
v
0
a
9
=
v
0
a
6
=
v
0
a
12
=
v − 1
−1
a
11
=
v − 1
−v
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 1
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
6
, c
7
c
8
, c
9
u
2
c
4
(u + 1)
2
c
5
, c
12
u
2
− u + 1
c
10
, c
11
u
2
+ u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
6
, c
7
c
8
, c
9
y
2
c
5
, c
10
, c
11
c
12
y
2
+ y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−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 −3.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 1.00000
c = 0.500000 − 0.866025I
d = 0
−1.64493 − 2.02988I −3.00000 + 3.46410I
24
V. I
v
3
= ha, d + 1, c + a, b − 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
1
0
a
4
=
1
0
a
5
=
0
1
a
8
=
1
0
a
2
=
1
−1
a
1
=
0
−1
a
10
=
0
−1
a
9
=
1
−1
a
6
=
0
1
a
12
=
0
−1
a
11
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
c
9
u − 1
c
3
, c
5
, c
7
c
10
, c
11
, c
12
u
c
4
, c
6
u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
8
, c
9
y − 1
c
3
, c
5
, c
7
c
10
, c
11
, c
12
y
27
(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
0 0
28
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
7
=
v
0
a
4
=
1
0
a
5
=
0
1
a
8
=
v
0
a
2
=
1
−1
a
1
=
0
−1
a
10
=
c
d
a
9
=
c + v
d
a
6
=
−c
−d
a
12
=
c − 1
dc − 1
a
11
=
c − 1
dc − c
(ii) Obstruction class = −1
(iii) Cusp Shapes = −d
2
− v
2
− 4c + 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.
29
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
− 2.02988I 2.25553 + 3.87325I
30
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 1)
3
(u
12
+ 8u
11
+ ··· − 10u + 1)
· (u
41
+ 50u
40
+ ··· + 8224u + 256)
c
2
u
2
(u − 1)
3
(u
12
− 4u
10
+ ··· + 2u + 1)(u
41
− 8u
40
+ ··· − 8u − 16)
c
3
, c
7
u
5
(u
4
− u
3
+ 3u
2
− 2u + 1)
3
(u
41
+ 2u
40
+ ··· − 512u
2
− 512)
c
4
u
2
(u + 1)
3
(u
12
− 4u
10
+ ··· + 2u + 1)(u
41
− 8u
40
+ ··· − 8u − 16)
c
5
, c
11
u(u
2
− u + 1)(u
2
+ u + 1)(u
4
− u
3
+ u
2
+ 1)
3
(u
41
− 2u
40
+ ··· + 16u − 4)
c
6
u
2
(u + 1)
3
(u
12
− 4u
10
+ ··· + 2u + 1)(u
41
+ 8u
40
+ ··· − 8u − 16)
c
8
u
2
(u − 1)
3
(u
12
− 4u
10
+ ··· + 2u + 1)(u
41
+ 8u
40
+ ··· − 8u − 16)
c
9
u
2
(u − 1)
3
(u
12
− 8u
11
+ ··· + 10u + 1)
· (u
41
− 10u
40
+ ··· + 2080u − 256)
c
10
u(u
2
+ u + 1)
2
(u
4
− u
3
+ 3u
2
− 2u + 1)
3
· (u
41
− 12u
40
+ ··· + 344u + 16)
c
12
u(u
2
− u + 1)
2
(u
4
− u
3
+ 3u
2
− 2u + 1)
3
· (u
41
− 12u
40
+ ··· + 344u + 16)
31
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y − 1)
3
(y
12
− 8y
11
+ ··· − 78y + 1)
· (y
41
− 110y
40
+ ··· + 25092608y − 65536)
c
2
, c
4
y
2
(y − 1)
3
(y
12
− 8y
11
+ ··· + 10y + 1)
· (y
41
− 50y
40
+ ··· + 8224y − 256)
c
3
, c
7
y
5
(y
4
+ 5y
3
+ ··· + 2y + 1)
3
(y
41
+ 30y
40
+ ··· − 524288y − 262144)
c
5
, c
11
y(y
2
+ y + 1)
2
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
3
· (y
41
+ 12y
40
+ ··· + 344y − 16)
c
6
, c
8
y
2
(y − 1)
3
(y
12
− 8y
11
+ ··· + 10y + 1)
· (y
41
− 10y
40
+ ··· + 2080y − 256)
c
9
y
2
(y − 1)
3
(y
12
− 8y
11
+ ··· − 78y + 1)
· (y
41
+ 50y
40
+ ··· − 663040y − 65536)
c
10
, c
12
y(y
2
+ y + 1)
2
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
3
· (y
41
+ 36y
40
+ ··· + 135968y − 256)
32
