12n
0518
(K12n
0518
)
A knot diagram
1
Linearized knot diagam
3 6 10 8 2 12 4 7 3 9 1 7
Solving Sequence
3,6
2 1
5,8
4 7 9 10 12 11
c
2
c
1
c
5
c
4
c
7
c
8
c
9
c
12
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
2
+ b + u − 1, u
4
− u
2
+ 2a + u + 1, u
5
− u
4
− u
3
+ 2u
2
+ 2u − 1i
I
u
2
= hu
6
a + u
5
a + u
6
+ u
4
a + u
5
− u
4
+ 4u
2
a − 2u
3
− au + 2u
2
+ 2b + u − 2,
4u
6
a + 2u
5
a − u
6
− 2u
4
a − 2u
3
a + 2u
4
+ 16u
2
a + u
3
+ 4a
2
− 2u
2
− 2a + u + 3, u
7
+ u
6
− u
4
+ 3u
3
+ u
2
− 1i
I
u
3
= h−898u
13
+ 485u
12
+ ··· + 11257b − 16952, −21137u
13
+ 40486u
12
+ ··· + 157598a − 1559,
u
14
− 3u
13
+ 2u
12
+ 8u
11
− 18u
10
+ 6u
9
+ 27u
8
− 40u
7
+ 5u
6
+ 37u
5
− 36u
4
+ 4u
3
+ 20u
2
− 18u + 7i
I
u
4
= h−u
3
+ b + u − 1, −u
2
+ 2a + u, u
4
− u
2
+ 2i
I
u
5
= h2a
3
− 2a
2
+ b + 5a − 3, 2a
4
− 2a
3
+ 5a
2
− 4a + 1, u + 1i
I
u
6
= h−u
6
+ 2u
5
− u
4
− 2u
2
+ 2b + 4, −u
7
+ 3u
6
− 4u
5
+ 3u
4
− 3u
3
+ 2u
2
+ 2a + 2u − 2,
u
8
− 2u
7
+ 2u
6
+ u
4
− 2u
2
+ 2u + 2i
I
u
7
= hu
4
+ u
3
+ b − u, −2u
5
− 4u
4
− 3u
3
+ u
2
+ a + 2u − 3, u
6
+ u
5
− 2u
3
+ 2u − 1i
I
u
8
= h2u
5
+ 3u
4
+ 2u
3
− 2u
2
+ b − 2u + 2, 4u
5
+ 6u
4
+ 4u
3
− 5u
2
+ a − 2u + 5, u
6
+ u
5
− 2u
3
+ 2u − 1i
I
u
9
= hb − 5u − 6, 2a − 5, u
2
+ 2u + 1i
I
u
10
= hb + u, 2a + 3, u
2
+ 2u + 1i
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).
1
I
u
11
= hb, a + 1, u − 1i
I
u
12
= hu
3
+ b − u + 1, −u
3
+ u
2
+ 2a − u + 1, u
4
+ 1i
I
u
13
= h2a
3
+ 4a
2
+ b + 6a + 3, 2a
4
+ 4a
3
+ 6a
2
+ 4a + 1, u − 1i
I
u
14
= hb − 1, u + 1i
I
v
1
= ha, b + 1, v + 1i
* 14 irreducible components of dim
C
= 0, with total 75 representations.
* 1 irreducible components of dim
C
= 1
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= hu
2
+ b + u − 1, u
4
− u
2
+ 2a + u + 1, u
5
− u
4
− u
3
+ 2u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
8
=
−
1
2
u
4
+
1
2
u
2
−
1
2
u −
1
2
−u
2
− u + 1
a
4
=
1
2
u
4
−
1
2
u
2
+
1
2
u +
1
2
u
2
a
7
=
−u
u
3
− u
2
− u + 1
a
9
=
−
1
2
u
4
+ u
3
+
1
2
u
2
−
1
2
u −
1
2
u
a
10
=
−
1
2
u
4
+ u
3
+
1
2
u
2
−
3
2
u −
1
2
u
a
12
=
1
−u
4
+ u
3
− u
a
11
=
u
4
− u
2
+ 1
u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
4
− 4u
3
+ 6u
2
+ 2u − 16
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
c
11
u
5
+ 3u
4
+ 9u
3
+ 10u
2
+ 8u + 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
12
u
5
+ u
4
− u
3
− 2u
2
+ 2u + 1
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
c
11
y
5
+ 9y
4
+ 37y
3
+ 38y
2
+ 44y −1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
12
y
5
− 3y
4
+ 9y
3
− 10y
2
+ 8y −1
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.937261 + 0.495129I
a = 0.515459 − 0.123840I
b = 1.303956 + 0.433001I
−2.12840 + 7.92450I −14.4593 − 11.6636I
u = −0.937261 − 0.495129I
a = 0.515459 + 0.123840I
b = 1.303956 − 0.433001I
−2.12840 − 7.92450I −14.4593 + 11.6636I
u = 1.24407 + 0.86929I
a = 1.29939 − 1.06631I
b = −1.03612 − 3.03218I
8.2190 − 15.4874I −13.2819 + 8.0512I
u = 1.24407 − 0.86929I
a = 1.29939 + 1.06631I
b = −1.03612 + 3.03218I
8.2190 + 15.4874I −13.2819 − 8.0512I
u = 0.386387
a = −0.629690
b = 0.464319
−0.666621 −14.5180
6
II.
I
u
2
= hu
6
a+u
6
+· · ·+2b−2, 4u
6
a−u
6
+· · ·−2a+3, u
7
+u
6
−u
4
+3u
3
+u
2
−1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
8
=
a
−
1
2
u
6
a −
1
2
u
6
+ ··· −
1
2
u + 1
a
4
=
−a
−
1
2
u
6
−
1
2
u
5
+ ··· −
1
2
u + 1
a
7
=
−u
1
2
u
5
+
1
2
u
4
+
1
2
u
3
+ u +
1
2
a
9
=
−
1
2
u
6
−
1
2
u
5
+ ··· + a +
1
2
u
1
2
u
5
a +
1
2
u
4
a + ··· +
1
2
a + 1
a
10
=
−
1
2
u
5
a −
1
2
u
6
+ ··· +
1
2
a − 1
1
2
u
5
a +
1
2
u
4
a + ··· +
1
2
a + 1
a
12
=
1
−
1
2
u
6
−
1
2
u
5
+ ··· − 2u
2
−
1
2
u
a
11
=
u
4
− u
2
+ 1
−
1
2
u
6
−
1
2
u
5
+ ··· − 2u
2
−
1
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
6
+ u
5
− u
4
− u
3
+ 10u
2
− 13
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
7
+ u
6
+ 8u
5
+ 3u
4
+ 13u
3
+ 3u
2
+ 2u + 1)
2
c
2
, c
5
, c
6
c
12
(u
7
− u
6
+ u
4
+ 3u
3
− u
2
+ 1)
2
c
3
, c
4
, c
7
c
9
u
14
+ 3u
13
+ ··· + 18u + 7
c
8
, c
10
u
14
+ 5u
13
+ ··· + 44u + 49
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
7
+ 15y
6
+ 84y
5
+ 197y
4
+ 181y
3
+ 37y
2
− 2y −1)
2
c
2
, c
5
, c
6
c
12
(y
7
− y
6
+ 8y
5
− 3y
4
+ 13y
3
− 3y
2
+ 2y −1)
2
c
3
, c
4
, c
7
c
9
y
14
− 5y
13
+ ··· − 44y + 49
c
8
, c
10
y
14
+ 7y
13
+ ··· + 1984y + 2401
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.828738 + 0.848640I
a = 0.011269 − 1.123254I
b = −0.970381 − 0.889581I
0.10917 − 5.13113I −11.29789 + 5.71003I
u = 0.828738 + 0.848640I
a = −0.395708 − 0.325161I
b = −1.78580 + 0.85701I
0.10917 − 5.13113I −11.29789 + 5.71003I
u = 0.828738 − 0.848640I
a = 0.011269 + 1.123254I
b = −0.970381 + 0.889581I
0.10917 + 5.13113I −11.29789 − 5.71003I
u = 0.828738 − 0.848640I
a = −0.395708 + 0.325161I
b = −1.78580 − 0.85701I
0.10917 + 5.13113I −11.29789 − 5.71003I
u = −0.441920 + 0.538118I
a = 0.251395 − 0.220170I
b = 1.71953 + 0.74035I
−3.48230 + 1.31889I −13.8490 − 4.9720I
u = −0.441920 + 0.538118I
a = 0.57883 + 2.23056I
b = −1.22991 + 1.18628I
−3.48230 + 1.31889I −13.8490 − 4.9720I
u = −0.441920 − 0.538118I
a = 0.251395 + 0.220170I
b = 1.71953 − 0.74035I
−3.48230 − 1.31889I −13.8490 + 4.9720I
u = −0.441920 − 0.538118I
a = 0.57883 − 2.23056I
b = −1.22991 − 1.18628I
−3.48230 − 1.31889I −13.8490 + 4.9720I
u = 0.610544
a = −0.451001 + 0.791376I
b = 0.811414 − 0.457455I
−0.187091 −9.45050
u = 0.610544
a = −0.451001 − 0.791376I
b = 0.811414 + 0.457455I
−0.187091 −9.45050
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.19209 + 0.98985I
a = 0.978445 + 0.731013I
b = −1.01911 + 1.81521I
10.04640 + 7.93647I −11.12788 − 4.07397I
u = −1.19209 + 0.98985I
a = −0.97323 − 1.05400I
b = 0.97426 − 2.78584I
10.04640 + 7.93647I −11.12788 − 4.07397I
u = −1.19209 − 0.98985I
a = 0.978445 − 0.731013I
b = −1.01911 − 1.81521I
10.04640 − 7.93647I −11.12788 + 4.07397I
u = −1.19209 − 0.98985I
a = −0.97323 + 1.05400I
b = 0.97426 + 2.78584I
10.04640 − 7.93647I −11.12788 + 4.07397I
11
III. I
u
3
= h−898u
13
+ 485u
12
+ · · · + 11257b − 16952, −21137u
13
+
40486u
12
+ · · · + 157598a − 1559, u
14
− 3u
13
+ · · · − 18u + 7i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
8
=
0.134120u
13
− 0.256894u
12
+ ··· + 0.0964923u + 0.00989226
0.0797726u
13
− 0.0430843u
12
+ ··· − 0.739362u + 1.50591
a
4
=
−0.101099u
13
+ 0.186881u
12
+ ··· + 0.264020u + 0.00957499
−0.0945190u
13
+ 0.218087u
12
+ ··· − 0.422404u − 0.107222
a
7
=
0.0552672u
13
+ 0.00848996u
12
+ ··· − 0.694070u − 0.311768
−0.0875899u
13
+ 0.437061u
12
+ ··· − 3.55121u + 2.25966
a
9
=
0.111772u
13
− 0.408203u
12
+ ··· + 3.58886u − 2.27231
0.0421071u
13
− 0.0539220u
12
+ ··· + 0.678778u − 0.0781736
a
10
=
0.0696646u
13
− 0.354281u
12
+ ··· + 2.91008u − 2.19413
0.0421071u
13
− 0.0539220u
12
+ ··· + 0.678778u − 0.0781736
a
12
=
−0.322809u
13
+ 0.880836u
12
+ ··· − 4.38369u + 1.25934
−1
a
11
=
−0.357987u
13
+ 1.15373u
12
+ ··· − 7.19127u + 2.70440
−0.209470u
13
+ 0.534068u
12
+ ··· − 3.49063u + 0.831927
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
3768
11257
u
13
+
10810
11257
u
12
+ ··· +
4236
11257
u −
140628
11257
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
14
+ 5u
13
+ ··· + 44u + 49
c
2
, c
5
, c
6
c
12
u
14
+ 3u
13
+ ··· + 18u + 7
c
3
, c
4
, c
7
c
9
(u
7
− u
6
+ u
4
+ 3u
3
− u
2
+ 1)
2
c
8
, c
10
(u
7
+ u
6
+ 8u
5
+ 3u
4
+ 13u
3
+ 3u
2
+ 2u + 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
14
+ 7y
13
+ ··· + 1984y + 2401
c
2
, c
5
, c
6
c
12
y
14
− 5y
13
+ ··· − 44y + 49
c
3
, c
4
, c
7
c
9
(y
7
− y
6
+ 8y
5
− 3y
4
+ 13y
3
− 3y
2
+ 2y −1)
2
c
8
, c
10
(y
7
+ 15y
6
+ 84y
5
+ 197y
4
+ 181y
3
+ 37y
2
− 2y −1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.055750 + 0.340120I
a = 1.06312 + 0.98114I
b = −0.175488 + 0.424946I
−3.48230 + 1.31889I −13.8490 − 4.9720I
u = −1.055750 − 0.340120I
a = 1.06312 − 0.98114I
b = −0.175488 − 0.424946I
−3.48230 − 1.31889I −13.8490 + 4.9720I
u = 0.668117 + 0.582359I
a = 0.124005 + 0.615095I
b = 1.10865
−0.187091 −9.45047 + 0.I
u = 0.668117 − 0.582359I
a = 0.124005 − 0.615095I
b = 1.10865
−0.187091 −9.45047 + 0.I
u = 1.177859 + 0.244275I
a = 0.045270 + 0.188069I
b = −0.175488 + 0.424946I
−3.48230 + 1.31889I −13.8490 − 4.9720I
u = 1.177859 − 0.244275I
a = 0.045270 − 0.188069I
b = −0.175488 − 0.424946I
−3.48230 − 1.31889I −13.8490 + 4.9720I
u = 0.251958 + 0.745305I
a = −0.750002 − 0.183784I
b = 0.171189 − 0.644973I
0.10917 − 5.13113I −11.29789 + 5.71003I
u = 0.251958 − 0.745305I
a = −0.750002 + 0.183784I
b = 0.171189 + 0.644973I
0.10917 + 5.13113I −11.29789 − 5.71003I
u = −1.302132 + 0.252907I
a = −0.579931 − 0.820184I
b = 0.171189 + 0.644973I
0.10917 + 5.13113I −11.29789 − 5.71003I
u = −1.302132 − 0.252907I
a = −0.579931 + 0.820184I
b = 0.171189 − 0.644973I
0.10917 − 5.13113I −11.29789 + 5.71003I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.70316 + 1.23343I
a = 0.94800 − 1.24603I
b = −0.05002 − 3.09525I
10.04640 + 7.93647I −11.12788 − 4.07397I
u = 0.70316 − 1.23343I
a = 0.94800 + 1.24603I
b = −0.05002 + 3.09525I
10.04640 − 7.93647I −11.12788 + 4.07397I
u = 1.05678 + 1.07858I
a = −0.921887 + 0.849036I
b = −0.05002 + 3.09525I
10.04640 − 7.93647I −11.12788 + 4.07397I
u = 1.05678 − 1.07858I
a = −0.921887 − 0.849036I
b = −0.05002 − 3.09525I
10.04640 + 7.93647I −11.12788 − 4.07397I
16
IV. I
u
4
= h−u
3
+ b + u − 1, −u
2
+ 2a + u, u
4
− u
2
+ 2i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
8
=
1
2
u
2
−
1
2
u
u
3
− u + 1
a
4
=
1
2
u
2
+
1
2
u
1
a
7
=
−u
u
3
− u
a
9
=
1
2
u
2
+
1
2
u
1
a
10
=
1
2
u
2
+
1
2
u − 1
1
a
12
=
1
−u
2
+ 2
a
11
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 20
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
2
− u + 2)
2
c
2
, c
5
, c
6
c
12
u
4
− u
2
+ 2
c
3
, c
7
(u − 1)
4
c
4
, c
8
, c
9
c
10
(u + 1)
4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
2
+ 3y + 4)
2
c
2
, c
5
, c
6
c
12
(y
2
− y + 2)
2
c
3
, c
4
, c
7
c
8
, c
9
, c
10
(y −1)
4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.978318 + 0.676097I
a = −0.239159 + 0.323389I
b = −0.383551 + 0.956145I
−2.46740 − 5.33349I −18.0000 + 5.2915I
u = 0.978318 − 0.676097I
a = −0.239159 − 0.323389I
b = −0.383551 − 0.956145I
−2.46740 + 5.33349I −18.0000 − 5.2915I
u = −0.978318 + 0.676097I
a = 0.739159 − 0.999486I
b = 2.38355 + 0.95615I
−2.46740 + 5.33349I −18.0000 − 5.2915I
u = −0.978318 − 0.676097I
a = 0.739159 + 0.999486I
b = 2.38355 − 0.95615I
−2.46740 − 5.33349I −18.0000 + 5.2915I
20
V. I
u
5
= h2a
3
− 2a
2
+ b + 5a − 3, 2a
4
− 2a
3
+ 5a
2
− 4a + 1, u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
−1
a
2
=
1
−1
a
1
=
0
−1
a
5
=
−1
0
a
8
=
a
−2a
3
+ 2a
2
− 5a + 3
a
4
=
−a
−4a
3
+ 2a
2
− 8a + 4
a
7
=
1
2a
3
+ 5a − 1
a
9
=
4a
3
− 2a
2
+ 9a − 4
2a
3
− 2a
2
+ 5a − 3
a
10
=
2a
3
+ 4a − 1
2a
3
− 2a
2
+ 5a − 3
a
12
=
−1
−2a
3
− 5a
a
11
=
−1
−2a
3
− 5a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −16a
3
+ 8a
2
− 32a − 4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
11
c
12
(u − 1)
4
c
2
, c
6
(u + 1)
4
c
3
, c
4
, c
7
c
9
u
4
− u
2
+ 2
c
8
, c
10
(u
2
+ u + 2)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
4
c
3
, c
4
, c
7
c
9
(y
2
− y + 2)
2
c
8
, c
10
(y
2
+ 3y + 4)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.04738 + 1.47756I
b = −0.978318 − 0.676097I
−2.46740 − 5.33349I −18.0000 + 5.2915I
u = −1.00000
a = 0.04738 − 1.47756I
b = −0.978318 + 0.676097I
−2.46740 + 5.33349I −18.0000 − 5.2915I
u = −1.00000
a = 0.452616 + 0.154683I
b = 0.978318 − 0.676097I
−2.46740 + 5.33349I −18.0000 − 5.2915I
u = −1.00000
a = 0.452616 − 0.154683I
b = 0.978318 + 0.676097I
−2.46740 − 5.33349I −18.0000 + 5.2915I
24
VI. I
u
6
= h−u
6
+ 2u
5
− u
4
− 2u
2
+ 2b + 4, −u
7
+ 3u
6
+ · · · + 2a − 2, u
8
−
2u
7
+ 2u
6
+ u
4
− 2u
2
+ 2u + 2i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
8
=
1
2
u
7
−
3
2
u
6
+ ··· − u + 1
1
2
u
6
− u
5
+
1
2
u
4
+ u
2
− 2
a
4
=
−
1
2
u
7
+
3
2
u
6
+ ··· + u − 1
1
2
u
7
−
3
2
u
6
+ ··· − u
2
+ 2
a
7
=
−u
1
2
u
7
− u
6
+
3
2
u
5
− u
4
+ 2u
3
− u
2
a
9
=
1
2
u
5
− u
4
+
1
2
u
3
1
2
u
7
− u
6
+
3
2
u
5
− u
4
+ u
3
− u + 1
a
10
=
−
1
2
u
7
+ u
6
− u
5
−
1
2
u
3
+ u − 1
1
2
u
7
− u
6
+
3
2
u
5
− u
4
+ u
3
− u + 1
a
12
=
1
−
1
2
u
6
+ u
5
−
3
2
u
4
+ u
3
− 2u
2
+ u + 1
a
11
=
u
4
− u
2
+ 1
−
1
2
u
6
+ u
5
−
1
2
u
4
+ u
3
− 2u
2
+ u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
7
− 2u
6
+ 3u
5
− 2u
4
+ 4u
3
− 2u
2
− 8
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
c
11
u
8
+ 6u
6
+ 5u
4
− 4u
3
+ 8u
2
+ 12u + 4
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
12
u
8
+ 2u
7
+ 2u
6
+ u
4
− 2u
2
− 2u + 2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
c
11
y
8
+ 12y
7
+ 46y
6
+ 76y
5
+ 129y
4
+ 112y
3
+ 200y
2
− 80y + 16
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
12
y
8
+ 6y
6
+ 5y
4
+ 4y
3
+ 8y
2
− 12y + 4
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.358336 + 1.049708I
a = −0.208739 − 0.611478I
b = −0.743190 − 0.752297I
3.87851 −7.20933 + 0.I
u = −0.358336 − 1.049708I
a = −0.208739 + 0.611478I
b = −0.743190 + 0.752297I
3.87851 −7.20933 + 0.I
u = 1.001167 + 0.618491I
a = −0.557384 − 0.409315I
b = −1.16144 + 0.94397I
−1.22898 − 4.85117I −10.92071 + 2.27864I
u = 1.001167 − 0.618491I
a = −0.557384 + 0.409315I
b = −1.16144 − 0.94397I
−1.22898 + 4.85117I −10.92071 − 2.27864I
u = −0.696290 + 0.136038I
a = 0.217827 + 1.126200I
b = −1.314927 − 0.483896I
−1.22898 − 4.85117I −10.92071 + 2.27864I
u = −0.696290 − 0.136038I
a = 0.217827 − 1.126200I
b = −1.314927 + 0.483896I
−1.22898 + 4.85117I −10.92071 − 2.27864I
u = 1.05346 + 1.10563I
a = −0.951704 + 0.998833I
b = 1.21955 + 2.32947I
10.0940 −10.94925 + 0.I
u = 1.05346 − 1.10563I
a = −0.951704 − 0.998833I
b = 1.21955 − 2.32947I
10.0940 −10.94925 + 0.I
28
VII.
I
u
7
= hu
4
+u
3
+b−u, −2u
5
−4u
4
−3u
3
+u
2
+a+2u−3, u
6
+u
5
−2u
3
+2u−1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
8
=
2u
5
+ 4u
4
+ 3u
3
− u
2
− 2u + 3
−u
4
− u
3
+ u
a
4
=
4u
5
+ 6u
4
+ 4u
3
− 5u
2
− 2u + 5
u
2
a
7
=
−2u
5
− 3u
4
− 2u
3
+ 3u
2
+ 2u − 3
−u
5
− 2u
4
− 2u
3
+ u
2
+ 2u − 1
a
9
=
4u
5
+ 8u
4
+ 6u
3
− 4u
2
− 4u + 6
u
a
10
=
4u
5
+ 8u
4
+ 6u
3
− 4u
2
− 5u + 6
u
a
12
=
−u
5
− 2u
4
− 2u
3
+ u − 1
−1
a
11
=
−2u
5
− 4u
4
− 2u
3
+ 2u
2
+ u − 2
u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
c
11
u
6
+ u
5
+ 4u
4
+ 10u
3
+ 8u
2
+ 4u + 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
12
u
6
− u
5
+ 2u
3
− 2u − 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
c
11
y
6
+ 7y
5
+ 12y
4
− 42y
3
− 8y
2
+ 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
12
y
6
− y
5
+ 4y
4
− 10y
3
+ 8y
2
− 4y + 1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −1.14526
a = 2.41334
b = −1.36347
−5.87476 −10.0000
u = 0.623490 + 0.407699I
a = 0.044073 + 0.916092I
b = 0.900969 − 0.226256I
−0.234991 −10.0000
u = 0.623490 − 0.407699I
a = 0.044073 − 0.916092I
b = 0.900969 + 0.226256I
−0.234991 −10.0000
u = 0.700221
a = 3.43751
b = 0.116492
−5.87476 −10.0000
u = −0.90097 + 1.19801I
a = −0.969501 − 0.960732I
b = 0.22252 − 2.69191I
11.0446 −10.0000
u = −0.90097 − 1.19801I
a = −0.969501 + 0.960732I
b = 0.22252 + 2.69191I
11.0446 −10.0000
32
VIII. I
u
8
= h2u
5
+ 3u
4
+ 2u
3
− 2u
2
+ b − 2u + 2, 4u
5
+ 6u
4
+ 4u
3
− 5u
2
+ a −
2u + 5, u
6
+ u
5
− 2u
3
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
8
=
−4u
5
− 6u
4
− 4u
3
+ 5u
2
+ 2u − 5
−2u
5
− 3u
4
− 2u
3
+ 2u
2
+ 2u − 2
a
4
=
2u
5
+ 4u
4
+ 3u
3
− 2u
2
− 2u + 4
u
5
+ 2u
4
+ u
3
− 2u
2
− u + 2
a
7
=
−2u
5
− 3u
4
− 2u
3
+ 3u
2
+ 2u − 3
−u
5
− 2u
4
− 2u
3
+ u
2
+ 2u − 1
a
9
=
−3u
5
− 5u
4
− 4u
3
+ 4u
2
+ 2u − 4
−u
5
− 2u
4
− 2u
3
+ u
2
+ u − 1
a
10
=
−2u
5
− 3u
4
− 2u
3
+ 3u
2
+ u − 3
−u
5
− 2u
4
− 2u
3
+ u
2
+ u − 1
a
12
=
−u
5
− 2u
4
− 2u
3
+ u − 1
−1
a
11
=
−2u
5
− 4u
4
− 2u
3
+ 2u
2
+ u − 2
u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
c
11
u
6
+ u
5
+ 4u
4
+ 10u
3
+ 8u
2
+ 4u + 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
12
u
6
− u
5
+ 2u
3
− 2u − 1
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
c
11
y
6
+ 7y
5
+ 12y
4
− 42y
3
− 8y
2
+ 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
12
y
6
− y
5
+ 4y
4
− 10y
3
+ 8y
2
− 4y + 1
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −1.14526
a = 2.83514
b = 0.116492
−5.87476 −10.0000
u = 0.623490 + 0.407699I
a = −0.222521 + 0.145506I
b = 0.900969 + 0.226256I
−0.234991 −10.0000
u = 0.623490 − 0.407699I
a = −0.222521 − 0.145506I
b = 0.900969 − 0.226256I
−0.234991 −10.0000
u = 0.700221
a = −4.63708
b = −1.36347
−5.87476 −10.0000
u = −0.90097 + 1.19801I
a = 0.623490 + 0.829051I
b = 0.22252 + 2.69191I
11.0446 −10.0000
u = −0.90097 − 1.19801I
a = 0.623490 − 0.829051I
b = 0.22252 − 2.69191I
11.0446 −10.0000
36
IX. I
u
9
= hb − 5u − 6, 2a − 5, u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
2u + 1
a
1
=
2u + 2
2u + 1
a
5
=
u
−2u − 2
a
8
=
2.5
5u + 6
a
4
=
−
3
2
u
2u + 3
a
7
=
3u + 4
4u + 4
a
9
=
−u +
1
2
u + 2
a
10
=
−2u −
3
2
u + 2
a
12
=
−2u − 3
−2u − 3
a
11
=
−4u − 5
−2u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
11
, c
12
(u − 1)
2
c
2
, c
4
, c
6
c
8
, c
9
, c
10
(u + 1)
2
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
(y −1)
2
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 2.50000
b = 1.00000
−6.57974 −24.0000
u = −1.00000
a = 2.50000
b = 1.00000
−6.57974 −24.0000
40
X. I
u
10
= hb + u, 2a + 3, u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
2u + 1
a
1
=
2u + 2
2u + 1
a
5
=
u
−2u − 2
a
8
=
−1.5
−u
a
4
=
−
1
2
u − 3
−2u − 1
a
7
=
3u + 4
0
a
9
=
−5u −
15
2
−u
a
10
=
−4u −
15
2
−u
a
12
=
−2u − 3
2u + 1
a
11
=
−4u − 5
2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24
41
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
11
, c
12
(u − 1)
2
c
2
, c
4
, c
6
c
8
, c
9
, c
10
(u + 1)
2
42
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
(y −1)
2
43
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.50000
b = 1.00000
−6.57974 −24.0000
u = −1.00000
a = −1.50000
b = 1.00000
−6.57974 −24.0000
44
XI. I
u
11
= hb, a + 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
5
=
1
0
a
8
=
−1
0
a
4
=
1
0
a
7
=
−1
0
a
9
=
−1
0
a
10
=
−1
0
a
12
=
−1
−1
a
11
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
45
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
11
u − 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
u
c
5
, c
12
u + 1
46
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
y −1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
y
47
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 0
−3.28987 −12.0000
48
XII. I
u
12
= hu
3
+ b − u + 1, −u
3
+ u
2
+ 2a − u + 1, u
4
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
8
=
1
2
u
3
−
1
2
u
2
+
1
2
u −
1
2
−u
3
+ u − 1
a
4
=
−
1
2
u
3
+
1
2
u
2
+
1
2
u +
1
2
1
a
7
=
u
−u
3
+ u
a
9
=
1
2
u
3
−
1
2
u
2
−
1
2
u −
1
2
−1
a
10
=
1
2
u
3
−
1
2
u
2
−
1
2
u +
1
2
−1
a
12
=
−u
2
−1
a
11
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −16
49
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
2
+ 1)
2
c
2
, c
5
, c
6
c
12
u
4
+ 1
c
3
, c
7
, c
8
c
10
(u + 1)
4
c
4
, c
9
(u − 1)
4
50
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y + 1)
4
c
2
, c
5
, c
6
c
12
(y
2
+ 1)
2
c
3
, c
4
, c
7
c
8
, c
9
, c
10
(y −1)
4
51
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707107 + 0.707107I
a = −0.500000 + 0.207107I
b = 0.414214
−1.64493 −16.0000
u = 0.707107 − 0.707107I
a = −0.500000 − 0.207107I
b = 0.414214
−1.64493 −16.0000
u = −0.707107 + 0.707107I
a = −0.500000 + 1.207107I
b = −2.41421
−1.64493 −16.0000
u = −0.707107 − 0.707107I
a = −0.500000 − 1.207107I
b = −2.41421
−1.64493 −16.0000
52
XIII. I
u
13
= h2a
3
+ 4a
2
+ b + 6a + 3, 2a
4
+ 4a
3
+ 6a
2
+ 4a + 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
5
=
1
0
a
8
=
a
−2a
3
− 4a
2
− 6a − 3
a
4
=
−a
−4a
3
− 6a
2
− 8a − 3
a
7
=
−1
−2a
2
− 2a − 2
a
9
=
4a
3
+ 6a
2
+ 9a + 3
2a
3
+ 2a
2
+ 4a + 1
a
10
=
2a
3
+ 4a
2
+ 5a + 2
2a
3
+ 2a
2
+ 4a + 1
a
12
=
−1
−2a
2
− 2a − 3
a
11
=
−1
−2a
2
− 2a − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −16
53
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
11
(u − 1)
4
c
3
, c
4
, c
7
c
9
u
4
+ 1
c
5
, c
12
(u + 1)
4
c
8
, c
10
(u
2
+ 1)
2
54
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
4
c
3
, c
4
, c
7
c
9
(y
2
+ 1)
2
c
8
, c
10
(y + 1)
4
55
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
13
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.500000 + 1.207107I
b = 0.707107 − 0.707107I
−1.64493 −16.0000
u = 1.00000
a = −0.500000 − 1.207107I
b = 0.707107 + 0.707107I
−1.64493 −16.0000
u = 1.00000
a = −0.500000 + 0.207107I
b = −0.707107 − 0.707107I
−1.64493 −16.0000
u = 1.00000
a = −0.500000 − 0.207107I
b = −0.707107 + 0.707107I
−1.64493 −16.0000
56
XIV. I
u
14
= hb − 1, u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
−1
a
2
=
1
−1
a
1
=
0
−1
a
5
=
−1
0
a
8
=
a
1
a
4
=
a − 1
1
a
7
=
1
0
a
9
=
a − 1
1
a
10
=
a − 2
1
a
12
=
−1
−1
a
11
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24
(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.
57
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
14
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
−6.57974 −24.0000
58
XV. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
−1
0
a
2
=
1
0
a
1
=
1
0
a
5
=
−1
0
a
8
=
0
−1
a
4
=
−1
1
a
7
=
−1
0
a
9
=
1
−1
a
10
=
2
−1
a
12
=
1
0
a
11
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
59
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
u
c
3
, c
7
, c
8
c
10
u + 1
c
4
, c
9
u − 1
60
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
y
c
3
, c
4
, c
7
c
8
, c
9
, c
10
y −1
61
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
−3.28987 −12.0000
62
XVI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
u(u − 1)
13
(u
2
+ 1)
2
(u
2
− u + 2)
2
(u
5
+ 3u
4
+ 9u
3
+ 10u
2
+ 8u + 1)
· (u
6
+ u
5
+ 4u
4
+ 10u
3
+ 8u
2
+ 4u + 1)
2
· (u
7
+ u
6
+ 8u
5
+ 3u
4
+ 13u
3
+ 3u
2
+ 2u + 1)
2
· (u
8
+ 6u
6
+ ··· + 12u + 4)(u
14
+ 5u
13
+ ··· + 44u + 49)
c
2
, c
4
, c
6
c
9
u(u − 1)
5
(u + 1)
8
(u
4
+ 1)(u
4
− u
2
+ 2)(u
5
+ u
4
+ ··· + 2u + 1)
· (u
6
− u
5
+ 2u
3
− 2u − 1)
2
(u
7
− u
6
+ u
4
+ 3u
3
− u
2
+ 1)
2
· (u
8
+ 2u
7
+ 2u
6
+ u
4
− 2u
2
− 2u + 2)(u
14
+ 3u
13
+ ··· + 18u + 7)
c
3
, c
5
, c
7
c
12
u(u − 1)
8
(u + 1)
5
(u
4
+ 1)(u
4
− u
2
+ 2)(u
5
+ u
4
+ ··· + 2u + 1)
· (u
6
− u
5
+ 2u
3
− 2u − 1)
2
(u
7
− u
6
+ u
4
+ 3u
3
− u
2
+ 1)
2
· (u
8
+ 2u
7
+ 2u
6
+ u
4
− 2u
2
− 2u + 2)(u
14
+ 3u
13
+ ··· + 18u + 7)
c
8
, c
10
u(u + 1)
13
(u
2
+ 1)
2
(u
2
+ u + 2)
2
(u
5
+ 3u
4
+ 9u
3
+ 10u
2
+ 8u + 1)
· (u
6
+ u
5
+ 4u
4
+ 10u
3
+ 8u
2
+ 4u + 1)
2
· (u
7
+ u
6
+ 8u
5
+ 3u
4
+ 13u
3
+ 3u
2
+ 2u + 1)
2
· (u
8
+ 6u
6
+ ··· + 12u + 4)(u
14
+ 5u
13
+ ··· + 44u + 49)
63
XVII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
c
11
y(y − 1)
13
(y + 1)
4
(y
2
+ 3y + 4)
2
(y
5
+ 9y
4
+ ··· + 44y −1)
· (y
6
+ 7y
5
+ 12y
4
− 42y
3
− 8y
2
+ 1)
2
· (y
7
+ 15y
6
+ 84y
5
+ 197y
4
+ 181y
3
+ 37y
2
− 2y −1)
2
· (y
8
+ 12y
7
+ 46y
6
+ 76y
5
+ 129y
4
+ 112y
3
+ 200y
2
− 80y + 16)
· (y
14
+ 7y
13
+ ··· + 1984y + 2401)
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
12
y(y − 1)
13
(y
2
+ 1)
2
(y
2
− y + 2)
2
(y
5
− 3y
4
+ 9y
3
− 10y
2
+ 8y −1)
· (y
6
− y
5
+ 4y
4
− 10y
3
+ 8y
2
− 4y + 1)
2
· (y
7
− y
6
+ 8y
5
− 3y
4
+ 13y
3
− 3y
2
+ 2y −1)
2
· (y
8
+ 6y
6
+ ··· − 12y + 4)(y
14
− 5y
13
+ ··· − 44y + 49)
64
