12n
0838
(K12n
0838
)
A knot diagram
1
Linearized knot diagam
4 12 6 1 8 12 3 1 4 8 3 10
Solving Sequence
1,4 5,9
10 8 6 3 12 7 2 11
c
4
c
9
c
8
c
5
c
3
c
12
c
6
c
2
c
11
c
1
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −2u
3
+ u
2
+ 3a − 10u − 1, u
4
+ 4u
2
+ 3u + 1i
I
u
2
= hb + u, −u
5
− 3u
3
+ u
2
+ 2a + 3u − 2, u
6
+ 4u
4
− u
3
+ 2u
2
+ u + 1i
I
u
3
= h−25u
7
+ 373u
6
− 939u
5
+ 3197u
4
− 5553u
3
+ 8389u
2
+ 2846b − 5460u + 4816,
306u
7
+ 1468u
6
− 1769u
5
+ 14032u
4
− 19745u
3
+ 37228u
2
+ 36998a − 6881u + 6624,
u
8
− 2u
7
+ 11u
6
− 16u
5
+ 43u
4
− 34u
3
+ 70u
2
− 12u + 52i
I
u
4
= hb + u, u
2
+ a + 1, u
4
+ 2u
2
+ u + 1i
I
u
5
= hb − u, 11u
9
+ 7u
8
+ 80u
7
+ 17u
6
+ 144u
5
− 42u
4
+ 13u
3
− 51u
2
+ 4a + 22u − 13,
u
10
+ 7u
8
− 3u
7
+ 13u
6
− 12u
5
+ 5u
4
− 6u
3
+ 5u
2
− 3u + 1i
I
u
6
= hb + u + 1, a + 1, u
2
+ u + 1i
I
u
7
= hb + u + 1, a + u, u
2
+ u + 1i
I
u
8
= hb − u + 1, 3a − 2u + 2, u
2
− u + 3i
I
u
9
= hb + u − 1, a, u
2
− u + 1i
I
u
10
= hb, a − 1, u
2
+ u + 1i
I
v
1
= ha, b
2
− b + 1, v −1i
* 11 irreducible components of dim
C
= 0, with total 44 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
1
I. I
u
1
= hb − u, −2u
3
+ u
2
+ 3a − 10u − 1, u
4
+ 4u
2
+ 3u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
2
3
u
3
−
1
3
u
2
+
10
3
u +
1
3
u
a
10
=
2
3
u
3
−
1
3
u
2
+
7
3
u +
1
3
u
a
8
=
2
3
u
3
−
1
3
u
2
+
10
3
u +
1
3
2
3
u
3
−
1
3
u
2
+
4
3
u +
1
3
a
6
=
−
1
3
u
3
+
2
3
u
2
−
5
3
u +
1
3
−
1
3
u
3
−
1
3
u
2
−
5
3
u −
2
3
a
3
=
−
1
3
u
3
+
2
3
u
2
−
2
3
u +
1
3
1
3
u
3
−
2
3
u
2
−
1
3
u −
1
3
a
12
=
−
1
3
u
3
−
1
3
u
2
−
2
3
u −
2
3
1
3
u
3
+
1
3
u
2
+
2
3
u −
1
3
a
7
=
−
2
3
u
3
+
4
3
u
2
−
4
3
u +
2
3
−u
2
− 3u − 1
a
2
=
−u
u
a
11
=
1
3
u
3
+
1
3
u
2
+
2
3
u −
1
3
−
1
3
u
3
−
4
3
u
2
−
2
3
u −
2
3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
16
3
u
3
+
2
3
u
2
−
56
3
u −
41
3
in decimal forms when there is not enough margin.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
u
4
+ 4u
2
+ 3u + 1
c
3
, c
12
u
4
+ 3u
3
+ 4u
2
+ 1
c
7
, c
8
u
4
− 5u
3
+ 7u
2
− 3u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
y
4
+ 8y
3
+ 18y
2
− y + 1
c
3
, c
12
y
4
− y
3
+ 18y
2
+ 8y + 1
c
7
, c
8
y
4
− 11y
3
+ 25y
2
+ 33y + 9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.367893 + 0.310982I
a = −0.86789 + 1.17701I
b = −0.367893 + 0.310982I
−0.650203 + 1.076870I −7.07727 − 6.47057I
u = −0.367893 − 0.310982I
a = −0.86789 − 1.17701I
b = −0.367893 − 0.310982I
−0.650203 − 1.076870I −7.07727 + 6.47057I
u = 0.36789 + 2.04303I
a = −0.132107 + 1.177010I
b = 0.36789 + 2.04303I
−15.7991 − 11.1024I 1.07727 + 3.92173I
u = 0.36789 − 2.04303I
a = −0.132107 − 1.177010I
b = 0.36789 − 2.04303I
−15.7991 + 11.1024I 1.07727 − 3.92173I
5
II. I
u
2
= hb + u, −u
5
− 3u
3
+ u
2
+ 2a + 3u − 2, u
6
+ 4u
4
− u
3
+ 2u
2
+ u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
1
2
u
5
+
3
2
u
3
−
1
2
u
2
−
3
2
u + 1
−u
a
10
=
1
2
u
5
+
3
2
u
3
−
1
2
u
2
−
1
2
u + 1
−u
a
8
=
1
2
u
5
+
3
2
u
3
−
1
2
u
2
−
3
2
u + 1
−
1
2
u
5
−
5
2
u
3
+
1
2
u
2
−
3
2
u
a
6
=
1
2
u
4
+
5
2
u
2
−
1
2
u +
3
2
1
2
u
4
+
3
2
u
2
−
1
2
u −
1
2
a
3
=
−
1
4
u
5
−
1
4
u
4
+ ··· −
3
2
u −
3
4
−
1
4
u
5
−
3
4
u
4
+ ··· −
5
2
u
2
−
1
4
a
12
=
−
1
4
u
5
+
1
4
u
4
+ ··· − u +
3
4
−
1
2
u
5
−
3
2
u
3
+
1
2
u
2
+
1
2
u
a
7
=
1
4
u
5
+
3
4
u
4
+ ··· +
7
2
u
2
+
9
4
1
4
u
5
+
5
4
u
4
+ ··· +
1
2
u −
1
4
a
2
=
−u
u
a
11
=
3
4
u
5
+
3
4
u
4
+ ··· −
1
2
u +
1
4
1
2
u
5
+
3
2
u
3
−
3
2
u
2
−
3
2
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1
4
u
5
+
3
4
u
4
+
9
4
u
3
+
7
2
u
2
+ 2u +
5
4
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
11
u
6
+ 4u
4
+ u
3
+ 2u
2
− u + 1
c
2
, c
4
, c
9
c
10
u
6
+ 4u
4
− u
3
+ 2u
2
+ u + 1
c
3
u
6
+ 3u
5
+ 3u
4
+ u
3
+ u
2
+ u + 1
c
7
u
6
+ 5u
5
+ 10u
4
+ 13u
3
+ 12u
2
+ 10u + 13
c
8
u
6
− 5u
5
+ 10u
4
− 13u
3
+ 12u
2
− 10u + 13
c
12
u
6
− 3u
5
+ 3u
4
− u
3
+ u
2
− u + 1
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
y
6
+ 8y
5
+ 20y
4
+ 17y
3
+ 14y
2
+ 3y + 1
c
3
, c
12
y
6
− 3y
5
+ 5y
4
+ y
3
+ 5y
2
+ y + 1
c
7
, c
8
y
6
− 5y
5
− 6y
4
− 3y
3
+ 144y
2
+ 212y + 169
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.531659 + 0.753297I
a = −0.76444 − 1.54585I
b = −0.531659 − 0.753297I
9.81524 − 4.74950I −0.79071 + 4.27718I
u = 0.531659 − 0.753297I
a = −0.76444 + 1.54585I
b = −0.531659 + 0.753297I
9.81524 + 4.74950I −0.79071 − 4.27718I
u = −0.341164 + 0.448642I
a = 1.80674 − 0.44864I
b = 0.341164 − 0.448642I
0.108732 − 60.581412 + 0.10I
u = −0.341164 − 0.448642I
a = 1.80674 + 0.44864I
b = 0.341164 + 0.448642I
0.108732 − 60.581412 + 0.10I
u = −0.19050 + 1.91484I
a = −0.042290 − 1.122290I
b = 0.19050 − 1.91484I
9.81524 + 4.74950I −0.79071 − 4.27718I
u = −0.19050 − 1.91484I
a = −0.042290 + 1.122290I
b = 0.19050 + 1.91484I
9.81524 − 4.74950I −0.79071 + 4.27718I
9
III. I
u
3
= h−25u
7
+ 373u
6
+ · · · + 2846b + 4816, 306u
7
+ 1468u
6
+ · · · +
36998a + 6624, u
8
− 2u
7
+ · · · − 12u + 52i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
−0.00827072u
7
− 0.0396778u
6
+ ··· + 0.185983u − 0.179037
0.00878426u
7
− 0.131061u
6
+ ··· + 1.91848u − 1.69220
a
10
=
−0.0170550u
7
+ 0.0913833u
6
+ ··· − 1.73250u + 1.51316
0.00878426u
7
− 0.131061u
6
+ ··· + 1.91848u − 1.69220
a
8
=
−0.00827072u
7
− 0.0396778u
6
+ ··· + 0.185983u − 0.179037
0.0351370u
7
− 0.0242446u
6
+ ··· + 1.67393u + 1.23120
a
6
=
0.0925050u
7
− 0.268636u
6
+ ··· + 3.35694u − 1.17401
−0.0562193u
7
+ 0.138791u
6
+ ··· − 0.278285u − 0.569923
a
3
=
−0.0345424u
7
+ 0.0107573u
6
+ ··· − 1.10560u − 2.92421
−0.00878426u
7
+ 0.131061u
6
+ ··· − 2.91848u + 3.69220
a
12
=
−0.0255014u
7
+ 0.0443267u
6
+ ··· + 1.61511u − 0.552030
0.0101897u
7
− 0.0720309u
6
+ ··· − 1.37456u − 1.60295
a
7
=
0.214593u
7
− 0.333261u
6
+ ··· + 5.11320u + 4.17471
−0.131061u
7
− 0.00456781u
6
+ ··· + 2.57625u − 8.07238
a
2
=
−u
u
a
11
=
−0.111844u
7
+ 0.264095u
6
+ ··· − 4.98824u + 3.16714
0.197119u
7
− 0.221012u
6
+ ··· + 3.65074u + 2.26704
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
3
1423
u
7
+
126
1423
u
6
−
115
1423
u
5
+
584
1423
u
4
+
211
1423
u
3
+
644
1423
u
2
+
2932
1423
u +
3748
1423
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
u
8
− 2u
7
+ 11u
6
− 16u
5
+ 43u
4
− 34u
3
+ 70u
2
− 12u + 52
c
3
, c
12
(u
4
− 3u
2
+ 2u + 5)
2
c
7
, c
8
(u
4
+ 4u
3
+ 3u
2
+ 5)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
y
8
+ 18y
7
+ ··· + 7136y + 2704
c
3
, c
12
(y
4
− 6y
3
+ 19y
2
− 34y + 25)
2
c
7
, c
8
(y
4
− 10y
3
+ 19y
2
+ 30y + 25)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.318348 + 0.988585I
a = 0.902055 + 0.085959I
b = 1.18274 + 1.38356I
12.33700 − 3.66386I 2.00000 + 2.00000I
u = −0.318348 − 0.988585I
a = 0.902055 − 0.085959I
b = 1.18274 − 1.38356I
12.33700 + 3.66386I 2.00000 − 2.00000I
u = 0.24810 + 1.76504I
a = 0.260593 − 1.307340I
b = −0.11249 − 2.13718I
12.33700 − 3.66386I 2.00000 + 2.00000I
u = 0.24810 − 1.76504I
a = 0.260593 + 1.307340I
b = −0.11249 + 2.13718I
12.33700 + 3.66386I 2.00000 − 2.00000I
u = 1.18274 + 1.38356I
a = 0.228120 + 0.463986I
b = −0.318348 + 0.988585I
12.33700 − 3.66386I 2.00000 + 2.00000I
u = 1.18274 − 1.38356I
a = 0.228120 − 0.463986I
b = −0.318348 − 0.988585I
12.33700 + 3.66386I 2.00000 − 2.00000I
u = −0.11249 + 2.13718I
a = −0.121537 − 1.103540I
b = 0.24810 − 1.76504I
12.33700 + 3.66386I 2.00000 − 2.00000I
u = −0.11249 − 2.13718I
a = −0.121537 + 1.103540I
b = 0.24810 + 1.76504I
12.33700 − 3.66386I 2.00000 + 2.00000I
13
IV. I
u
4
= hb + u, u
2
+ a + 1, u
4
+ 2u
2
+ u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
−u
2
− 1
−u
a
10
=
−u
2
+ u − 1
−u
a
8
=
−u
2
− 1
u
2
+ 1
a
6
=
u
3
+ u + 1
−u
3
+ u
2
− u
a
3
=
−u
3
− 2u + 1
u
3
+ u − 1
a
12
=
−u
3
− u
2
− 2u − 2
u
3
+ u
2
+ 2u + 1
a
7
=
2u
3
+ 2u
−2u
3
+ u
2
− u + 1
a
2
=
−u
u
a
11
=
−u
3
− u
2
− 1
u
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
3
+ 2u
2
− 12u − 7
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
11
u
4
+ 2u
2
− u + 1
c
2
, c
4
, c
9
c
10
u
4
+ 2u
2
+ u + 1
c
3
u
4
+ u
3
+ 4u
2
+ 2u + 3
c
7
u
4
+ 3u
3
+ 3u
2
+ u + 1
c
8
u
4
− 3u
3
+ 3u
2
− u + 1
c
12
u
4
− u
3
+ 4u
2
− 2u + 3
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
y
4
+ 4y
3
+ 6y
2
+ 3y + 1
c
3
, c
12
y
4
+ 7y
3
+ 18y
2
+ 20y + 9
c
7
, c
8
y
4
− 3y
3
+ 5y
2
+ 5y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.343815 + 0.625358I
a = −0.727136 + 0.430014I
b = 0.343815 − 0.625358I
−1.13814 + 3.38562I −6.32177 − 8.18198I
u = −0.343815 − 0.625358I
a = −0.727136 − 0.430014I
b = 0.343815 + 0.625358I
−1.13814 − 3.38562I −6.32177 + 8.18198I
u = 0.343815 + 1.358440I
a = 0.727136 − 0.934099I
b = −0.343815 − 1.358440I
4.42801 − 2.37936I 0.32177 + 1.76734I
u = 0.343815 − 1.358440I
a = 0.727136 + 0.934099I
b = −0.343815 + 1.358440I
4.42801 + 2.37936I 0.32177 − 1.76734I
17
V. I
u
5
= hb − u, 11u
9
+ 7u
8
+ · · · + 4a − 13, u
10
+ 7u
8
+ · · · − 3u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
9
=
−
11
4
u
9
−
7
4
u
8
+ ··· −
11
2
u +
13
4
u
a
10
=
−
11
4
u
9
−
7
4
u
8
+ ··· −
13
2
u +
13
4
u
a
8
=
−
11
4
u
9
−
7
4
u
8
+ ··· −
11
2
u +
13
4
−
3
4
u
9
−
1
4
u
8
+ ··· −
3
2
u +
7
4
a
6
=
−
7
4
u
9
−
3
4
u
8
+ ··· − 5u +
15
4
−
1
4
u
9
−
1
4
u
8
+ ··· −
1
2
u +
3
4
a
3
=
−2u
9
− u
8
+ ··· −
9
2
u + 5
−
3
4
u
9
−
1
4
u
8
+ ··· −
3
2
u +
5
4
a
12
=
7
4
u
9
+
7
4
u
8
+ ··· + u −
9
4
3
4
u
9
+
1
4
u
8
+ ··· +
7
2
u −
7
4
a
7
=
−
15
4
u
9
−
7
4
u
8
+ ··· −
17
2
u +
35
4
−u
9
−
1
2
u
8
+ ··· − 3u + 2
a
2
=
−u
u
a
11
=
−
11
2
u
9
−
7
2
u
8
+ ··· −
29
2
u +
15
2
−
11
4
u
9
−
7
4
u
8
+ ··· − 5u +
15
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1
4
u
9
+
3
4
u
8
− u
7
+
27
4
u
6
−
1
2
u
5
+
31
2
u
4
−
11
4
u
3
+
19
4
u
2
−
15
2
u −
3
4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
u
10
+ 7u
8
− 3u
7
+ 13u
6
− 12u
5
+ 5u
4
− 6u
3
+ 5u
2
− 3u + 1
c
3
, c
12
u
10
+ 6u
9
+ ··· + 8u + 4
c
7
, c
8
u
10
− 8u
9
+ ··· − 34u + 4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
y
10
+ 14y
9
+ 75y
8
+ 183y
7
+ 177y
6
+ 22y
5
+ 7y
4
− 32y
3
− y
2
+ y + 1
c
3
, c
12
y
10
+ 2y
9
+ ··· + 120y + 16
c
7
, c
8
y
10
− 20y
9
+ ··· − 300y + 16
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.486518 + 0.632836I
a = 0.079644 + 0.328409I
b = −0.486518 + 0.632836I
−0.61761 + 1.79087I −3.17008 − 3.84422I
u = −0.486518 − 0.632836I
a = 0.079644 − 0.328409I
b = −0.486518 − 0.632836I
−0.61761 − 1.79087I −3.17008 + 3.84422I
u = 0.621008 + 0.075641I
a = 1.79439 − 1.51840I
b = 0.621008 + 0.075641I
9.12328 − 3.14851I −1.88527 + 0.97081I
u = 0.621008 − 0.075641I
a = 1.79439 + 1.51840I
b = 0.621008 − 0.075641I
9.12328 + 3.14851I −1.88527 − 0.97081I
u = 0.239585 + 0.499962I
a = −1.76390 + 0.24899I
b = 0.239585 + 0.499962I
−0.61761 + 1.79087I −3.17008 − 3.84422I
u = 0.239585 − 0.499962I
a = −1.76390 − 0.24899I
b = 0.239585 − 0.499962I
−0.61761 − 1.79087I −3.17008 + 3.84422I
u = −0.06345 + 1.88716I
a = −0.084885 + 1.197580I
b = −0.06345 + 1.88716I
9.12328 + 3.14851I −1.88527 − 0.97081I
u = −0.06345 − 1.88716I
a = −0.084885 − 1.197580I
b = −0.06345 − 1.88716I
9.12328 − 3.14851I −1.88527 + 0.97081I
u = −0.31062 + 1.88752I
a = 0.474749 + 1.077290I
b = −0.31062 + 1.88752I
−17.0114 − 61.110699 + 0.10I
u = −0.31062 − 1.88752I
a = 0.474749 − 1.077290I
b = −0.31062 − 1.88752I
−17.0114 − 61.110699 + 0.10I
21
VI. I
u
6
= hb + u + 1, a + 1, u
2
+ u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
−u − 1
a
9
=
−1
−u − 1
a
10
=
u
−u − 1
a
8
=
−1
0
a
6
=
u + 2
−u − 1
a
3
=
−2u
u
a
12
=
−1
0
a
7
=
2u + 3
−u − 1
a
2
=
−u
u
a
11
=
2u + 1
−u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u − 2
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
u
2
+ u + 1
c
3
, c
12
u
2
− u + 1
23
(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
2
+ y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.00000
b = −0.500000 − 0.866025I
2.02988I 0. − 3.46410I
u = −0.500000 − 0.866025I
a = −1.00000
b = −0.500000 + 0.866025I
− 2.02988I 0. + 3.46410I
25
VII. I
u
7
= hb + u + 1, a + u, u
2
+ u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
−u − 1
a
9
=
−u
−u − 1
a
10
=
1
−u − 1
a
8
=
−u
−u − 2
a
6
=
0
u
a
3
=
1
−u − 1
a
12
=
−u
u − 1
a
7
=
−1
2u + 2
a
2
=
−u
u
a
11
=
0
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u + 2
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
u
2
+ u + 1
c
3
, c
12
u
2
− u + 1
27
(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
2
+ y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = −0.500000 − 0.866025I
− 2.02988I 0. + 3.46410I
u = −0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = −0.500000 + 0.866025I
2.02988I 0. − 3.46410I
29
VIII. I
u
8
= hb − u + 1, 3a − 2u + 2, u
2
− u + 3i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u − 3
a
9
=
2
3
u −
2
3
u − 1
a
10
=
−
1
3
u +
1
3
u − 1
a
8
=
2
3
u −
2
3
−u − 1
a
6
=
−
2
3
u −
1
3
1
a
3
=
−
2
3
u +
2
3
1
a
12
=
1
3
u −
1
3
1
a
7
=
−
2
3
u +
2
3
−u + 1
a
2
=
−u
u
a
11
=
−
1
3
u −
5
3
−u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
11
u
2
+ u + 3
c
2
, c
4
, c
9
c
10
u
2
− u + 3
c
3
(u − 1)
2
c
7
(u − 2)
2
c
8
(u + 2)
2
c
12
(u + 1)
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
y
2
+ 5y + 9
c
3
, c
12
(y − 1)
2
c
7
, c
8
(y − 4)
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.50000 + 1.65831I
a = −0.333333 + 1.105540I
b = −0.50000 + 1.65831I
13.1595 3.00000
u = 0.50000 − 1.65831I
a = −0.333333 − 1.105540I
b = −0.50000 − 1.65831I
13.1595 3.00000
33
IX. I
u
9
= hb + u − 1, a, u
2
− u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u − 1
a
9
=
0
−u + 1
a
10
=
u − 1
−u + 1
a
8
=
0
−u + 1
a
6
=
1
−1
a
3
=
0
1
a
12
=
u − 1
1
a
7
=
0
u − 1
a
2
=
−u
u
a
11
=
u − 1
−u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
u
2
− u + 1
c
3
, c
12
(u − 1)
2
c
7
, c
8
u
2
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
y
2
+ y + 1
c
3
, c
12
(y − 1)
2
c
7
, c
8
y
2
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0
b = 0.500000 − 0.866025I
3.28987 3.00000
u = 0.500000 − 0.866025I
a = 0
b = 0.500000 + 0.866025I
3.28987 3.00000
37
X. I
u
10
= hb, a − 1, u
2
+ u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
−u − 1
a
9
=
1
0
a
10
=
1
0
a
8
=
1
−u − 1
a
6
=
1
−u − 1
a
3
=
−u
u
a
12
=
−u
u
a
7
=
2
−u − 2
a
2
=
−u
u
a
11
=
−u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
38
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
12
u
2
− u + 1
c
2
, c
5
, c
9
c
11
u
2
c
3
, c
4
, c
8
c
10
u
2
+ u + 1
39
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
8
c
10
, c
12
y
2
+ y + 1
c
2
, c
5
, c
9
c
11
y
2
40
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.00000
b = 0
0 0
u = −0.500000 − 0.866025I
a = 1.00000
b = 0
0 0
41
XI. I
v
1
= ha, b
2
− b + 1, v − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
1
0
a
5
=
1
0
a
9
=
0
b
a
10
=
−b
b
a
8
=
−b
b
a
6
=
−b + 2
b − 1
a
3
=
2b
−b
a
12
=
−b + 2
b − 1
a
7
=
−b + 2
b − 1
a
2
=
1
0
a
11
=
−b
b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
42
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u
2
c
2
, c
3
, c
8
c
9
u
2
+ u + 1
c
5
, c
7
, c
11
c
12
u
2
− u + 1
43
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
2
c
2
, c
3
, c
5
c
7
, c
8
, c
9
c
11
, c
12
y
2
+ y + 1
44
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−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
45
XII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
11
u
2
(u
2
− u + 1)
2
(u
2
+ u + 1)
2
(u
2
+ u + 3)(u
4
+ 2u
2
− u + 1)
· (u
4
+ 4u
2
+ 3u + 1)(u
6
+ 4u
4
+ u
3
+ 2u
2
− u + 1)
· (u
8
− 2u
7
+ 11u
6
− 16u
5
+ 43u
4
− 34u
3
+ 70u
2
− 12u + 52)
· (u
10
+ 7u
8
− 3u
7
+ 13u
6
− 12u
5
+ 5u
4
− 6u
3
+ 5u
2
− 3u + 1)
c
2
, c
4
, c
9
c
10
u
2
(u
2
− u + 1)(u
2
− u + 3)(u
2
+ u + 1)
3
(u
4
+ 2u
2
+ u + 1)(u
4
+ 4u
2
+ 3u + 1)
· (u
6
+ 4u
4
− u
3
+ 2u
2
+ u + 1)
· (u
8
− 2u
7
+ 11u
6
− 16u
5
+ 43u
4
− 34u
3
+ 70u
2
− 12u + 52)
· (u
10
+ 7u
8
− 3u
7
+ 13u
6
− 12u
5
+ 5u
4
− 6u
3
+ 5u
2
− 3u + 1)
c
3
(u − 1)
4
(u
2
− u + 1)
2
(u
2
+ u + 1)
2
(u
4
− 3u
2
+ 2u + 5)
2
· (u
4
+ u
3
+ 4u
2
+ 2u + 3)(u
4
+ 3u
3
+ 4u
2
+ 1)
· (u
6
+ 3u
5
+ 3u
4
+ u
3
+ u
2
+ u + 1)(u
10
+ 6u
9
+ ··· + 8u + 4)
c
7
u
2
(u − 2)
2
(u
2
− u + 1)
2
(u
2
+ u + 1)
2
(u
4
− 5u
3
+ 7u
2
− 3u + 3)
· (u
4
+ 3u
3
+ 3u
2
+ u + 1)(u
4
+ 4u
3
+ 3u
2
+ 5)
2
· (u
6
+ 5u
5
+ ··· + 10u + 13)(u
10
− 8u
9
+ ··· − 34u + 4)
c
8
u
2
(u + 2)
2
(u
2
+ u + 1)
4
(u
4
− 5u
3
+ 7u
2
− 3u + 3)
· (u
4
− 3u
3
+ 3u
2
− u + 1)(u
4
+ 4u
3
+ 3u
2
+ 5)
2
· (u
6
− 5u
5
+ ··· − 10u + 13)(u
10
− 8u
9
+ ··· − 34u + 4)
c
12
(u − 1)
2
(u + 1)
2
(u
2
− u + 1)
4
(u
4
− 3u
2
+ 2u + 5)
2
· (u
4
− u
3
+ 4u
2
− 2u + 3)(u
4
+ 3u
3
+ 4u
2
+ 1)
· (u
6
− 3u
5
+ 3u
4
− u
3
+ u
2
− u + 1)(u
10
+ 6u
9
+ ··· + 8u + 4)
46
XIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
y
2
(y
2
+ y + 1)
4
(y
2
+ 5y + 9)(y
4
+ 4y
3
+ 6y
2
+ 3y + 1)
· (y
4
+ 8y
3
+ 18y
2
− y + 1)(y
6
+ 8y
5
+ 20y
4
+ 17y
3
+ 14y
2
+ 3y + 1)
· (y
8
+ 18y
7
+ ··· + 7136y + 2704)
· (y
10
+ 14y
9
+ 75y
8
+ 183y
7
+ 177y
6
+ 22y
5
+ 7y
4
− 32y
3
− y
2
+ y + 1)
c
3
, c
12
(y − 1)
4
(y
2
+ y + 1)
4
(y
4
− 6y
3
+ 19y
2
− 34y + 25)
2
· (y
4
− y
3
+ 18y
2
+ 8y + 1)(y
4
+ 7y
3
+ 18y
2
+ 20y + 9)
· (y
6
− 3y
5
+ 5y
4
+ y
3
+ 5y
2
+ y + 1)(y
10
+ 2y
9
+ ··· + 120y + 16)
c
7
, c
8
y
2
(y − 4)
2
(y
2
+ y + 1)
4
(y
4
− 11y
3
+ 25y
2
+ 33y + 9)
· (y
4
− 10y
3
+ 19y
2
+ 30y + 25)
2
(y
4
− 3y
3
+ 5y
2
+ 5y + 1)
· (y
6
− 5y
5
− 6y
4
− 3y
3
+ 144y
2
+ 212y + 169)
· (y
10
− 20y
9
+ ··· − 300y + 16)
47
