12a
0215
(K12a
0215
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 10 2 11 12 5 4 1 8
Solving Sequence
2,7
6 3
4,10
11 8 1 5 9 12
c
6
c
2
c
3
c
10
c
7
c
1
c
5
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
25
+ u
24
+ ··· + 2b + 1, u
25
− u
24
+ ··· + 2a − 1, u
27
− u
26
+ ··· + 2u − 1i
I
u
2
= h−8.39891 × 10
38
u
81
+ 2.15045 × 10
38
u
80
+ ··· + 2.93276 × 10
39
b − 1.22548 × 10
40
,
2.50222 × 10
40
u
81
− 4.66705 × 10
40
u
80
+ ··· + 2.05293 × 10
40
a − 7.74216 × 10
40
, u
82
− 2u
81
+ ··· − 19u + 7i
I
u
3
= hb + a + u, a
2
− 2a − 2u + 1, u
2
+ u + 1i
I
u
4
= hb + u − 1, a + 1, u
2
− u + 1i
I
u
5
= hb + a + 1, a
2
+ 2au + 2a − u, u
2
+ u + 1i
I
u
6
= hb − u, a + u − 1, u
2
− u + 1i
* 6 irreducible components of dim
C
= 0, with total 121 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
= h−u
25
+u
24
+· · ·+2b+1, u
25
−u
24
+· · ·+2a−1, u
27
−u
26
+· · ·+2u−1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
10
=
−
1
2
u
25
+
1
2
u
24
+ ··· − 2u +
1
2
1
2
u
25
−
1
2
u
24
+ ··· + 2u −
1
2
a
11
=
−
1
2
u
23
+
1
2
u
22
+ ··· − 2u +
1
2
u
3
+ u
a
8
=
−
1
2
u
26
+
1
2
u
25
+ ··· +
1
2
u + 1
u
6
+ 2u
4
+ u
2
a
1
=
u
3
u
5
+ u
3
+ u
a
5
=
−
1
2
u
26
− 3u
24
+ ··· − 2u +
3
2
1
2
u
25
−
1
2
u
24
+ ··· + 2u −
1
2
a
9
=
1
2
u
26
−
1
2
u
25
+ ··· −
1
2
u
3
− 1
−u
8
− 2u
6
− 2u
4
a
12
=
−
1
2
u
23
+
1
2
u
22
+ ··· − 2u +
1
2
−u
7
− u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 5u
26
−2u
25
+ 36u
24
−11u
23
+ 127u
22
−33u
21
+ 270u
20
−62u
19
+
367u
18
− 85u
17
+ 313u
16
− 86u
15
+ 164u
14
− 67u
13
+ 84u
12
− 29u
11
+ 98u
10
− 8u
9
+
82u
8
− 9u
7
+ 17u
6
− 25u
5
− 9u
3
+ 9u
2
− 2u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
27
+ 15u
26
+ ··· − 2u − 1
c
2
, c
6
, c
8
c
12
u
27
− u
26
+ ··· + 2u − 1
c
3
, c
7
u
27
+ u
26
+ ··· − 3u − 2
c
4
, c
5
, c
9
u
27
+ 5u
26
+ ··· + 4u − 4
c
10
u
27
− 15u
26
+ ··· + 212u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
27
− y
26
+ ··· − 2y −1
c
2
, c
6
, c
8
c
12
y
27
+ 15y
26
+ ··· − 2y −1
c
3
, c
7
y
27
− 17y
26
+ ··· − 35y −4
c
4
, c
5
, c
9
y
27
− 25y
26
+ ··· + 48y −16
c
10
y
27
− 5y
26
+ ··· + 206224y −1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.803618 + 0.349348I
a = 1.007060 + 0.949020I
b = −1.41653 + 1.34230I
5.22371 − 6.72306I 9.84931 + 3.39478I
u = 0.803618 − 0.349348I
a = 1.007060 − 0.949020I
b = −1.41653 − 1.34230I
5.22371 + 6.72306I 9.84931 − 3.39478I
u = −0.299281 + 0.820284I
a = −0.48606 − 1.73494I
b = 0.88880 + 1.18954I
4.11938 − 2.82450I 2.13183 + 1.79598I
u = −0.299281 − 0.820284I
a = −0.48606 + 1.73494I
b = 0.88880 − 1.18954I
4.11938 + 2.82450I 2.13183 − 1.79598I
u = 0.116549 + 0.860765I
a = 0.078400 − 1.016090I
b = −0.278709 + 0.364691I
−1.97453 + 1.43518I −2.24818 − 4.96930I
u = 0.116549 − 0.860765I
a = 0.078400 + 1.016090I
b = −0.278709 − 0.364691I
−1.97453 − 1.43518I −2.24818 + 4.96930I
u = −0.513874 + 1.069060I
a = 0.352532 + 0.981625I
b = −0.76543 − 1.34247I
4.01281 − 6.61800I 3.83990 + 7.93477I
u = −0.513874 − 1.069060I
a = 0.352532 − 0.981625I
b = −0.76543 + 1.34247I
4.01281 + 6.61800I 3.83990 − 7.93477I
u = −0.615180 + 0.518291I
a = 1.61732 + 1.21180I
b = −0.501601 − 0.764150I
7.40368 − 2.31507I 12.17043 + 2.39012I
u = −0.615180 − 0.518291I
a = 1.61732 − 1.21180I
b = −0.501601 + 0.764150I
7.40368 + 2.31507I 12.17043 − 2.39012I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.743850 + 0.296760I
a = −0.370434 + 0.541518I
b = 0.339092 + 1.113750I
−0.14900 + 3.15153I 5.48053 − 3.24594I
u = −0.743850 − 0.296760I
a = −0.370434 − 0.541518I
b = 0.339092 − 1.113750I
−0.14900 − 3.15153I 5.48053 + 3.24594I
u = 0.264221 + 1.179210I
a = −1.117430 + 0.645366I
b = −0.213710 − 1.207370I
−4.23123 − 0.71359I −1.52661 − 0.31939I
u = 0.264221 − 1.179210I
a = −1.117430 − 0.645366I
b = −0.213710 + 1.207370I
−4.23123 + 0.71359I −1.52661 + 0.31939I
u = −0.338826 + 1.179080I
a = 0.42150 + 1.47832I
b = 0.72240 − 1.41289I
−8.48034 − 3.42330I −5.15562 + 3.33733I
u = −0.338826 − 1.179080I
a = 0.42150 − 1.47832I
b = 0.72240 + 1.41289I
−8.48034 + 3.42330I −5.15562 − 3.33733I
u = 0.411435 + 1.173870I
a = 0.52311 + 1.66108I
b = −1.11519 − 1.11629I
−5.27423 + 7.72991I −0.94876 − 7.44715I
u = 0.411435 − 1.173870I
a = 0.52311 − 1.66108I
b = −1.11519 + 1.11629I
−5.27423 − 7.72991I −0.94876 + 7.44715I
u = 0.528079 + 1.138480I
a = 0.703762 − 0.059607I
b = 0.123706 + 0.371890I
−3.65072 + 8.53958I 0.93638 − 5.62468I
u = 0.528079 − 1.138480I
a = 0.703762 + 0.059607I
b = 0.123706 − 0.371890I
−3.65072 − 8.53958I 0.93638 + 5.62468I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.568964 + 1.151920I
a = −0.84587 − 1.38262I
b = −0.64504 + 1.69437I
−5.12208 − 13.17930I −0.30650 + 10.03114I
u = −0.568964 − 1.151920I
a = −0.84587 + 1.38262I
b = −0.64504 − 1.69437I
−5.12208 + 13.17930I −0.30650 − 10.03114I
u = 0.597410 + 1.146880I
a = 0.30821 − 2.43725I
b = 1.60210 + 2.43878I
0.5058 + 17.2462I 3.99567 − 10.69153I
u = 0.597410 − 1.146880I
a = 0.30821 + 2.43725I
b = 1.60210 − 2.43878I
0.5058 − 17.2462I 3.99567 + 10.69153I
u = 0.541018 + 0.346561I
a = −0.594979 + 0.357100I
b = 0.282228 + 0.197681I
1.153800 + 0.433800I 8.89068 − 3.10738I
u = 0.541018 − 0.346561I
a = −0.594979 − 0.357100I
b = 0.282228 − 0.197681I
1.153800 − 0.433800I 8.89068 + 3.10738I
u = 0.635291
a = −0.194238
b = 0.955765
1.41139 7.78190
7
II. I
u
2
= h−8.40 × 10
38
u
81
+ 2.15 × 10
38
u
80
+ · · · + 2.93 × 10
39
b − 1.23 ×
10
40
, 2.50 × 10
40
u
81
− 4.67 × 10
40
u
80
+ · · · + 2.05 × 10
40
a − 7.74 ×
10
40
, u
82
− 2u
81
+ · · · − 19u + 7i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
10
=
−1.21886u
81
+ 2.27336u
80
+ ··· − 12.9728u + 3.77127
0.286383u
81
− 0.0733251u
80
+ ··· − 4.86257u + 4.17860
a
11
=
−0.411067u
81
− 0.288547u
80
+ ··· + 4.78352u − 3.00988
−0.614218u
81
+ 1.70547u
80
+ ··· − 15.3414u + 6.51871
a
8
=
0.318231u
81
− 2.32467u
80
+ ··· + 24.6828u − 12.1894
−1.92973u
81
+ 3.70643u
80
+ ··· − 27.3383u + 10.1543
a
1
=
u
3
u
5
+ u
3
+ u
a
5
=
−0.371191u
81
+ 0.108615u
80
+ ··· + 1.54552u + 0.653397
−0.134364u
81
+ 0.768131u
80
+ ··· − 5.41326u + 3.53888
a
9
=
0.932035u
81
− 1.61400u
80
+ ··· + 1.95754u + 0.0479519
−0.335091u
81
+ 0.133733u
80
+ ··· + 9.76711u − 6.52731
a
12
=
−0.854155u
81
+ 0.424449u
80
+ ··· + 5.52400u − 3.77735
−0.0430260u
81
+ 1.07121u
80
+ ··· − 14.4429u + 9.10127
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.08647u
81
+ 2.72577u
80
+ ··· − 37.5801u + 26.3020
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
82
+ 38u
81
+ ··· + 171u + 49
c
2
, c
6
, c
8
c
12
u
82
− 2u
81
+ ··· − 19u + 7
c
3
, c
7
u
82
+ 2u
81
+ ··· + 653965u + 115507
c
4
, c
5
, c
9
(u
41
− 2u
40
+ ··· + 4u + 2)
2
c
10
(u
41
+ 6u
40
+ ··· − 144u − 32)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
82
+ 14y
81
+ ··· + 65427y + 2401
c
2
, c
6
, c
8
c
12
y
82
+ 38y
81
+ ··· + 171y + 49
c
3
, c
7
y
82
− 10y
81
+ ··· − 231414356651y + 13341867049
c
4
, c
5
, c
9
(y
41
− 38y
40
+ ··· − 32y −4)
2
c
10
(y
41
+ 2y
40
+ ··· − 3456y −1024)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.689028 + 0.715237I
a = 0.426260 − 0.243286I
b = 0.022676 − 0.162534I
−0.36156 + 5.69573I 0
u = 0.689028 − 0.715237I
a = 0.426260 + 0.243286I
b = 0.022676 + 0.162534I
−0.36156 − 5.69573I 0
u = −0.765330 + 0.659348I
a = −1.34566 − 0.92456I
b = 0.239119 + 0.976808I
4.65659 − 8.77727I 0
u = −0.765330 − 0.659348I
a = −1.34566 + 0.92456I
b = 0.239119 − 0.976808I
4.65659 + 8.77727I 0
u = −0.695472 + 0.747401I
a = −1.19111 − 0.96963I
b = 0.366764 + 1.155420I
2.83527 − 1.77985I 0
u = −0.695472 − 0.747401I
a = −1.19111 + 0.96963I
b = 0.366764 − 1.155420I
2.83527 + 1.77985I 0
u = −0.719446 + 0.634218I
a = 1.37551 + 0.99667I
b = −0.323967 − 0.941289I
6.76688 − 4.02505I 11.00664 + 3.97880I
u = −0.719446 − 0.634218I
a = 1.37551 − 0.99667I
b = −0.323967 + 0.941289I
6.76688 + 4.02505I 11.00664 − 3.97880I
u = 0.283270 + 1.031430I
a = 2.04178 − 0.89333I
b = −0.20075 + 1.91629I
2.83527 − 1.77985I 0
u = 0.283270 − 1.031430I
a = 2.04178 + 0.89333I
b = −0.20075 − 1.91629I
2.83527 + 1.77985I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.341629 + 1.027430I
a = −2.44843 + 0.21696I
b = 0.90934 − 1.82491I
2.46019 + 3.45470I 0
u = 0.341629 − 1.027430I
a = −2.44843 − 0.21696I
b = 0.90934 + 1.82491I
2.46019 − 3.45470I 0
u = 0.839192 + 0.351360I
a = −1.044020 − 0.844502I
b = 1.31623 − 1.40977I
2.88789 − 11.91530I 6.77003 + 7.12233I
u = 0.839192 − 0.351360I
a = −1.044020 + 0.844502I
b = 1.31623 + 1.40977I
2.88789 + 11.91530I 6.77003 − 7.12233I
u = 0.644899 + 0.881737I
a = 0.401320 − 0.122971I
b = 0.0900442 − 0.0322691I
−0.847371 − 0.579153I 0
u = 0.644899 − 0.881737I
a = 0.401320 + 0.122971I
b = 0.0900442 + 0.0322691I
−0.847371 + 0.579153I 0
u = −0.396078 + 1.023630I
a = 0.282828 + 1.206450I
b = −0.79733 − 1.30420I
3.09696 0
u = −0.396078 − 1.023630I
a = 0.282828 − 1.206450I
b = −0.79733 + 1.30420I
3.09696 0
u = −0.672412 + 0.878423I
a = 0.862261 + 0.794570I
b = −0.57402 − 1.37006I
2.46019 − 3.45470I 0
u = −0.672412 − 0.878423I
a = 0.862261 − 0.794570I
b = −0.57402 + 1.37006I
2.46019 + 3.45470I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.564931 + 0.954516I
a = −0.417859 − 0.016464I
b = −0.0477010 − 0.0604940I
0.44383 + 3.16653I 0
u = 0.564931 − 0.954516I
a = −0.417859 + 0.016464I
b = −0.0477010 + 0.0604940I
0.44383 − 3.16653I 0
u = −0.452391 + 1.015630I
a = −0.71504 − 1.98517I
b = −1.13769 + 1.76536I
−0.847371 − 0.579153I 0
u = −0.452391 − 1.015630I
a = −0.71504 + 1.98517I
b = −1.13769 − 1.76536I
−0.847371 + 0.579153I 0
u = 0.605854 + 0.628370I
a = −0.424775 + 0.321065I
b = 0.075036 + 0.153636I
1.40425 + 1.45669I 6.96953 − 5.06575I
u = 0.605854 − 0.628370I
a = −0.424775 − 0.321065I
b = 0.075036 − 0.153636I
1.40425 − 1.45669I 6.96953 + 5.06575I
u = −0.808418 + 0.297201I
a = 0.342419 − 0.461894I
b = −0.319219 − 1.185340I
−2.58795 + 8.05246I 2.39091 − 6.67607I
u = −0.808418 − 0.297201I
a = 0.342419 + 0.461894I
b = −0.319219 + 1.185340I
−2.58795 − 8.05246I 2.39091 + 6.67607I
u = −0.544403 + 1.015420I
a = −0.463853 − 0.980844I
b = 0.73592 + 1.33469I
5.94556 − 2.27206I 0
u = −0.544403 − 1.015420I
a = −0.463853 + 0.980844I
b = 0.73592 − 1.33469I
5.94556 + 2.27206I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.633782 + 0.965157I
a = −0.619693 − 0.846918I
b = 0.67438 + 1.36329I
5.78705 − 1.14285I 0
u = −0.633782 − 0.965157I
a = −0.619693 + 0.846918I
b = 0.67438 − 1.36329I
5.78705 + 1.14285I 0
u = 0.797763 + 0.273658I
a = −0.790370 − 0.865730I
b = 1.28854 − 1.12842I
0.33937 − 3.94176I 3.80485 + 2.05545I
u = 0.797763 − 0.273658I
a = −0.790370 + 0.865730I
b = 1.28854 + 1.12842I
0.33937 + 3.94176I 3.80485 − 2.05545I
u = −0.502229 + 1.050420I
a = 0.89797 + 1.74531I
b = 0.87575 − 1.84134I
−0.36156 − 5.69573I 0
u = −0.502229 − 1.050420I
a = 0.89797 − 1.74531I
b = 0.87575 + 1.84134I
−0.36156 + 5.69573I 0
u = −0.279574 + 1.135010I
a = −0.30915 − 1.50867I
b = −0.74203 + 1.28219I
−4.43409 + 0.19849I 0
u = −0.279574 − 1.135010I
a = −0.30915 + 1.50867I
b = −0.74203 − 1.28219I
−4.43409 − 0.19849I 0
u = 0.201185 + 1.156190I
a = 1.10226 − 0.88862I
b = 0.338911 + 1.367520I
0.33937 − 3.94176I 0
u = 0.201185 − 1.156190I
a = 1.10226 + 0.88862I
b = 0.338911 − 1.367520I
0.33937 + 3.94176I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.680761 + 0.963853I
a = 0.637175 + 0.746660I
b = −0.66131 − 1.39711I
3.75302 + 3.33055I 0
u = −0.680761 − 0.963853I
a = 0.637175 − 0.746660I
b = −0.66131 + 1.39711I
3.75302 − 3.33055I 0
u = 0.383840 + 1.124570I
a = −0.75917 − 1.43709I
b = 1.058920 + 0.664259I
−1.78976 + 3.63396I 0
u = 0.383840 − 1.124570I
a = −0.75917 + 1.43709I
b = 1.058920 − 0.664259I
−1.78976 − 3.63396I 0
u = 0.525005 + 1.078820I
a = −0.57133 − 3.05080I
b = 2.61883 + 1.84930I
3.75302 + 3.33055I 0
u = 0.525005 − 1.078820I
a = −0.57133 + 3.05080I
b = 2.61883 − 1.84930I
3.75302 − 3.33055I 0
u = 0.324132 + 1.156920I
a = 0.470124 + 1.324050I
b = −0.643195 − 0.862446I
−5.04218 − 0.52120I 0
u = 0.324132 − 1.156920I
a = 0.470124 − 1.324050I
b = −0.643195 + 0.862446I
−5.04218 + 0.52120I 0
u = 0.502544 + 1.098810I
a = −0.713487 − 0.031522I
b = −0.016767 − 0.335638I
−1.04581 + 3.83403I 0
u = 0.502544 − 1.098810I
a = −0.713487 + 0.031522I
b = −0.016767 + 0.335638I
−1.04581 − 3.83403I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.184539 + 1.194310I
a = −0.968047 + 0.860870I
b = −0.414774 − 1.294930I
−2.25867 − 8.98287I 0
u = 0.184539 − 1.194310I
a = −0.968047 − 0.860870I
b = −0.414774 + 1.294930I
−2.25867 + 8.98287I 0
u = −0.246275 + 1.183340I
a = 0.30446 + 1.42791I
b = 0.63553 − 1.29001I
−7.30150 + 4.90350I 0
u = −0.246275 − 1.183340I
a = 0.30446 − 1.42791I
b = 0.63553 + 1.29001I
−7.30150 − 4.90350I 0
u = −0.759560 + 0.170105I
a = 0.206959 − 0.563917I
b = −0.190983 − 1.102140I
−4.43409 + 0.19849I −0.855132 − 0.263674I
u = −0.759560 − 0.170105I
a = 0.206959 + 0.563917I
b = −0.190983 + 1.102140I
−4.43409 − 0.19849I −0.855132 + 0.263674I
u = 0.548764 + 1.094240I
a = 0.18219 + 2.93809I
b = −2.31640 − 2.17267I
4.65659 + 8.77727I 0
u = 0.548764 − 1.094240I
a = 0.18219 − 2.93809I
b = −2.31640 + 2.17267I
4.65659 − 8.77727I 0
u = 0.679190 + 0.367886I
a = 0.86819 + 1.43693I
b = −1.82727 + 1.10121I
6.76688 − 4.02505I 11.00664 + 3.97880I
u = 0.679190 − 0.367886I
a = 0.86819 − 1.43693I
b = −1.82727 − 1.10121I
6.76688 + 4.02505I 11.00664 − 3.97880I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.447381 + 1.149980I
a = 0.883459 − 0.065760I
b = 0.005837 + 0.564784I
−5.04218 + 0.52120I 0
u = 0.447381 − 1.149980I
a = 0.883459 + 0.065760I
b = 0.005837 − 0.564784I
−5.04218 − 0.52120I 0
u = −0.440145 + 0.608096I
a = 0.95391 − 1.06892I
b = −1.052950 − 0.702852I
0.44383 − 3.16653I 4.71993 − 0.58973I
u = −0.440145 − 0.608096I
a = 0.95391 + 1.06892I
b = −1.052950 + 0.702852I
0.44383 + 3.16653I 4.71993 + 0.58973I
u = 0.712533 + 0.226602I
a = 0.563149 − 0.287019I
b = −0.383162 − 0.371369I
−1.04581 − 3.83403I 4.44538 + 2.12907I
u = 0.712533 − 0.226602I
a = 0.563149 + 0.287019I
b = −0.383162 + 0.371369I
−1.04581 + 3.83403I 4.44538 − 2.12907I
u = −0.551632 + 1.132560I
a = 0.85256 + 1.44076I
b = 0.67530 − 1.71516I
−2.58795 − 8.05246I 0
u = −0.551632 − 1.132560I
a = 0.85256 − 1.44076I
b = 0.67530 + 1.71516I
−2.58795 + 8.05246I 0
u = 0.735105 + 0.006056I
a = 0.436191 − 0.362330I
b = −0.791059 − 0.477947I
−1.78976 + 3.63396I 3.00355 − 4.41372I
u = 0.735105 − 0.006056I
a = 0.436191 + 0.362330I
b = −0.791059 + 0.477947I
−1.78976 − 3.63396I 3.00355 + 4.41372I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.512115 + 1.158870I
a = −0.74554 − 1.45277I
b = −0.70751 + 1.65463I
−7.30150 − 4.90350I 0
u = −0.512115 − 1.158870I
a = −0.74554 + 1.45277I
b = −0.70751 − 1.65463I
−7.30150 + 4.90350I 0
u = 0.585200 + 1.135380I
a = −0.22170 + 2.53693I
b = −1.73675 − 2.39250I
2.88789 + 11.91530I 0
u = 0.585200 − 1.135380I
a = −0.22170 − 2.53693I
b = −1.73675 + 2.39250I
2.88789 − 11.91530I 0
u = 0.556886 + 1.153190I
a = 0.00759 − 2.38243I
b = 1.66909 + 2.10879I
−2.25867 + 8.98287I 0
u = 0.556886 − 1.153190I
a = 0.00759 + 2.38243I
b = 1.66909 − 2.10879I
−2.25867 − 8.98287I 0
u = 0.592687 + 0.369522I
a = −0.61966 − 1.82844I
b = 2.04999 − 0.82047I
5.78705 + 1.14285I 9.35767 − 1.34968I
u = 0.592687 − 0.369522I
a = −0.61966 + 1.82844I
b = 2.04999 + 0.82047I
5.78705 − 1.14285I 9.35767 + 1.34968I
u = −0.532881 + 0.446002I
a = −0.675343 + 0.806391I
b = 0.633559 + 0.875574I
1.40425 + 1.45669I 6.96953 − 5.06575I
u = −0.532881 − 0.446002I
a = −0.675343 − 0.806391I
b = 0.633559 − 0.875574I
1.40425 − 1.45669I 6.96953 + 5.06575I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.552652 + 0.404350I
a = −1.98289 − 1.32692I
b = 0.605079 + 0.596657I
5.94556 + 2.27206I 8.68115 − 3.66498I
u = −0.552652 − 0.404350I
a = −1.98289 + 1.32692I
b = 0.605079 − 0.596657I
5.94556 − 2.27206I 8.68115 + 3.66498I
19
III. I
u
3
= hb + a + u, a
2
− 2a − 2u + 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u − 1
a
3
=
u
u + 1
a
4
=
−1
u + 1
a
10
=
a
−a − u
a
11
=
au + a − u
−u − 1
a
8
=
−au
u
a
1
=
1
0
a
5
=
au − 3u − 1
a + u
a
9
=
−au − a + u
u + 1
a
12
=
au + a + 1
−u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u + 12
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
c
11
(u
2
− u + 1)
2
c
3
, c
6
, c
7
c
12
(u
2
+ u + 1)
2
c
4
, c
5
, c
9
c
10
(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
8
c
11
, c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
9
c
10
(y −2)
4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.292893 − 1.224750I
b = 0.207107 + 0.358719I
4.93480 − 4.05977I 8.00000 + 6.92820I
u = −0.500000 + 0.866025I
a = 1.70711 + 1.22474I
b = −1.20711 − 2.09077I
4.93480 − 4.05977I 8.00000 + 6.92820I
u = −0.500000 − 0.866025I
a = 0.292893 + 1.224750I
b = 0.207107 − 0.358719I
4.93480 + 4.05977I 8.00000 − 6.92820I
u = −0.500000 − 0.866025I
a = 1.70711 − 1.22474I
b = −1.20711 + 2.09077I
4.93480 + 4.05977I 8.00000 − 6.92820I
23
IV. I
u
4
= hb + u − 1, a + 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u − 1
a
3
=
u
u − 1
a
4
=
1
u − 1
a
10
=
−1
−u + 1
a
11
=
−1
−u + 1
a
8
=
u
−u
a
1
=
−1
0
a
5
=
1
u − 1
a
9
=
−1
−u + 1
a
12
=
u − 2
−u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u + 4
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
11
, c
12
u
2
− u + 1
c
2
, c
8
u
2
+ u + 1
c
4
, c
5
, c
9
c
10
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
8
c
11
, c
12
y
2
+ y + 1
c
4
, c
5
, c
9
c
10
y
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.00000
b = 0.500000 − 0.866025I
4.05977I 0. − 6.92820I
u = 0.500000 − 0.866025I
a = −1.00000
b = 0.500000 + 0.866025I
− 4.05977I 0. + 6.92820I
27
V. I
u
5
= hb + a + 1, a
2
+ 2au + 2a − u, u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u − 1
a
3
=
u
u + 1
a
4
=
−1
u + 1
a
10
=
a
−a − 1
a
11
=
au + a − 1
u
a
8
=
−a − u + 1
−u − 1
a
1
=
1
0
a
5
=
a − u
−au − a + 1
a
9
=
−au − a + 1
−u
a
12
=
au + a − u − 1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
c
11
(u
2
− u + 1)
2
c
3
, c
6
, c
7
c
12
(u
2
+ u + 1)
2
c
4
, c
5
, c
9
c
10
(u
2
− 2)
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
8
c
11
, c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
9
c
10
(y −2)
4
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.207107 + 0.358719I
b = −1.207110 − 0.358719I
4.93480 8.00000
u = −0.500000 + 0.866025I
a = −1.20711 − 2.09077I
b = 0.20711 + 2.09077I
4.93480 8.00000
u = −0.500000 − 0.866025I
a = 0.207107 − 0.358719I
b = −1.207110 + 0.358719I
4.93480 8.00000
u = −0.500000 − 0.866025I
a = −1.20711 + 2.09077I
b = 0.20711 − 2.09077I
4.93480 8.00000
31
VI. I
u
6
= hb − u, a + u − 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u − 1
a
3
=
u
u − 1
a
4
=
1
u − 1
a
10
=
−u + 1
u
a
11
=
−u + 1
u
a
8
=
2
u − 1
a
1
=
−1
0
a
5
=
1
u − 1
a
9
=
−u + 1
u
a
12
=
−2u + 1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
11
, c
12
u
2
− u + 1
c
2
, c
8
u
2
+ u + 1
c
4
, c
5
, c
9
c
10
u
2
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
c
11
, c
12
y
2
+ y + 1
c
4
, c
5
, c
9
c
10
y
2
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = 0.500000 + 0.866025I
0 6.00000
u = 0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = 0.500000 − 0.866025I
0 6.00000
35
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
((u
2
− u + 1)
6
)(u
27
+ 15u
26
+ ··· − 2u − 1)
· (u
82
+ 38u
81
+ ··· + 171u + 49)
c
2
, c
8
((u
2
− u + 1)
4
)(u
2
+ u + 1)
2
(u
27
− u
26
+ ··· + 2u − 1)
· (u
82
− 2u
81
+ ··· − 19u + 7)
c
3
, c
7
((u
2
− u + 1)
2
)(u
2
+ u + 1)
4
(u
27
+ u
26
+ ··· − 3u − 2)
· (u
82
+ 2u
81
+ ··· + 653965u + 115507)
c
4
, c
5
, c
9
u
4
(u
2
− 2)
4
(u
27
+ 5u
26
+ ··· + 4u − 4)(u
41
− 2u
40
+ ··· + 4u + 2)
2
c
6
, c
12
((u
2
− u + 1)
2
)(u
2
+ u + 1)
4
(u
27
− u
26
+ ··· + 2u − 1)
· (u
82
− 2u
81
+ ··· − 19u + 7)
c
10
u
4
(u
2
− 2)
4
(u
27
− 15u
26
+ ··· + 212u + 32)
· (u
41
+ 6u
40
+ ··· − 144u − 32)
2
36
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y
2
+ y + 1)
6
)(y
27
− y
26
+ ··· − 2y −1)
· (y
82
+ 14y
81
+ ··· + 65427y + 2401)
c
2
, c
6
, c
8
c
12
((y
2
+ y + 1)
6
)(y
27
+ 15y
26
+ ··· − 2y −1)
· (y
82
+ 38y
81
+ ··· + 171y + 49)
c
3
, c
7
((y
2
+ y + 1)
6
)(y
27
− 17y
26
+ ··· − 35y −4)
· (y
82
− 10y
81
+ ··· − 231414356651y + 13341867049)
c
4
, c
5
, c
9
y
4
(y −2)
8
(y
27
− 25y
26
+ ··· + 48y −16)
· (y
41
− 38y
40
+ ··· − 32y −4)
2
c
10
y
4
(y −2)
8
(y
27
− 5y
26
+ ··· + 206224y −1024)
· (y
41
+ 2y
40
+ ··· − 3456y −1024)
2
37
