ropelength 33.61
p3.1.idealr1.vect
m3.1.idealr1.vect
On this page, you will find ideal/tight knots computed with our Ridgerunner software. These are prime knots and we show both chiralities (when the knot type is chiral).
There is a prefix which is a, p, m, or h. The a means that the knot type is achiral. The p and m are for the plus and minus versions, respectively. The designations of which are plus and which are minus is a long story. I would suggest you just trust me, or ask me if you are skeptical. The h means that the knot type is chiral but the HOMFLYPT polynomial cannot tell the difference between the two chiralities. For ideal/tight configurations, we could figure out which chirality we have, but I choose not to here. The reason is that I analyze lots of random knots and there we cannot always know. So I prefer to be consistent.
These configurations are at a resolution of approximately one. This means that the number of edges is about the same as the ropelength. There is some beauty in that, although one would probably label this as fairly coarse. We ran these to a residual of around 0.01 (maybe lower). That means that approximately 99% of the movement that the polygon wants to make to shorten its length is absorbed by the strut structure. If you do not know what some of these terms mean, but would like to, check out our paper:
Ted Ashton, Jason Cantarella, Michael Piatek, and Eric J. Rawdon. Knot tightening by constrained gradient descent. Experiment. Math., 20(1): 57-90, 2011.
The configurations all have a thickness radius of about 0.5. I would like to have the thickness at 1, but we have it at 0.5 for historical reasons.
I have included an image of the p (i.e. positive) version (if the knot type is chiral, otherwise there is just the a or h choice), a VECT file for both chiralities, and the ropelength of this configuration (using my definition).
You can download a file with all of the vect files: IdealR1VectFiles.zip.
You can download a file with all of the ropelength values: idealr1ropelengthvalues.txt.
p3.1
ropelength 33.61
p3.1.idealr1.vect
m3.1.idealr1.vect
a4.1
ropelength 42.91
a4.1.idealr1.vect
p5.1
ropelength 48.44
p5.1.idealr1.vect
m5.1.idealr1.vect
p5.2
ropelength 50.50
p5.2.idealr1.vect
m5.2.idealr1.vect
p6.1
ropelength 57.92
p6.1.idealr1.vect
m6.1.idealr1.vect
p6.2
ropelength 58.21
p6.2.idealr1.vect
m6.2.idealr1.vect
a6.3
ropelength 58.96
a6.3.idealr1.vect
p7.1
ropelength 63.06
p7.1.idealr1.vect
m7.1.idealr1.vect
p7.2
ropelength 65.25
p7.2.idealr1.vect
m7.2.idealr1.vect
p7.3
ropelength 65.40
p7.3.idealr1.vect
m7.3.idealr1.vect
p7.4
ropelength 65.67
p7.4.idealr1.vect
m7.4.idealr1.vect
p7.5
ropelength 66.54
p7.5.idealr1.vect
m7.5.idealr1.vect
p7.6
ropelength 66.98
p7.6.idealr1.vect
m7.6.idealr1.vect
p7.7
ropelength 66.87
p7.7.idealr1.vect
m7.7.idealr1.vect
p8.1
ropelength 72.62
p8.1.idealr1.vect
m8.1.idealr1.vect
p8.2
ropelength 72.98
p8.2.idealr1.vect
m8.2.idealr1.vect
a8.3
ropelength 72.74
a8.3.idealr1.vect
p8.4
ropelength 73.09
p8.4.idealr1.vect
m8.4.idealr1.vect
p8.5
ropelength 73.78
p8.5.idealr1.vect
m8.5.idealr1.vect
p8.6
ropelength 74.02
p8.6.idealr1.vect
m8.6.idealr1.vect
p8.7
ropelength 73.69
p8.7.idealr1.vect
m8.7.idealr1.vect
p8.8
ropelength 74.25
p8.8.idealr1.vect
m8.8.idealr1.vect
a8.9
ropelength 73.98
a8.9.idealr1.vect
p8.10
ropelength 74.50
p8.10.idealr1.vect
m8.10.idealr1.vect
p8.11
ropelength 74.42
p8.11.idealr1.vect
m8.11.idealr1.vect
a8.12
ropelength 75.38
a8.12.idealr1.vect
p8.13
ropelength 74.28
p8.13.idealr1.vect
m8.13.idealr1.vect
p8.14
ropelength 75.16
p8.14.idealr1.vect
m8.14.idealr1.vect
p8.15
ropelength 75.03
p8.15.idealr1.vect
m8.15.idealr1.vect
p8.16
ropelength 74.93
p8.16.idealr1.vect
m8.16.idealr1.vect
a8.17
ropelength 75.98
a8.17.idealr1.vect
a8.18
ropelength 76.41
a8.18.idealr1.vect
p8.19
ropelength 61.85
p8.19.idealr1.vect
m8.19.idealr1.vect
p8.20
ropelength 64.28
p8.20.idealr1.vect
m8.20.idealr1.vect
p8.21
ropelength 66.77
p8.21.idealr1.vect
m8.21.idealr1.vect
p9.1
ropelength 77.62
p9.1.idealr1.vect
m9.1.idealr1.vect
p9.2
ropelength 79.91
p9.2.idealr1.vect
m9.2.idealr1.vect
p9.3
ropelength 79.99
p9.3.idealr1.vect
m9.3.idealr1.vect
p9.4
ropelength 80.03
p9.4.idealr1.vect
m9.4.idealr1.vect
p9.5
ropelength 80.44
p9.5.idealr1.vect
m9.5.idealr1.vect
p9.6
ropelength 81.27
p9.6.idealr1.vect
m9.6.idealr1.vect
p9.7
ropelength 81.41
p9.7.idealr1.vect
m9.7.idealr1.vect
p9.8
ropelength 81.68
p9.8.idealr1.vect
m9.8.idealr1.vect
p9.9
ropelength 81.58
p9.9.idealr1.vect
m9.9.idealr1.vect
p9.10
ropelength 81.50
p9.10.idealr1.vect
m9.10.idealr1.vect
p9.11
ropelength 81.81
p9.11.idealr1.vect
m9.11.idealr1.vect
p9.12
ropelength 81.77
p9.12.idealr1.vect
m9.12.idealr1.vect
p9.13
ropelength 81.96
p9.13.idealr1.vect
m9.13.idealr1.vect
p9.14
ropelength 81.70
p9.14.idealr1.vect
m9.14.idealr1.vect
p9.15
ropelength 82.45
p9.15.idealr1.vect
m9.15.idealr1.vect
p9.16
ropelength 81.71
p9.16.idealr1.vect
m9.16.idealr1.vect
p9.17
ropelength 82.05
p9.17.idealr1.vect
m9.17.idealr1.vect
p9.18
ropelength 82.84
p9.18.idealr1.vect
m9.18.idealr1.vect
p9.19
ropelength 82.52
p9.19.idealr1.vect
m9.19.idealr1.vect
p9.20
ropelength 81.82
p9.20.idealr1.vect
m9.20.idealr1.vect
p9.21
ropelength 82.67
p9.21.idealr1.vect
m9.21.idealr1.vect
p9.22
ropelength 82.66
p9.22.idealr1.vect
m9.22.idealr1.vect
p9.23
ropelength 82.78
p9.23.idealr1.vect
m9.23.idealr1.vect
p9.24
ropelength 82.47
p9.24.idealr1.vect
m9.24.idealr1.vect
p9.25
ropelength 82.65
p9.25.idealr1.vect
m9.25.idealr1.vect
p9.26
ropelength 82.53
p9.26.idealr1.vect
m9.26.idealr1.vect
p9.27
ropelength 82.71
p9.27.idealr1.vect
m9.27.idealr1.vect
p9.28
ropelength 82.60
p9.28.idealr1.vect
m9.28.idealr1.vect
p9.29
ropelength 82.73
p9.29.idealr1.vect
m9.29.idealr1.vect
p9.30
ropelength 83.01
p9.30.idealr1.vect
m9.30.idealr1.vect
p9.31
ropelength 83.20
p9.31.idealr1.vect
m9.31.idealr1.vect
p9.32
ropelength 83.02
p9.32.idealr1.vect
m9.32.idealr1.vect
p9.33
ropelength 83.91
p9.33.idealr1.vect
m9.33.idealr1.vect
p9.34
ropelength 83.75
p9.34.idealr1.vect
m9.34.idealr1.vect
p9.35
ropelength 81.03
p9.35.idealr1.vect
m9.35.idealr1.vect
p9.36
ropelength 81.91
p9.36.idealr1.vect
m9.36.idealr1.vect
p9.37
ropelength 82.71
p9.37.idealr1.vect
m9.37.idealr1.vect
p9.38
ropelength 83.40
p9.38.idealr1.vect
m9.38.idealr1.vect
p9.39
ropelength 83.43
p9.39.idealr1.vect
m9.39.idealr1.vect
p9.40
ropelength 83.12
p9.40.idealr1.vect
m9.40.idealr1.vect
p9.41
ropelength 82.98
p9.41.idealr1.vect
m9.41.idealr1.vect
h9.42
ropelength 70.53
h9.42.idealr1.vect
p9.43
ropelength 72.63
p9.43.idealr1.vect
m9.43.idealr1.vect
p9.44
ropelength 72.86
p9.44.idealr1.vect
m9.44.idealr1.vect
p9.45
ropelength 75.29
p9.45.idealr1.vect
m9.45.idealr1.vect
p9.46
ropelength 69.90
p9.46.idealr1.vect
m9.46.idealr1.vect
p9.47
ropelength 76.13
p9.47.idealr1.vect
m9.47.idealr1.vect
p9.48
ropelength 75.36
p9.48.idealr1.vect
m9.48.idealr1.vect
p9.49
ropelength 75.20
p9.49.idealr1.vect
m9.49.idealr1.vect
p10.1
ropelength 87.11
p10.1.idealr1.vect
m10.1.idealr1.vect
p10.2
ropelength 87.58
p10.2.idealr1.vect
m10.2.idealr1.vect
p10.3
ropelength 87.45
p10.3.idealr1.vect
m10.3.idealr1.vect
p10.4
ropelength 87.81
p10.4.idealr1.vect
m10.4.idealr1.vect
p10.5
ropelength 88.37
p10.5.idealr1.vect
m10.5.idealr1.vect
p10.6
ropelength 88.76
p10.6.idealr1.vect
m10.6.idealr1.vect
p10.7
ropelength 89.15
p10.7.idealr1.vect
m10.7.idealr1.vect
p10.8
ropelength 87.88
p10.8.idealr1.vect
m10.8.idealr1.vect
p10.9
ropelength 88.74
p10.9.idealr1.vect
m10.9.idealr1.vect
p10.10
ropelength 89.06
p10.10.idealr1.vect
m10.10.idealr1.vect
p10.11
ropelength 88.93
p10.11.idealr1.vect
m10.11.idealr1.vect
p10.12
ropelength 88.97
p10.12.idealr1.vect
m10.12.idealr1.vect
p10.13
ropelength 90.36
p10.13.idealr1.vect
m10.13.idealr1.vect
p10.14
ropelength 90.07
p10.14.idealr1.vect
m10.14.idealr1.vect
p10.15
ropelength 89.33
p10.15.idealr1.vect
m10.15.idealr1.vect
p10.16
ropelength 89.36
p10.16.idealr1.vect
m10.16.idealr1.vect
a10.17
ropelength 88.89
a10.17.idealr1.vect
p10.18
ropelength 90.20
p10.18.idealr1.vect
m10.18.idealr1.vect
p10.19
ropelength 89.38
p10.19.idealr1.vect
m10.19.idealr1.vect
p10.20
ropelength 88.76
p10.20.idealr1.vect
m10.20.idealr1.vect
p10.21
ropelength 88.91
p10.21.idealr1.vect
m10.21.idealr1.vect
p10.22
ropelength 89.18
p10.22.idealr1.vect
m10.22.idealr1.vect
p10.23
ropelength 90.51
p10.23.idealr1.vect
m10.23.idealr1.vect
p10.24
ropelength 90.14
p10.24.idealr1.vect
m10.24.idealr1.vect
p10.25
ropelength 90.52
p10.25.idealr1.vect
m10.25.idealr1.vect
p10.26
ropelength 90.29
p10.26.idealr1.vect
m10.26.idealr1.vect
p10.27
ropelength 90.72
p10.27.idealr1.vect
m10.27.idealr1.vect
p10.28
ropelength 89.31
p10.28.idealr1.vect
m10.28.idealr1.vect
p10.29
ropelength 90.12
p10.29.idealr1.vect
m10.29.idealr1.vect
p10.30
ropelength 90.13
p10.30.idealr1.vect
m10.30.idealr1.vect
p10.31
ropelength 90.07
p10.31.idealr1.vect
m10.31.idealr1.vect
p10.32
ropelength 90.46
p10.32.idealr1.vect
m10.32.idealr1.vect
a10.33
ropelength 90.08
a10.33.idealr1.vect
p10.34
ropelength 88.81
p10.34.idealr1.vect
m10.34.idealr1.vect
p10.35
ropelength 89.81
p10.35.idealr1.vect
m10.35.idealr1.vect
p10.36
ropelength 89.76
p10.36.idealr1.vect
m10.36.idealr1.vect
a10.37
ropelength 89.89
a10.37.idealr1.vect
p10.38
ropelength 90.12
p10.38.idealr1.vect
m10.38.idealr1.vect
p10.39
ropelength 90.15
p10.39.idealr1.vect
m10.39.idealr1.vect
p10.40
ropelength 90.90
p10.40.idealr1.vect
m10.40.idealr1.vect
p10.41
ropelength 90.70
p10.41.idealr1.vect
m10.41.idealr1.vect
p10.42
ropelength 91.60
p10.42.idealr1.vect
m10.42.idealr1.vect
a10.43
ropelength 90.99
a10.43.idealr1.vect
p10.44
ropelength 90.64
p10.44.idealr1.vect
m10.44.idealr1.vect
a10.45
ropelength 91.12
a10.45.idealr1.vect
p10.46
ropelength 88.41
p10.46.idealr1.vect
m10.46.idealr1.vect
p10.47
ropelength 89.19
p10.47.idealr1.vect
m10.47.idealr1.vect
h10.48
ropelength 89.34
h10.48.idealr1.vect
p10.49
ropelength 90.05
p10.49.idealr1.vect
m10.49.idealr1.vect
p10.50
ropelength 89.26
p10.50.idealr1.vect
m10.50.idealr1.vect
p10.51
ropelength 90.08
p10.51.idealr1.vect
m10.51.idealr1.vect
p10.52
ropelength 89.88
p10.52.idealr1.vect
m10.52.idealr1.vect
p10.53
ropelength 90.62
p10.53.idealr1.vect
m10.53.idealr1.vect
p10.54
ropelength 89.40
p10.54.idealr1.vect
m10.54.idealr1.vect
p10.55
ropelength 90.20
p10.55.idealr1.vect
m10.55.idealr1.vect
p10.56
ropelength 90.78
p10.56.idealr1.vect
m10.56.idealr1.vect
p10.57
ropelength 91.36
p10.57.idealr1.vect
m10.57.idealr1.vect
p10.58
ropelength 90.80
p10.58.idealr1.vect
m10.58.idealr1.vect
p10.59
ropelength 90.89
p10.59.idealr1.vect
m10.59.idealr1.vect
p10.60
ropelength 91.03
p10.60.idealr1.vect
m10.60.idealr1.vect
p10.61
ropelength 88.38
p10.61.idealr1.vect
m10.61.idealr1.vect
p10.62
ropelength 89.42
p10.62.idealr1.vect
m10.62.idealr1.vect
p10.63
ropelength 90.20
p10.63.idealr1.vect
m10.63.idealr1.vect
p10.64
ropelength 89.39
p10.64.idealr1.vect
m10.64.idealr1.vect
p10.65
ropelength 90.20
p10.65.idealr1.vect
m10.65.idealr1.vect
p10.66
ropelength 90.88
p10.66.idealr1.vect
m10.66.idealr1.vect
p10.67
ropelength 90.26
p10.67.idealr1.vect
m10.67.idealr1.vect
p10.68
ropelength 89.85
p10.68.idealr1.vect
m10.68.idealr1.vect
p10.69
ropelength 90.82
p10.69.idealr1.vect
m10.69.idealr1.vect
p10.70
ropelength 90.89
p10.70.idealr1.vect
m10.70.idealr1.vect
h10.71
ropelength 90.73
h10.71.idealr1.vect
p10.72
ropelength 90.84
p10.72.idealr1.vect
m10.72.idealr1.vect
p10.73
ropelength 91.08
p10.73.idealr1.vect
m10.73.idealr1.vect
p10.74
ropelength 89.96
p10.74.idealr1.vect
m10.74.idealr1.vect
p10.75
ropelength 90.65
p10.75.idealr1.vect
m10.75.idealr1.vect
p10.76
ropelength 90.15
p10.76.idealr1.vect
m10.76.idealr1.vect
p10.77
ropelength 90.34
p10.77.idealr1.vect
m10.77.idealr1.vect
p10.78
ropelength 90.30
p10.78.idealr1.vect
m10.78.idealr1.vect
a10.79
ropelength 90.83
a10.79.idealr1.vect
p10.80
ropelength 90.84
p10.80.idealr1.vect
m10.80.idealr1.vect
a10.81
ropelength 91.67
a10.81.idealr1.vect
p10.82
ropelength 90.52
p10.82.idealr1.vect
m10.82.idealr1.vect
p10.83
ropelength 91.38
p10.83.idealr1.vect
m10.83.idealr1.vect
p10.84
ropelength 91.27
p10.84.idealr1.vect
m10.84.idealr1.vect
p10.85
ropelength 89.68
p10.85.idealr1.vect
m10.85.idealr1.vect
p10.86
ropelength 90.44
p10.86.idealr1.vect
m10.86.idealr1.vect
p10.87
ropelength 90.88
p10.87.idealr1.vect
m10.87.idealr1.vect
a10.88
ropelength 91.22
a10.88.idealr1.vect
p10.89
ropelength 91.08
p10.89.idealr1.vect
m10.89.idealr1.vect
p10.90
ropelength 90.74
p10.90.idealr1.vect
m10.90.idealr1.vect
h10.91
ropelength 90.74
h10.91.idealr1.vect
p10.92
ropelength 91.31
p10.92.idealr1.vect
m10.92.idealr1.vect
p10.93
ropelength 90.14
p10.93.idealr1.vect
m10.93.idealr1.vect
p10.94
ropelength 90.66
p10.94.idealr1.vect
m10.94.idealr1.vect
p10.95
ropelength 91.35
p10.95.idealr1.vect
m10.95.idealr1.vect
p10.96
ropelength 91.24
p10.96.idealr1.vect
m10.96.idealr1.vect
p10.97
ropelength 91.11
p10.97.idealr1.vect
m10.97.idealr1.vect
p10.98
ropelength 91.50
p10.98.idealr1.vect
m10.98.idealr1.vect
a10.99
ropelength 90.67
a10.99.idealr1.vect
p10.100
ropelength 90.57
p10.100.idealr1.vect
m10.100.idealr1.vect
p10.101
ropelength 91.46
p10.101.idealr1.vect
m10.101.idealr1.vect
p10.102
ropelength 90.60
p10.102.idealr1.vect
m10.102.idealr1.vect
p10.103
ropelength 90.62
p10.103.idealr1.vect
m10.103.idealr1.vect
h10.104
ropelength 90.83
h10.104.idealr1.vect
p10.105
ropelength 91.55
p10.105.idealr1.vect
m10.105.idealr1.vect
p10.106
ropelength 90.69
p10.106.idealr1.vect
m10.106.idealr1.vect
p10.107
ropelength 91.44
p10.107.idealr1.vect
m10.107.idealr1.vect
p10.108
ropelength 90.34
p10.108.idealr1.vect
m10.108.idealr1.vect
a10.109
ropelength 91.54
a10.109.idealr1.vect
p10.110
ropelength 91.11
p10.110.idealr1.vect
m10.110.idealr1.vect
p10.111
ropelength 91.50
p10.111.idealr1.vect
m10.111.idealr1.vect
p10.112
ropelength 91.28
p10.112.idealr1.vect
m10.112.idealr1.vect
p10.113
ropelength 91.85
p10.113.idealr1.vect
m10.113.idealr1.vect
p10.114
ropelength 91.04
p10.114.idealr1.vect
m10.114.idealr1.vect
a10.115
ropelength 92.00
a10.115.idealr1.vect
p10.116
ropelength 92.02
p10.116.idealr1.vect
m10.116.idealr1.vect
p10.117
ropelength 91.14
p10.117.idealr1.vect
m10.117.idealr1.vect
a10.118
ropelength 91.16
a10.118.idealr1.vect
p10.119
ropelength 91.82
p10.119.idealr1.vect
m10.119.idealr1.vect
p10.120
ropelength 91.92
p10.120.idealr1.vect
m10.120.idealr1.vect
p10.121
ropelength 91.66
p10.121.idealr1.vect
m10.121.idealr1.vect
p10.122
ropelength 91.49
p10.122.idealr1.vect
m10.122.idealr1.vect
a10.123
ropelength 94.34
a10.123.idealr1.vect
p10.124
ropelength 72.49
p10.124.idealr1.vect
m10.124.idealr1.vect
h10.125
ropelength 76.66
h10.125.idealr1.vect
p10.126
ropelength 79.16
p10.126.idealr1.vect
m10.126.idealr1.vect
p10.127
ropelength 81.63
p10.127.idealr1.vect
m10.127.idealr1.vect
p10.128
ropelength 77.54
p10.128.idealr1.vect
m10.128.idealr1.vect
p10.129
ropelength 79.96
p10.129.idealr1.vect
m10.129.idealr1.vect
p10.130
ropelength 80.22
p10.130.idealr1.vect
m10.130.idealr1.vect
p10.131
ropelength 82.73
p10.131.idealr1.vect
m10.131.idealr1.vect
p10.132
ropelength 75.78
p10.132.idealr1.vect
m10.132.idealr1.vect
p10.133
ropelength 78.49
p10.133.idealr1.vect
m10.133.idealr1.vect
p10.134
ropelength 80.15
p10.134.idealr1.vect
m10.134.idealr1.vect
p10.135
ropelength 82.65
p10.135.idealr1.vect
m10.135.idealr1.vect
p10.136
ropelength 79.26
p10.136.idealr1.vect
m10.136.idealr1.vect
p10.137
ropelength 81.01
p10.137.idealr1.vect
m10.137.idealr1.vect
p10.138
ropelength 83.80
p10.138.idealr1.vect
m10.138.idealr1.vect
p10.139
ropelength 74.05
p10.139.idealr1.vect
m10.139.idealr1.vect
p10.140
ropelength 75.29
p10.140.idealr1.vect
m10.140.idealr1.vect
p10.141
ropelength 78.44
p10.141.idealr1.vect
m10.141.idealr1.vect
p10.142
ropelength 77.42
p10.142.idealr1.vect
m10.142.idealr1.vect
p10.143
ropelength 79.82
p10.143.idealr1.vect
m10.143.idealr1.vect
p10.144
ropelength 82.46
p10.144.idealr1.vect
m10.144.idealr1.vect
p10.145
ropelength 77.14
p10.145.idealr1.vect
m10.145.idealr1.vect
p10.146
ropelength 81.10
p10.146.idealr1.vect
m10.146.idealr1.vect
p10.147
ropelength 80.62
p10.147.idealr1.vect
m10.147.idealr1.vect
p10.148
ropelength 80.44
p10.148.idealr1.vect
m10.148.idealr1.vect
p10.149
ropelength 82.52
p10.149.idealr1.vect
m10.149.idealr1.vect
p10.150
ropelength 81.36
p10.150.idealr1.vect
m10.150.idealr1.vect
p10.151
ropelength 83.40
p10.151.idealr1.vect
m10.151.idealr1.vect
p10.152
ropelength 80.44
p10.152.idealr1.vect
m10.152.idealr1.vect
p10.153
ropelength 81.74
p10.153.idealr1.vect
m10.153.idealr1.vect
p10.154
ropelength 82.86
p10.154.idealr1.vect
m10.154.idealr1.vect
p10.155
ropelength 79.26
p10.155.idealr1.vect
m10.155.idealr1.vect
p10.156
ropelength 80.97
p10.156.idealr1.vect
m10.156.idealr1.vect
p10.157
ropelength 82.96
p10.157.idealr1.vect
m10.157.idealr1.vect
p10.158
ropelength 83.04
p10.158.idealr1.vect
m10.158.idealr1.vect
p10.159
ropelength 81.29
p10.159.idealr1.vect
m10.159.idealr1.vect
p10.160
ropelength 79.43
p10.160.idealr1.vect
m10.160.idealr1.vect
p10.161
ropelength 75.78
p10.161.idealr1.vect
m10.161.idealr1.vect
p10.162
ropelength 82.50
p10.162.idealr1.vect
m10.162.idealr1.vect
p10.163
ropelength 84.12
p10.163.idealr1.vect
m10.163.idealr1.vect
p10.164
ropelength 83.53
p10.164.idealr1.vect
m10.164.idealr1.vect
p10.165
ropelength 84.31
p10.165.idealr1.vect
m10.165.idealr1.vect
This work has been supported by NFS DMS grant numbers 0074315, 0296098, 0311010, 0621903, 0810415, 1115722, and 1418869. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.