knots {knotR} | R Documentation |
Optimized knots
Description
A variety of knots with optimized forms
Details
A selection of knots that have been optimized for visual appearance. The list makes no claims for completeness; the examples are intended to show the abilities of the package.
Knots with names like k7_3
use the naming scheme of Rolfsen.
Knots with names like k11n157
follow the nomenclature of the
Hoste-Thistlethwaite table; ‘a’ means ‘alternating’
and ‘n’ means ‘nonalternating’.
Knot k12a_614
is drawn from the “Table of Knot
Invariants” by Livingstone and Cha.
Knot amphichiral15
is the unique amphichiral knot with crossing
number 15, due to Hoste, Thistlethwaite, and Weeks.
Knots k12n_0411
and k11a203
show that partial symmetry
may be enforced.
Knot k8_18
is an exceptional knot.
Knot pretzel_p3_p5_p7_m3_m5
is drawn from a knot appearing in
Bryant 2016. The notation specifies the sense (‘p’ for plus
and ‘m’ for minus) of the twists.
Knot T20
is a “remarkable 20-crossing tangle”; see
references
Knots k12a1202
and k12n838
are named following Lamm.
As of version 1.0-4, the complete list of knots is:
k10_1
, k10_123
, k10_47
, k10_61
,
k12a1202
, k12n838
, k3_1
, k3_1a
, k4_1
,
k4_1a
, k5_1
, k5_2
, k6_1
, k6_2
,
k6_3
, k7_1
, k7_2
, k7_3
, k7_4
,
k7_5
, k7_6
, k7_7
, k7_7a
, k8_1
,
k8_10
, k8_11
, k8_12
, k8_13
, k8_14
,
k8_15
, k8_16
, k8_17
, k8_18
, k8_19
,
k8_19a
, k8_19b
, k8_2
, k8_20
, k8_21
,
k8_3
, k8_3_90deg_crossing
,
k8_4
, k8_4a
, k8_5
, k8_6
,
k8_7
, k8_8
, k8_9
, k9_1
, k9_10
,
k9_11
, k9_12
, k9_13
, k9_14
, k9_15
,
k9_16
, k9_17
, k9_18
, k9_19
, k9_2
,
k9_20
, k9_21
, k9_22
, k9_23
, k9_23a
,
k9_24
, k9_25
, k9_26
, k9_27
, k9_28
,
k9_29
, k9_3
, k9_30
, k9_31
, k9_32
,
k9_33
, k9_34
, k9_35
, k9_36
, k9_37
,
k9_38
, k9_39
, k9_4
, k9_40
, k9_41
,
k9_42
, k9_43
, k9_44
, k9_45
, k9_46
,
k9_47
, k9_48
, k9_49
, k9_5
, k9_6
,
k9_7
, k9_8
, k9_9
, D16
, T20
,
amphichiral15
, celtic3
, fiveloops
, flower
,
fourloops
, hexknot
, hexknot2
, hexknot3
,
k_infinity
, k11a1
, k11a179
, k11a361
,
k11n157
, k11n157_morenodes
, k11n22
,
k12n_0242
, k12n_0411
, longthin
, ochiai
,
ornamental20
, perko_A
, perko_B
,
pretzel_2_3_7
, pretzel_7_3_7
,
pretzel_p3_p5_p7_m3_m5
, reefknot
, satellite
,
sum_31_41
, three_figure_eights
,
trefoil_of_trefoils
, triloop
, unknot
References
K. A. Bryant, 2016. Slice implies mutant-ribbon for odd, 5-stranded pretzel knots,
arXiv:1511.07009v2
S. Eliahou and J. Fromentin 2017. “A remarkable 20-crossing tangle”. Arxiv, https://arxiv.org/abs/1610.05560v2
Examples
knotplot(k3_1)
## maybe str(k3_1) ; plot(k3_1) ...