knots: Optimized knots

In knotR: Knot Diagrams using Bezier Curves

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) ...

knotR documentation built on June 22, 2024, 6:56 p.m.