The Argoknot
Knot_Smooth

Names and notations

Rolfsen notation

$7_2$

Dowker-Thistlethwaite notation

12 10 8 14 4 2 6

Conway notation

-5 -2

Braid notation

TBD

Signed Planar Graph

PlanarGraph2.png

Knot properties

Alternating knot

Yes

Tricolorable

No

Amphicheiral

Yes/No


Numerical knot invariants

Unknotting number

1

Bridge number

2

Crossing number

7

Genus

1


Knot polynomials

Jones polynomial

$t^{-1} - t^{-2} + 2t^{-3} - 2t^{-4} + 2t^{-5} - t^{-6} + t^{-7} - t^{-8}$

Alexander polynomial

$3t -5 + 3t^{-1}$

HOMFLY polynomial

$−L^8 + M^2L^6 + L^6 + M^2L^4 + M^2L^2 + L^2$

Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License