Figure eight knot—Dave Richeson
FigEight.png

Names and notations

Rolfsen notation

41

Dowker-Thistlethwaite notation

4 6 8 2

Conway notation

TBD

Braid notation

TBD


Knot properties

Alternating knot

Yes

Tricolorable

No

Amphicheiral

Yes


Numerical knot invariants

Unknotting number

1

Bridge number

2

Crossing number

4

Genus

1


Knot polynomials

Jones polynomial

$q^2-q + 1-q^{-1} + q^{-2}$

Alexander polynomial

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

HOMFLY polynomial

$a^2-z^2-1 + a^{-2}$

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