The Entangled Hearts Knot
7.4.png

Names and notations

Rolfsen notation

7.4

Dowker-Thistlethwaite notation

8 12 10 2 14 4 6

Conway notation

313

Signed planar graph

7.4signedgraph2.jpg

Braid notation

σ-1σ-2σ-1σ-3σ-2σ-1σ-1σ2σ-1σ3σ2σ2σ3σ-1σ-2


Knot properties

Alternating knot

Yes

Tricolorable

Yes

Amphicheiral

No


Numerical knot invariants

Unknotting number

2

Bridge number

2

Crossing number

7

Genus

1

Span of the bracket polynomial

28


Knot polynomials

Jones polynomial

-q8 + q7 - 2q6 + 3q5 - 2q4 + 3q3 - 2q2 + q

Alexander polynomial

4t - 7 + 4t -1

HOMFLY polynomial

z2a -2 + 2z2a -4 + z2a -6 + 2a -4 - a -8

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