7₁ knot

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7₁ knot
Blue 7 1 Knot.png
Arf invariant0
Braid length7
Braid no.2
Bridge no.2
Crosscap no.1
Crossing no.7
Genus3
Hyperbolic volume0
Stick no.9
Unknotting no.3
Conway notation[7]
A-B notation71
Dowker notation8, 10, 12, 14, 2, 4, 6
Last /Next6372
Other
alternating, torus, fibered, prime, reversible


In knot theory, the 71 knot, also known as the septoil knot, the septafoil knot, or the (7, 2)-torus knot, is one of seven prime knots with crossing number seven. It is the simplest torus knot after the trefoil and cinquefoil.

Properties[edit]

The 71 knot is invertible but not amphichiral. Its Alexander polynomial is

its Conway polynomial is

and its Jones polynomial is

[1]

Example[edit]

Assembling of 7₁ knot.


See also[edit]

References[edit]