71 knot

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.

71 knot
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 / Next63 / 72
Other
alternating, torus, fibered, prime, reversible

Properties

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

its Conway polynomial is

and its Jones polynomial is

[1]

Example


See also

References
  1. "7_1", The Knot Atlas.
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