// Workers AI · dad joke modeWhy did 7 2 knot go to therapy? It was feeling tied up.

Pentatwist knot, five-twist knot
Arf invariant	1
Braid length	9
Braid no.	4
Bridge no.	2
Crosscap no.	2
Crossing no.	7
Genus	1
Hyperbolic volume	2.82812
Stick no.	9
Unknotting no.	1
Conway notation	[52]
A–B notation	72
Dowker notation	4, 8, 12, 14, 2, 6, 10
Last / Next	71 / 73
Other
alternating, prime, reversible

In knot theory, the Pentatwist knot, also known as the five-twist knot, or the 7₂, is one of seven prime knots with crossing number seven. It is the fifth twist knot.

Invariants

Its Alexander polynomial is

$\Delta (t)=3t-5+3t^{-1},\,$

its Conway polynomial is

$\nabla (z)=3z^{2}+1,\,$

and its Jones polynomial is

$V(q)=-q^{-8}+q^{-7}-q^{-6}+2q^{-5}-2q^{-4}+2q^{-3}-q^{-2}+q^{-1}.\,$

Example

Assembling of 7₂ knot.