[en] | Cinquefoil knot

Δ ( t ) = t 2 − t + 1 − t − 1 + t − 2 {displaystyle Delta (t)=t^{2}-t+1-t^{-1}+t^{-2}},

its Conway polynomial is

∇ ( z ) = z 4 + 3 z 2 + 1 {displaystyle nabla (z)=z^{4}+3z^{2}+1},

and its Jones polynomial is

V ( q ) = q − 2 + q − 4 − q − 5 + q − 6 − q − 7 . {displaystyle V(q)=q^{-2}+q^{-4}-q^{-5}+q^{-6}-q^{-7}.}

These are the same as the Alexander, Conway, and Jones polynomials of the knot 10₁₃₂. However, the Kauffman polynomial can be used to distinguish between these two knots.

• Pentagram
• Trefoil knot
• 7₁ knot
• Skein relation

• A Pentafoil Knot at the Wayback Machine (archived June 4, 2004)