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Two figure 8 knots on a loop, doubly interlinked.


Knot presentations

Dowker-Thistlethwaite code 6 10 20 24 14 4 18 22 8 12 2 16

Notes on presentations of K12a991

Polynomial invariants

Jones polynomial q^2-4 q+10-17 q^{-1} +25 q^{-2} -30 q^{-3} +33 q^{-4} -31 q^{-5} +25 q^{-6} -18 q^{-7} +10 q^{-8} -4 q^{-9} + q^{-10}
Alexander polynomial t^4-8 t^3+25 t^2-44 t+53-44 t^{-1} +25 t^{-2} -8 t^{-3} + t^{-4}
Conway polynomial z^8-3 z^4+1
Determinant 209
Signature -4
HOMFLY-PT polynomial z^4 a^8+2 z^2 a^8+a^8-2 z^6 a^6-6 z^4 a^6-6 z^2 a^6-3 a^6+z^8 a^4+4 z^6 a^4+7 z^4 a^4+7 z^2 a^4+3 a^4-2 z^6 a^2-6 z^4 a^2-5 z^2 a^2-a^2+z^4+2 z^2+1
Kauffman polynomial z^4 a^{12}+4 z^5 a^{11}+10 z^6 a^{10}-6 z^4 a^{10}+2 z^2 a^{10}+18 z^7 a^9-24 z^5 a^9+12 z^3 a^9-2 z a^9+23 z^8 a^8-41 z^6 a^8+22 z^4 a^8-6 z^2 a^8+a^8+21 z^9 a^7-39 z^7 a^7+12 z^5 a^7+z^3 a^7-2 z a^7+12 z^{10} a^6-7 z^8 a^6-47 z^6 a^6+51 z^4 a^6-19 z^2 a^6+3 a^6+3 z^{11} a^5+24 z^9 a^5-99 z^7 a^5+100 z^5 a^5-36 z^3 a^5+4 z a^5+18 z^{10} a^4-50 z^8 a^4+19 z^6 a^4+28 z^4 a^4-17 z^2 a^4+3 a^4+3 z^{11} a^3+7 z^9 a^3-58 z^7 a^3+82 z^5 a^3-37 z^3 a^3+6 z a^3+6 z^{10} a^2-19 z^8 a^2+11 z^6 a^2+12 z^4 a^2-10 z^2 a^2+a^2+4 z^9 a-16 z^7 a+22 z^5 a-12 z^3 a+2 z a+z^8-4 z^6+6 z^4-4 z^2+1

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