K12a477

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Knotscape
Symmetrical representation as decorative knot


Contents

Knot presentations

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

Notes on presentations of K12a477

Polynomial invariants

Jones polynomial q^6-3 q^5+8 q^4-14 q^3+20 q^2-25 q+27-25 q^{-1} +20 q^{-2} -14 q^{-3} +8 q^{-4} -3 q^{-5} + q^{-6}
Alexander polynomial -t^3+11 t^2-41 t+63-41 t^{-1} +11 t^{-2} - t^{-3}
Conway polynomial -z^6+5 z^4-6 z^2+1
Determinant 169
Signature 0
HOMFLY-PT polynomial a^6-3 z^2 a^4-a^4+3 z^4 a^2+2 z^2 a^2+a^2-z^6-z^4-4 z^2-1+3 z^4 a^{-2} +2 z^2 a^{-2} + a^{-2} -3 z^2 a^{-4} - a^{-4} + a^{-6}
Kauffman polynomial a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+3 z^{10} a^{-2} +6 z^{10}+5 a^3 z^9+8 a z^9+8 z^9 a^{-1} +5 z^9 a^{-3} +5 a^4 z^8+5 a^2 z^8+5 z^8 a^{-2} +5 z^8 a^{-4} +3 a^5 z^7-4 a^3 z^7-7 a z^7-7 z^7 a^{-1} -4 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-9 a^4 z^6-14 a^2 z^6-14 z^6 a^{-2} -9 z^6 a^{-4} +z^6 a^{-6} -8 z^6-7 a^5 z^5-5 a^3 z^5-9 a z^5-9 z^5 a^{-1} -5 z^5 a^{-3} -7 z^5 a^{-5} -3 a^6 z^4+3 a^4 z^4+5 a^2 z^4+5 z^4 a^{-2} +3 z^4 a^{-4} -3 z^4 a^{-6} -2 z^4+5 a^5 z^3+4 a^3 z^3+8 a z^3+8 z^3 a^{-1} +4 z^3 a^{-3} +5 z^3 a^{-5} +3 a^6 z^2+2 a^4 z^2+2 a^2 z^2+2 z^2 a^{-2} +2 z^2 a^{-4} +3 z^2 a^{-6} +6 z^2-a^5 z-a z-z a^{-1} -z a^{-5} -a^6-a^4-a^2- a^{-2} - a^{-4} - a^{-6} -1



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