K12a561

Knotscape

Three-fold symmetrical depiction as decorative knot

Inside triangle

Knot presentations

Dowker-Thistlethwaite code

4 12 16 14 20 2 24 18 6 22 10 8

Notes on presentations of K12a561

Polynomial invariants

Jones polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{11}+5 q^{10}-12 q^9+20 q^8-29 q^7+34 q^6-35 q^5+33 q^4-25 q^3+17 q^2-9 q+4- q^{-1} }
Alexander polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^4-7 t^3+25 t^2-49 t+61-49 t^{-1} +25 t^{-2} -7 t^{-3} + t^{-4} }
Conway polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^8+z^6+3 z^4+4 z^2+1}
Determinant	225
Signature	4
HOMFLY-PT polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^8 a^{-4} -z^6 a^{-2} +5 z^6 a^{-4} -3 z^6 a^{-6} -3 z^4 a^{-2} +12 z^4 a^{-4} -9 z^4 a^{-6} +3 z^4 a^{-8} -3 z^2 a^{-2} +13 z^2 a^{-4} -9 z^2 a^{-6} +4 z^2 a^{-8} -z^2 a^{-10} - a^{-2} +5 a^{-4} -3 a^{-6} }
Kauffman polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^{11} a^{-5} +z^{11} a^{-7} +4 z^{10} a^{-4} +10 z^{10} a^{-6} +6 z^{10} a^{-8} +6 z^9 a^{-3} +20 z^9 a^{-5} +28 z^9 a^{-7} +14 z^9 a^{-9} +4 z^8 a^{-2} +7 z^8 a^{-4} +12 z^8 a^{-6} +26 z^8 a^{-8} +17 z^8 a^{-10} +z^7 a^{-1} -14 z^7 a^{-3} -51 z^7 a^{-5} -53 z^7 a^{-7} -5 z^7 a^{-9} +12 z^7 a^{-11} -13 z^6 a^{-2} -47 z^6 a^{-4} -85 z^6 a^{-6} -79 z^6 a^{-8} -23 z^6 a^{-10} +5 z^6 a^{-12} -3 z^5 a^{-1} +6 z^5 a^{-3} +26 z^5 a^{-5} +8 z^5 a^{-7} -24 z^5 a^{-9} -14 z^5 a^{-11} +z^5 a^{-13} +15 z^4 a^{-2} +59 z^4 a^{-4} +91 z^4 a^{-6} +62 z^4 a^{-8} +12 z^4 a^{-10} -3 z^4 a^{-12} +3 z^3 a^{-1} +6 z^3 a^{-3} +12 z^3 a^{-5} +21 z^3 a^{-7} +18 z^3 a^{-9} +6 z^3 a^{-11} -7 z^2 a^{-2} -28 z^2 a^{-4} -33 z^2 a^{-6} -17 z^2 a^{-8} -5 z^2 a^{-10} -z a^{-1} -4 z a^{-3} -9 z a^{-5} -7 z a^{-7} -2 z a^{-9} -z a^{-11} + a^{-2} +5 a^{-4} +3 a^{-6} }

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