K12a503

Knotscape

Three-fold symmetrical depiction as decorative knot around triangle

Symmetrical decorative knot around hexagon

Symmetrical decorative knot in form of three triquetras

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a503

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^7-4 q^6+7 q^5-11 q^4+17 q^3-19 q^2+20 q-19+15 q^{-1} -11 q^{-2} +7 q^{-3} -3 q^{-4} + q^{-5} }
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^3-19 t^2+27 t-27+27 t^{-1} -19 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^4-2 z^2+1}
Determinant	135
Signature	2
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^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +3 z^6-3 a^2 z^4-9 z^4 a^{-2} +3 z^4 a^{-4} +12 z^4+a^4 z^2-9 a^2 z^2-7 z^2 a^{-2} +z^2 a^{-4} +12 z^2+2 a^4-4 a^2+3}
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 a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+4 z^{10} a^{-2} +7 z^{10}+3 a^3 z^9+7 a z^9+11 z^9 a^{-1} +7 z^9 a^{-3} +a^4 z^8-8 a^2 z^8+2 z^8 a^{-2} +8 z^8 a^{-4} -15 z^8-14 a^3 z^7-41 a z^7-41 z^7 a^{-1} -6 z^7 a^{-3} +8 z^7 a^{-5} -5 a^4 z^6-7 a^2 z^6-26 z^6 a^{-2} -4 z^6 a^{-4} +7 z^6 a^{-6} -17 z^6+21 a^3 z^5+53 a z^5+29 z^5 a^{-1} -12 z^5 a^{-3} -5 z^5 a^{-5} +4 z^5 a^{-7} +9 a^4 z^4+30 a^2 z^4+18 z^4 a^{-2} -14 z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} +45 z^4-12 a^3 z^3-18 a z^3+6 z^3 a^{-1} +12 z^3 a^{-3} -3 z^3 a^{-5} -3 z^3 a^{-7} -7 a^4 z^2-22 a^2 z^2+z^2 a^{-2} +10 z^2 a^{-4} +3 z^2 a^{-6} -21 z^2+2 a^3 z-a z-7 z a^{-1} -5 z a^{-3} -z a^{-5} +2 a^4+4 a^2+3}

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