K12a503

Knotscape

Three-fold symmetrical depiction as decorative knot around triangle

Symmetrical decorative knot around hexagon

Symmetrical decorative knot in form of three triquetras

Dowker-Thistlethwaite code

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

Jones polynomial	$q^{7}-4q^{6}+7q^{5}-11q^{4}+17q^{3}-19q^{2}+20q-19+15q^{-1}-11q^{-2}+7q^{-3}-3q^{-4}+q^{-5}$
Alexander polynomial	$-t^{4}+7t^{3}-19t^{2}+27t-27+27t^{-1}-19t^{-2}+7t^{-3}-t^{-4}$
Conway polynomial	$-z^{8}-z^{6}+3z^{4}-2z^{2}+1$
Determinant	135
Signature	2
HOMFLY-PT polynomial	$-z^{8}a^{-2}-5z^{6}a^{-2}+z^{6}a^{-4}+3z^{6}-3a^{2}z^{4}-9z^{4}a^{-2}+3z^{4}a^{-4}+12z^{4}+a^{4}z^{2}-9a^{2}z^{2}-7z^{2}a^{-2}+z^{2}a^{-4}+12z^{2}+2a^{4}-4a^{2}+3$
Kauffman polynomial	$az^{11}+z^{11}a^{-1}+3a^{2}z^{10}+4z^{10}a^{-2}+7z^{10}+3a^{3}z^{9}+7az^{9}+11z^{9}a^{-1}+7z^{9}a^{-3}+a^{4}z^{8}-8a^{2}z^{8}+2z^{8}a^{-2}+8z^{8}a^{-4}-15z^{8}-14a^{3}z^{7}-41az^{7}-41z^{7}a^{-1}-6z^{7}a^{-3}+8z^{7}a^{-5}-5a^{4}z^{6}-7a^{2}z^{6}-26z^{6}a^{-2}-4z^{6}a^{-4}+7z^{6}a^{-6}-17z^{6}+21a^{3}z^{5}+53az^{5}+29z^{5}a^{-1}-12z^{5}a^{-3}-5z^{5}a^{-5}+4z^{5}a^{-7}+9a^{4}z^{4}+30a^{2}z^{4}+18z^{4}a^{-2}-14z^{4}a^{-4}-7z^{4}a^{-6}+z^{4}a^{-8}+45z^{4}-12a^{3}z^{3}-18az^{3}+6z^{3}a^{-1}+12z^{3}a^{-3}-3z^{3}a^{-5}-3z^{3}a^{-7}-7a^{4}z^{2}-22a^{2}z^{2}+z^{2}a^{-2}+10z^{2}a^{-4}+3z^{2}a^{-6}-21z^{2}+2a^{3}z-az-7za^{-1}-5za^{-3}-za^{-5}+2a^{4}+4a^{2}+3$