# K12a975

Knotscape
Four-fold symmetrical depiction as decorative knot
Square depiction as two doubly-interlinked 4_1 knots on a closed loop.
Simple symmetrical squared depiction.
Circular cross decorative knot.
(alternate).

## Contents

### Knot presentations

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

### Polynomial invariants

 Jones polynomial $q^4-4 q^3+10 q^2-19 q+28-33 q^{-1} +36 q^{-2} -33 q^{-3} +27 q^{-4} -19 q^{-5} +10 q^{-6} -4 q^{-7} + q^{-8}$ Alexander polynomial $-4 t^3+22 t^2-52 t+69-52 t^{-1} +22 t^{-2} -4 t^{-3}$ Conway polynomial $-4 z^6-2 z^4+1$ Determinant 225 Signature 0 HOMFLY-PT polynomial $a^8-4 z^2 a^6-4 a^6+6 z^4 a^4+12 z^2 a^4+6 a^4-3 z^6 a^2-9 z^4 a^2-11 z^2 a^2-4 a^2-z^6+2 z^2+2+z^4 a^{-2} +z^2 a^{-2}$ Kauffman polynomial $3 a^5 z^{11}+3 a^3 z^{11}+6 a^6 z^{10}+20 a^4 z^{10}+14 a^2 z^{10}+4 a^7 z^9+11 a^5 z^9+33 a^3 z^9+26 a z^9+a^8 z^8-17 a^6 z^8-50 a^4 z^8-5 a^2 z^8+27 z^8-16 a^7 z^7-73 a^5 z^7-131 a^3 z^7-55 a z^7+19 z^7 a^{-1} -4 a^8 z^6+5 a^6 z^6-72 a^2 z^6+10 z^6 a^{-2} -53 z^6+24 a^7 z^5+105 a^5 z^5+139 a^3 z^5+30 a z^5-24 z^5 a^{-1} +4 z^5 a^{-3} +6 a^8 z^4+21 a^6 z^4+61 a^4 z^4+88 a^2 z^4-5 z^4 a^{-2} +z^4 a^{-4} +36 z^4-16 a^7 z^3-56 a^5 z^3-60 a^3 z^3-10 a z^3+10 z^3 a^{-1} -4 a^8 z^2-18 a^6 z^2-38 a^4 z^2-37 a^2 z^2+z^2 a^{-2} -12 z^2+4 a^7 z+12 a^5 z+12 a^3 z+4 a z+a^8+4 a^6+6 a^4+4 a^2+2$