# 9 20 (KnotPlot image) See the full Rolfsen Knot Table. Visit 9 20's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 9 20 at Knotilus!

### Knot presentations

 Planar diagram presentation X1425 X3,10,4,11 X5,14,6,15 X7,16,8,17 X11,1,12,18 X15,6,16,7 X17,13,18,12 X13,8,14,9 X9,2,10,3 Gauss code -1, 9, -2, 1, -3, 6, -4, 8, -9, 2, -5, 7, -8, 3, -6, 4, -7, 5 Dowker-Thistlethwaite code 4 10 14 16 2 18 8 6 12 Conway Notation 

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 2 3-genus 3 Bridge index 2 Super bridge index $\{4,6\}$ Nakanishi index 1 Maximal Thurston-Bennequin number [-12] Hyperbolic Volume 9.6443 A-Polynomial See Data:9 20/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $2$ Topological 4 genus $2$ Concordance genus $3$ Rasmussen s-Invariant -4

### Polynomial invariants

 Alexander polynomial $-t^3+5 t^2-9 t+11-9 t^{-1} +5 t^{-2} - t^{-3}$ Conway polynomial $-z^6-z^4+2 z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 41, -4 } Jones polynomial $1-2 q^{-1} +4 q^{-2} -5 q^{-3} +7 q^{-4} -7 q^{-5} +6 q^{-6} -5 q^{-7} +3 q^{-8} - q^{-9}$ HOMFLY-PT polynomial (db, data sources) $-z^2 a^8-a^8+2 z^4 a^6+5 z^2 a^6+2 a^6-z^6 a^4-4 z^4 a^4-5 z^2 a^4-2 a^4+z^4 a^2+3 z^2 a^2+2 a^2$ Kauffman polynomial (db, data sources) $z^3 a^{11}+3 z^4 a^{10}-z^2 a^{10}+5 z^5 a^9-5 z^3 a^9+2 z a^9+5 z^6 a^8-6 z^4 a^8+3 z^2 a^8-a^8+3 z^7 a^7-7 z^3 a^7+2 z a^7+z^8 a^6+5 z^6 a^6-16 z^4 a^6+10 z^2 a^6-2 a^6+5 z^7 a^5-12 z^5 a^5+5 z^3 a^5+z^8 a^4+z^6 a^4-11 z^4 a^4+11 z^2 a^4-2 a^4+2 z^7 a^3-7 z^5 a^3+6 z^3 a^3+z^6 a^2-4 z^4 a^2+5 z^2 a^2-2 a^2$ The A2 invariant $-q^{28}+q^{24}-q^{22}+q^{20}-q^{18}+q^{14}-q^{12}+2 q^{10}-q^8+q^6+q^4+1$ The G2 invariant $q^{148}-2 q^{146}+3 q^{144}-4 q^{142}+2 q^{140}-q^{138}-2 q^{136}+9 q^{134}-12 q^{132}+15 q^{130}-13 q^{128}+5 q^{126}+2 q^{124}-13 q^{122}+23 q^{120}-27 q^{118}+23 q^{116}-13 q^{114}-q^{112}+15 q^{110}-23 q^{108}+25 q^{106}-21 q^{104}+5 q^{102}+7 q^{100}-17 q^{98}+16 q^{96}-5 q^{94}-9 q^{92}+23 q^{90}-24 q^{88}+14 q^{86}+3 q^{84}-26 q^{82}+44 q^{80}-44 q^{78}+30 q^{76}-4 q^{74}-21 q^{72}+43 q^{70}-45 q^{68}+33 q^{66}-17 q^{64}-6 q^{62}+22 q^{60}-28 q^{58}+22 q^{56}-6 q^{54}-9 q^{52}+19 q^{50}-19 q^{48}+7 q^{46}+8 q^{44}-23 q^{42}+31 q^{40}-28 q^{38}+12 q^{36}+10 q^{34}-26 q^{32}+36 q^{30}-30 q^{28}+17 q^{26}-q^{24}-13 q^{22}+21 q^{20}-19 q^{18}+14 q^{16}-3 q^{14}-2 q^{12}+5 q^{10}-5 q^8+4 q^6-q^4+q^2$