# 10 42 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 42's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 42 at Knotilus!

### Knot presentations

 Planar diagram presentation X1425 X3,10,4,11 X11,1,12,20 X5,13,6,12 X15,18,16,19 X13,9,14,8 X17,7,18,6 X7,17,8,16 X19,14,20,15 X9,2,10,3 Gauss code -1, 10, -2, 1, -4, 7, -8, 6, -10, 2, -3, 4, -6, 9, -5, 8, -7, 5, -9, 3 Dowker-Thistlethwaite code 4 10 12 16 2 20 8 18 6 14 Conway Notation 

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 1 3-genus 3 Bridge index 2 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-6][-6] Hyperbolic Volume 13.2398 A-Polynomial See Data:10 42/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $0$ Topological 4 genus $0$ Concordance genus $0$ Rasmussen s-Invariant 0

### Polynomial invariants

 Alexander polynomial $-t^3+7 t^2-19 t+27-19 t^{-1} +7 t^{-2} - t^{-3}$ Conway polynomial $-z^6+z^4+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 81, 0 } Jones polynomial $-q^5+3 q^4-6 q^3+10 q^2-12 q+14-13 q^{-1} +10 q^{-2} -7 q^{-3} +4 q^{-4} - q^{-5}$ HOMFLY-PT polynomial (db, data sources) $-z^6+2 a^2 z^4+2 z^4 a^{-2} -3 z^4-a^4 z^2+3 a^2 z^2+4 z^2 a^{-2} -z^2 a^{-4} -5 z^2+a^2+3 a^{-2} - a^{-4} -2$ Kauffman polynomial (db, data sources) $a z^9+z^9 a^{-1} +4 a^2 z^8+3 z^8 a^{-2} +7 z^8+6 a^3 z^7+11 a z^7+9 z^7 a^{-1} +4 z^7 a^{-3} +4 a^4 z^6+2 z^6 a^{-2} +3 z^6 a^{-4} -5 z^6+a^5 z^5-11 a^3 z^5-24 a z^5-18 z^5 a^{-1} -5 z^5 a^{-3} +z^5 a^{-5} -7 a^4 z^4-10 a^2 z^4-11 z^4 a^{-2} -6 z^4 a^{-4} -8 z^4-a^5 z^3+5 a^3 z^3+14 a z^3+10 z^3 a^{-1} -2 z^3 a^{-5} +2 a^4 z^2+6 a^2 z^2+9 z^2 a^{-2} +4 z^2 a^{-4} +9 z^2-a z-z a^{-1} +z a^{-3} +z a^{-5} -a^2-3 a^{-2} - a^{-4} -2$ The A2 invariant $-q^{16}+q^{14}+2 q^{12}-2 q^{10}+2 q^8-q^6-2 q^4+2 q^2-2+3 q^{-2} - q^{-4} + q^{-6} +3 q^{-8} -2 q^{-10} + q^{-12} - q^{-16}$ The G2 invariant $q^{80}-3 q^{78}+7 q^{76}-13 q^{74}+14 q^{72}-11 q^{70}-2 q^{68}+27 q^{66}-50 q^{64}+72 q^{62}-77 q^{60}+46 q^{58}+9 q^{56}-85 q^{54}+151 q^{52}-176 q^{50}+153 q^{48}-70 q^{46}-43 q^{44}+156 q^{42}-219 q^{40}+209 q^{38}-128 q^{36}+4 q^{34}+105 q^{32}-160 q^{30}+140 q^{28}-53 q^{26}-50 q^{24}+135 q^{22}-152 q^{20}+76 q^{18}+46 q^{16}-181 q^{14}+262 q^{12}-253 q^{10}+150 q^8+16 q^6-182 q^4+299 q^2-322+238 q^{-2} -86 q^{-4} -82 q^{-6} +199 q^{-8} -227 q^{-10} +171 q^{-12} -51 q^{-14} -60 q^{-16} +126 q^{-18} -121 q^{-20} +43 q^{-22} +66 q^{-24} -153 q^{-26} +181 q^{-28} -130 q^{-30} +27 q^{-32} +93 q^{-34} -177 q^{-36} +209 q^{-38} -172 q^{-40} +90 q^{-42} +7 q^{-44} -92 q^{-46} +132 q^{-48} -130 q^{-50} +97 q^{-52} -45 q^{-54} -3 q^{-56} +35 q^{-58} -51 q^{-60} +46 q^{-62} -32 q^{-64} +16 q^{-66} -2 q^{-68} -7 q^{-70} +8 q^{-72} -8 q^{-74} +5 q^{-76} -2 q^{-78} + q^{-80}$