# 10 118 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 118's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 118 at Knotilus!

### Knot presentations

 Planar diagram presentation X6271 X18,6,19,5 X20,13,1,14 X12,19,13,20 X14,7,15,8 X8394 X2,16,3,15 X10,18,11,17 X16,10,17,9 X4,11,5,12 Gauss code 1, -7, 6, -10, 2, -1, 5, -6, 9, -8, 10, -4, 3, -5, 7, -9, 8, -2, 4, -3 Dowker-Thistlethwaite code 6 8 18 14 16 4 20 2 10 12 Conway Notation [8*2:.2]

### Three dimensional invariants

 Symmetry type Negative amphicheiral Unknotting number 1 3-genus 4 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-6][-6] Hyperbolic Volume 15.5452 A-Polynomial See Data:10 118/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $1$ Topological 4 genus $1$ Concordance genus $4$ Rasmussen s-Invariant 0

### Polynomial invariants

 Alexander polynomial $t^4-5 t^3+12 t^2-19 t+23-19 t^{-1} +12 t^{-2} -5 t^{-3} + t^{-4}$ Conway polynomial $z^8+3 z^6+2 z^4+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 97, 0 } Jones polynomial $-q^5+4 q^4-8 q^3+12 q^2-15 q+17-15 q^{-1} +12 q^{-2} -8 q^{-3} +4 q^{-4} - q^{-5}$ HOMFLY-PT polynomial (db, data sources) $z^8-a^2 z^6-z^6 a^{-2} +5 z^6-3 a^2 z^4-3 z^4 a^{-2} +8 z^4-2 a^2 z^2-2 z^2 a^{-2} +4 z^2+1$ Kauffman polynomial (db, data sources) $3 a z^9+3 z^9 a^{-1} +7 a^2 z^8+7 z^8 a^{-2} +14 z^8+7 a^3 z^7+6 a z^7+6 z^7 a^{-1} +7 z^7 a^{-3} +4 a^4 z^6-11 a^2 z^6-11 z^6 a^{-2} +4 z^6 a^{-4} -30 z^6+a^5 z^5-12 a^3 z^5-20 a z^5-20 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} -6 a^4 z^4+6 a^2 z^4+6 z^4 a^{-2} -6 z^4 a^{-4} +24 z^4-a^5 z^3+5 a^3 z^3+15 a z^3+15 z^3 a^{-1} +5 z^3 a^{-3} -z^3 a^{-5} +a^4 z^2-2 a^2 z^2-2 z^2 a^{-2} +z^2 a^{-4} -6 z^2-a^3 z-3 a z-3 z a^{-1} -z a^{-3} +1$ The A2 invariant $-q^{14}+2 q^{12}-2 q^{10}+2 q^8-2 q^4+4 q^2-3+4 q^{-2} -2 q^{-4} +2 q^{-8} -2 q^{-10} +2 q^{-12} - q^{-14}$ The G2 invariant $q^{80}-3 q^{78}+7 q^{76}-13 q^{74}+15 q^{72}-13 q^{70}+2 q^{68}+22 q^{66}-48 q^{64}+77 q^{62}-93 q^{60}+75 q^{58}-27 q^{56}-60 q^{54}+162 q^{52}-237 q^{50}+259 q^{48}-188 q^{46}+27 q^{44}+173 q^{42}-342 q^{40}+401 q^{38}-319 q^{36}+115 q^{34}+129 q^{32}-313 q^{30}+362 q^{28}-237 q^{26}+12 q^{24}+212 q^{22}-326 q^{20}+260 q^{18}-55 q^{16}-209 q^{14}+412 q^{12}-458 q^{10}+343 q^8-79 q^6-234 q^4+477 q^2-571+477 q^{-2} -234 q^{-4} -79 q^{-6} +343 q^{-8} -458 q^{-10} +412 q^{-12} -209 q^{-14} -55 q^{-16} +260 q^{-18} -326 q^{-20} +212 q^{-22} +12 q^{-24} -237 q^{-26} +362 q^{-28} -313 q^{-30} +129 q^{-32} +115 q^{-34} -319 q^{-36} +401 q^{-38} -342 q^{-40} +173 q^{-42} +27 q^{-44} -188 q^{-46} +259 q^{-48} -237 q^{-50} +162 q^{-52} -60 q^{-54} -27 q^{-56} +75 q^{-58} -93 q^{-60} +77 q^{-62} -48 q^{-64} +22 q^{-66} +2 q^{-68} -13 q^{-70} +15 q^{-72} -13 q^{-74} +7 q^{-76} -3 q^{-78} + q^{-80}$