# 10 112 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 112's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 112 at Knotilus!

### Knot presentations

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

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 2 3-genus 4 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-9][-3] Hyperbolic Volume 14.7559 A-Polynomial See Data:10 112/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $1$ Topological 4 genus $1$ Concordance genus $4$ Rasmussen s-Invariant 2

### Polynomial invariants

 Alexander polynomial $-t^4+5 t^3-11 t^2+17 t-19+17 t^{-1} -11 t^{-2} +5 t^{-3} - t^{-4}$ Conway polynomial $-z^8-3 z^6-z^4+2 z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 87, -2 } Jones polynomial $q^3-4 q^2+7 q-10+14 q^{-1} -14 q^{-2} +14 q^{-3} -11 q^{-4} +7 q^{-5} -4 q^{-6} + q^{-7}$ HOMFLY-PT polynomial (db, data sources) $-a^2 z^8+a^4 z^6-5 a^2 z^6+z^6+3 a^4 z^4-7 a^2 z^4+3 z^4+a^4 z^2+z^2-2 a^4+4 a^2-1$ Kauffman polynomial (db, data sources) $3 a^3 z^9+3 a z^9+7 a^4 z^8+13 a^2 z^8+6 z^8+8 a^5 z^7+4 a^3 z^7+4 z^7 a^{-1} +7 a^6 z^6-9 a^4 z^6-35 a^2 z^6+z^6 a^{-2} -18 z^6+4 a^7 z^5-8 a^5 z^5-17 a^3 z^5-16 a z^5-11 z^5 a^{-1} +a^8 z^4-7 a^6 z^4+3 a^4 z^4+28 a^2 z^4-2 z^4 a^{-2} +15 z^4-3 a^7 z^3-a^5 z^3+9 a^3 z^3+13 a z^3+6 z^3 a^{-1} +a^6 z^2+a^4 z^2-3 a^2 z^2-3 z^2+2 a^5 z+2 a^3 z-2 a^4-4 a^2-1$ The A2 invariant $q^{20}-2 q^{18}+q^{16}-3 q^{14}-q^{12}+2 q^{10}-q^8+6 q^6-q^4+3 q^2-2 q^{-2} + q^{-4} -2 q^{-6} + q^{-8}$ The G2 invariant $q^{114}-3 q^{112}+6 q^{110}-10 q^{108}+9 q^{106}-6 q^{104}-2 q^{102}+18 q^{100}-32 q^{98}+47 q^{96}-50 q^{94}+34 q^{92}-6 q^{90}-34 q^{88}+75 q^{86}-104 q^{84}+117 q^{82}-101 q^{80}+50 q^{78}+25 q^{76}-110 q^{74}+182 q^{72}-205 q^{70}+161 q^{68}-63 q^{66}-68 q^{64}+177 q^{62}-218 q^{60}+166 q^{58}-45 q^{56}-99 q^{54}+184 q^{52}-176 q^{50}+58 q^{48}+108 q^{46}-239 q^{44}+275 q^{42}-192 q^{40}+16 q^{38}+182 q^{36}-322 q^{34}+358 q^{32}-271 q^{30}+102 q^{28}+103 q^{26}-251 q^{24}+316 q^{22}-264 q^{20}+137 q^{18}+29 q^{16}-166 q^{14}+221 q^{12}-170 q^{10}+47 q^8+109 q^6-214 q^4+212 q^2-106-64 q^{-2} +214 q^{-4} -286 q^{-6} +244 q^{-8} -112 q^{-10} -54 q^{-12} +184 q^{-14} -238 q^{-16} +206 q^{-18} -112 q^{-20} +3 q^{-22} +71 q^{-24} -104 q^{-26} +94 q^{-28} -58 q^{-30} +25 q^{-32} +5 q^{-34} -17 q^{-36} +17 q^{-38} -14 q^{-40} +7 q^{-42} -3 q^{-44} + q^{-46}$