# 10 99 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 99's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 99 at Knotilus!

### Knot presentations

 Planar diagram presentation X6271 X10,4,11,3 X16,11,17,12 X14,7,15,8 X8,15,9,16 X20,13,1,14 X12,19,13,20 X18,6,19,5 X2,10,3,9 X4,18,5,17 Gauss code 1, -9, 2, -10, 8, -1, 4, -5, 9, -2, 3, -7, 6, -4, 5, -3, 10, -8, 7, -6 Dowker-Thistlethwaite code 6 10 18 14 2 16 20 8 4 12 Conway Notation [.2.2.20.20]

### Three dimensional invariants

 Symmetry type Fully amphicheiral Unknotting number 2 3-genus 4 Bridge index 3 Super bridge index Missing Nakanishi index 2 Maximal Thurston-Bennequin number [-6][-6] Hyperbolic Volume 14.3343 A-Polynomial See Data:10 99/A-polynomial

### Four dimensional invariants

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

### Polynomial invariants

 Alexander polynomial $t^4-4 t^3+10 t^2-16 t+19-16 t^{-1} +10 t^{-2} -4 t^{-3} + t^{-4}$ Conway polynomial $z^8+4 z^6+6 z^4+4 z^2+1$ 2nd Alexander ideal (db, data sources) $\left\{t^4-2 t^3+3 t^2-2 t+1\right\}$ Determinant and Signature { 81, 0 } Jones polynomial $-q^5+3 q^4-7 q^3+10 q^2-12 q+15-12 q^{-1} +10 q^{-2} -7 q^{-3} +3 q^{-4} - q^{-5}$ HOMFLY-PT polynomial (db, data sources) $z^8-a^2 z^6-z^6 a^{-2} +6 z^6-4 a^2 z^4-4 z^4 a^{-2} +14 z^4-6 a^2 z^2-6 z^2 a^{-2} +16 z^2-4 a^2-4 a^{-2} +9$ Kauffman polynomial (db, data sources) $2 a z^9+2 z^9 a^{-1} +5 a^2 z^8+5 z^8 a^{-2} +10 z^8+5 a^3 z^7+5 a z^7+5 z^7 a^{-1} +5 z^7 a^{-3} +3 a^4 z^6-9 a^2 z^6-9 z^6 a^{-2} +3 z^6 a^{-4} -24 z^6+a^5 z^5-9 a^3 z^5-18 a z^5-18 z^5 a^{-1} -9 z^5 a^{-3} +z^5 a^{-5} -5 a^4 z^4+9 a^2 z^4+9 z^4 a^{-2} -5 z^4 a^{-4} +28 z^4-2 a^5 z^3+5 a^3 z^3+21 a z^3+21 z^3 a^{-1} +5 z^3 a^{-3} -2 z^3 a^{-5} +a^4 z^2-8 a^2 z^2-8 z^2 a^{-2} +z^2 a^{-4} -18 z^2+a^5 z-3 a^3 z-10 a z-10 z a^{-1} -3 z a^{-3} +z a^{-5} +4 a^2+4 a^{-2} +9$ The A2 invariant $-q^{14}+q^{12}-3 q^{10}-q^6-q^4+6 q^2+1+6 q^{-2} - q^{-4} - q^{-6} -3 q^{-10} + q^{-12} - q^{-14}$ The G2 invariant $q^{80}-2 q^{78}+5 q^{76}-8 q^{74}+9 q^{72}-7 q^{70}+14 q^{66}-30 q^{64}+46 q^{62}-56 q^{60}+42 q^{58}-13 q^{56}-38 q^{54}+99 q^{52}-139 q^{50}+152 q^{48}-109 q^{46}+11 q^{44}+103 q^{42}-204 q^{40}+232 q^{38}-184 q^{36}+63 q^{34}+71 q^{32}-177 q^{30}+209 q^{28}-138 q^{26}+4 q^{24}+117 q^{22}-185 q^{20}+147 q^{18}-29 q^{16}-127 q^{14}+240 q^{12}-255 q^{10}+205 q^8-47 q^6-139 q^4+285 q^2-329+285 q^{-2} -139 q^{-4} -47 q^{-6} +205 q^{-8} -255 q^{-10} +240 q^{-12} -127 q^{-14} -29 q^{-16} +147 q^{-18} -185 q^{-20} +117 q^{-22} +4 q^{-24} -138 q^{-26} +209 q^{-28} -177 q^{-30} +71 q^{-32} +63 q^{-34} -184 q^{-36} +232 q^{-38} -204 q^{-40} +103 q^{-42} +11 q^{-44} -109 q^{-46} +152 q^{-48} -139 q^{-50} +99 q^{-52} -38 q^{-54} -13 q^{-56} +42 q^{-58} -56 q^{-60} +46 q^{-62} -30 q^{-64} +14 q^{-66} -7 q^{-70} +9 q^{-72} -8 q^{-74} +5 q^{-76} -2 q^{-78} + q^{-80}$