# 10 117 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 117's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 117 at Knotilus!

### Knot presentations

 Planar diagram presentation X1627 X5,16,6,17 X13,1,14,20 X7,15,8,14 X19,9,20,8 X3,11,4,10 X11,5,12,4 X9,19,10,18 X17,13,18,12 X15,2,16,3 Gauss code -1, 10, -6, 7, -2, 1, -4, 5, -8, 6, -7, 9, -3, 4, -10, 2, -9, 8, -5, 3 Dowker-Thistlethwaite code 6 10 16 14 18 4 20 2 12 8 Conway Notation [8*2:20]

### Three dimensional invariants

 Symmetry type Chiral Unknotting number 2 3-genus 3 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-2][-10] Hyperbolic Volume 16.1254 A-Polynomial See Data:10 117/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $1$ Topological 4 genus $1$ Concordance genus $3$ Rasmussen s-Invariant 2

### Polynomial invariants

 Alexander polynomial $2 t^3-10 t^2+24 t-31+24 t^{-1} -10 t^{-2} +2 t^{-3}$ Conway polynomial $2 z^6+2 z^4+2 z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 103, 2 } Jones polynomial $-q^8+4 q^7-9 q^6+13 q^5-16 q^4+18 q^3-16 q^2+13 q-8+4 q^{-1} - q^{-2}$ HOMFLY-PT polynomial (db, data sources) $z^6 a^{-2} +z^6 a^{-4} +2 z^4 a^{-2} +2 z^4 a^{-4} -z^4 a^{-6} -z^4+2 z^2 a^{-2} +2 z^2 a^{-4} -z^2 a^{-6} -z^2+ a^{-2} + a^{-4} - a^{-6}$ Kauffman polynomial (db, data sources) $3 z^9 a^{-3} +3 z^9 a^{-5} +7 z^8 a^{-2} +15 z^8 a^{-4} +8 z^8 a^{-6} +7 z^7 a^{-1} +9 z^7 a^{-3} +10 z^7 a^{-5} +8 z^7 a^{-7} -8 z^6 a^{-2} -28 z^6 a^{-4} -12 z^6 a^{-6} +4 z^6 a^{-8} +4 z^6+a z^5-11 z^5 a^{-1} -26 z^5 a^{-3} -29 z^5 a^{-5} -14 z^5 a^{-7} +z^5 a^{-9} +17 z^4 a^{-4} +6 z^4 a^{-6} -5 z^4 a^{-8} -6 z^4-a z^3+5 z^3 a^{-1} +18 z^3 a^{-3} +21 z^3 a^{-5} +8 z^3 a^{-7} -z^3 a^{-9} +2 z^2 a^{-2} -4 z^2 a^{-4} -3 z^2 a^{-6} +z^2 a^{-8} +2 z^2-z a^{-1} -3 z a^{-3} -5 z a^{-5} -3 z a^{-7} - a^{-2} + a^{-4} + a^{-6}$ The A2 invariant $-q^6+2 q^4-q^2-1+4 q^{-2} -3 q^{-4} +3 q^{-6} +3 q^{-12} -3 q^{-14} +3 q^{-16} -2 q^{-18} -2 q^{-20} +2 q^{-22} - q^{-24}$ The G2 invariant $q^{32}-3 q^{30}+7 q^{28}-13 q^{26}+15 q^{24}-14 q^{22}+3 q^{20}+21 q^{18}-49 q^{16}+81 q^{14}-100 q^{12}+87 q^{10}-40 q^8-54 q^6+173 q^4-269 q^2+308-240 q^{-2} +63 q^{-4} +178 q^{-6} -398 q^{-8} +501 q^{-10} -428 q^{-12} +190 q^{-14} +119 q^{-16} -379 q^{-18} +476 q^{-20} -352 q^{-22} +81 q^{-24} +223 q^{-26} -405 q^{-28} +367 q^{-30} -133 q^{-32} -203 q^{-34} +486 q^{-36} -585 q^{-38} +465 q^{-40} -143 q^{-42} -252 q^{-44} +583 q^{-46} -727 q^{-48} +629 q^{-50} -331 q^{-52} -66 q^{-54} +415 q^{-56} -593 q^{-58} +555 q^{-60} -307 q^{-62} -27 q^{-64} +311 q^{-66} -430 q^{-68} +315 q^{-70} -41 q^{-72} -263 q^{-74} +450 q^{-76} -428 q^{-78} +211 q^{-80} +108 q^{-82} -391 q^{-84} +522 q^{-86} -465 q^{-88} +250 q^{-90} +19 q^{-92} -247 q^{-94} +349 q^{-96} -321 q^{-98} +213 q^{-100} -69 q^{-102} -46 q^{-104} +107 q^{-106} -122 q^{-108} +94 q^{-110} -52 q^{-112} +18 q^{-114} +7 q^{-116} -16 q^{-118} +16 q^{-120} -13 q^{-122} +7 q^{-124} -3 q^{-126} + q^{-128}$