# 10 163 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 163's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 163 at Knotilus!

Warning. In 1973 K. Perko noticed that the knots that were later labeled 10161 and 10162 in Rolfsen's tables (which were published in 1976 and were based on earlier tables by Little (1900) and Conway (1970)) are in fact the same. In our table we removed Rolfsen's 10162 and renumbered the subsequent knots, so that our 10 crossings total is 165, one less than Rolfsen's 166. Read more:     .

### Knot presentations

 Planar diagram presentation X6271 X8394 X13,19,14,18 X11,1,12,20 X19,13,20,12 X2,16,3,15 X4,17,5,18 X10,6,11,5 X14,7,15,8 X16,10,17,9 Gauss code 1, -6, 2, -7, 8, -1, 9, -2, 10, -8, -4, 5, -3, -9, 6, -10, 7, 3, -5, 4 Dowker-Thistlethwaite code 6 8 10 14 16 -20 -18 2 4 -12 Conway Notation [8*-30]

### Three dimensional invariants

 Symmetry type Reversible Unknotting number $\{1,2\}$ 3-genus 3 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-2][-8] Hyperbolic Volume 13.29 A-Polynomial See Data:10 163/A-polynomial

### Four dimensional invariants

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

### Polynomial invariants

 Alexander polynomial $t^3-5 t^2+12 t-15+12 t^{-1} -5 t^{-2} + t^{-3}$ Conway polynomial $z^6+z^4+z^2+1$ 2nd Alexander ideal (db, data sources) $\left\{2,t^2+t+1\right\}$ Determinant and Signature { 51, 2 } Jones polynomial $-2 q^6+5 q^5-7 q^4+9 q^3-9 q^2+8 q-6+4 q^{-1} - q^{-2}$ HOMFLY-PT polynomial (db, data sources) $z^6 a^{-2} +3 z^4 a^{-2} -z^4 a^{-4} -z^4+2 z^2 a^{-2} -z^2- a^{-2} +2 a^{-4} - a^{-6} +1$ Kauffman polynomial (db, data sources) $2 z^8 a^{-2} +2 z^8 a^{-4} +5 z^7 a^{-1} +8 z^7 a^{-3} +3 z^7 a^{-5} +3 z^6 a^{-2} +z^6 a^{-6} +4 z^6+a z^5-10 z^5 a^{-1} -15 z^5 a^{-3} -4 z^5 a^{-5} -11 z^4 a^{-2} +z^4 a^{-4} +4 z^4 a^{-6} -8 z^4-a z^3+3 z^3 a^{-1} +8 z^3 a^{-3} +7 z^3 a^{-5} +3 z^3 a^{-7} +2 z^2 a^{-2} -4 z^2 a^{-4} -4 z^2 a^{-6} +2 z^2-z a^{-3} -3 z a^{-5} -2 z a^{-7} + a^{-2} +2 a^{-4} + a^{-6} +1$ The A2 invariant $-q^6+2 q^4+1+2 q^{-2} -3 q^{-4} + q^{-6} -2 q^{-8} +2 q^{-10} +2 q^{-12} +2 q^{-16} -2 q^{-18} - q^{-20}$ The G2 invariant $q^{32}-3 q^{30}+7 q^{28}-13 q^{26}+13 q^{24}-8 q^{22}-7 q^{20}+31 q^{18}-49 q^{16}+61 q^{14}-48 q^{12}+5 q^{10}+46 q^8-91 q^6+109 q^4-79 q^2+21+50 q^{-2} -92 q^{-4} +96 q^{-6} -53 q^{-8} -13 q^{-10} +68 q^{-12} -90 q^{-14} +59 q^{-16} +6 q^{-18} -74 q^{-20} +115 q^{-22} -108 q^{-24} +61 q^{-26} +6 q^{-28} -81 q^{-30} +123 q^{-32} -134 q^{-34} +101 q^{-36} -34 q^{-38} -40 q^{-40} +99 q^{-42} -113 q^{-44} +90 q^{-46} -30 q^{-48} -35 q^{-50} +79 q^{-52} -79 q^{-54} +39 q^{-56} +32 q^{-58} -85 q^{-60} +106 q^{-62} -70 q^{-64} +3 q^{-66} +62 q^{-68} -104 q^{-70} +100 q^{-72} -65 q^{-74} +13 q^{-76} +32 q^{-78} -59 q^{-80} +55 q^{-82} -36 q^{-84} +14 q^{-86} +5 q^{-88} -14 q^{-90} +9 q^{-92} -8 q^{-94} +5 q^{-96} -2 q^{-98} + q^{-100} + q^{-102}$