# 10 91 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 91's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 91 at Knotilus!

### Knot presentations

 Planar diagram presentation X6271 X20,6,1,5 X16,9,17,10 X10,3,11,4 X2,18,3,17 X14,7,15,8 X8,15,9,16 X12,20,13,19 X18,12,19,11 X4,13,5,14 Gauss code 1, -5, 4, -10, 2, -1, 6, -7, 3, -4, 9, -8, 10, -6, 7, -3, 5, -9, 8, -2 Dowker-Thistlethwaite code 6 10 20 14 16 18 4 8 2 12 Conway Notation [.3.2.20]

### Three dimensional invariants

 Symmetry type Chiral Unknotting number 1 3-genus 4 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-6][-6] Hyperbolic Volume 13.487 A-Polynomial See Data:10 91/A-polynomial

### Four dimensional invariants

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

### Polynomial invariants

 Alexander polynomial $t^4-4 t^3+9 t^2-14 t+17-14 t^{-1} +9 t^{-2} -4 t^{-3} + t^{-4}$ Conway polynomial $z^8+4 z^6+5 z^4+2 z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 73, 0 } Jones polynomial $-q^5+3 q^4-6 q^3+9 q^2-11 q+13-11 q^{-1} +9 q^{-2} -6 q^{-3} +3 q^{-4} - q^{-5}$ HOMFLY-PT polynomial (db, data sources) $z^8-a^2 z^6-z^6 a^{-2} +6 z^6-4 a^2 z^4-4 z^4 a^{-2} +13 z^4-5 a^2 z^2-5 z^2 a^{-2} +12 z^2-2 a^2-2 a^{-2} +5$ Kauffman polynomial (db, data sources) $2 a z^9+2 z^9 a^{-1} +4 a^2 z^8+5 z^8 a^{-2} +9 z^8+4 a^3 z^7+a z^7+2 z^7 a^{-1} +5 z^7 a^{-3} +3 a^4 z^6-7 a^2 z^6-13 z^6 a^{-2} +3 z^6 a^{-4} -26 z^6+a^5 z^5-6 a^3 z^5-7 a z^5-13 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} -6 a^4 z^4+7 a^2 z^4+16 z^4 a^{-2} -6 z^4 a^{-4} +35 z^4-2 a^5 z^3+9 a z^3+18 z^3 a^{-1} +9 z^3 a^{-3} -2 z^3 a^{-5} +2 a^4 z^2-7 a^2 z^2-9 z^2 a^{-2} +z^2 a^{-4} -19 z^2+a^5 z-4 a z-6 z a^{-1} -3 z a^{-3} +2 a^2+2 a^{-2} +5$ The A2 invariant $-q^{14}+q^{12}-2 q^{10}+q^8-q^4+4 q^2-1+4 q^{-2} - q^{-4} + q^{-8} -2 q^{-10} + q^{-12} - q^{-14}$ The G2 invariant $q^{80}-2 q^{78}+5 q^{76}-8 q^{74}+8 q^{72}-5 q^{70}-3 q^{68}+16 q^{66}-27 q^{64}+36 q^{62}-38 q^{60}+23 q^{58}-q^{56}-34 q^{54}+70 q^{52}-92 q^{50}+95 q^{48}-66 q^{46}+4 q^{44}+68 q^{42}-130 q^{40}+151 q^{38}-122 q^{36}+46 q^{34}+44 q^{32}-116 q^{30}+138 q^{28}-93 q^{26}+9 q^{24}+77 q^{22}-122 q^{20}+97 q^{18}-19 q^{16}-82 q^{14}+161 q^{12}-175 q^{10}+132 q^8-27 q^6-94 q^4+190 q^2-223+188 q^{-2} -92 q^{-4} -27 q^{-6} +132 q^{-8} -176 q^{-10} +165 q^{-12} -89 q^{-14} -10 q^{-16} +93 q^{-18} -126 q^{-20} +87 q^{-22} -3 q^{-24} -84 q^{-26} +137 q^{-28} -124 q^{-30} +54 q^{-32} +40 q^{-34} -124 q^{-36} +160 q^{-38} -142 q^{-40} +74 q^{-42} +7 q^{-44} -77 q^{-46} +108 q^{-48} -102 q^{-50} +72 q^{-52} -28 q^{-54} -10 q^{-56} +32 q^{-58} -42 q^{-60} +36 q^{-62} -23 q^{-64} +12 q^{-66} -6 q^{-70} +7 q^{-72} -7 q^{-74} +4 q^{-76} -2 q^{-78} + q^{-80}$