# 10 120 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 120's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 120 at Knotilus! Consists of two trefoils on a closed loop, where the trefoils are interlinked with each other. (See also 8 15.)  Symmetrical depiction using only circular arcs, and lines which are horizontal, vertical, or at a 45° angle.

### Knot presentations

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

### Three dimensional invariants

 Symmetry type Reversible Unknotting number $\{2,3\}$ 3-genus 2 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-15] Hyperbolic Volume 16.2714 A-Polynomial See Data:10 120/A-polynomial

### Four dimensional invariants

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

### Polynomial invariants

 Alexander polynomial $8 t^2-26 t+37-26 t^{-1} +8 t^{-2}$ Conway polynomial $8 z^4+6 z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 105, -4 } Jones polynomial $q^{-2} -4 q^{-3} +10 q^{-4} -13 q^{-5} +17 q^{-6} -18 q^{-7} +16 q^{-8} -13 q^{-9} +8 q^{-10} -4 q^{-11} + q^{-12}$ HOMFLY-PT polynomial (db, data sources) $a^{12}-4 z^2 a^{10}-3 a^{10}+3 z^4 a^8+3 z^2 a^8+4 z^4 a^6+7 z^2 a^6+3 a^6+z^4 a^4$ Kauffman polynomial (db, data sources) $z^6 a^{14}-2 z^4 a^{14}+z^2 a^{14}+4 z^7 a^{13}-10 z^5 a^{13}+8 z^3 a^{13}-2 z a^{13}+6 z^8 a^{12}-13 z^6 a^{12}+6 z^4 a^{12}+z^2 a^{12}+a^{12}+3 z^9 a^{11}+7 z^7 a^{11}-33 z^5 a^{11}+29 z^3 a^{11}-8 z a^{11}+16 z^8 a^{10}-33 z^6 a^{10}+17 z^4 a^{10}-7 z^2 a^{10}+3 a^{10}+3 z^9 a^9+16 z^7 a^9-44 z^5 a^9+26 z^3 a^9-4 z a^9+10 z^8 a^8-9 z^6 a^8-3 z^4 a^8+13 z^7 a^7-17 z^5 a^7+5 z^3 a^7+2 z a^7+10 z^6 a^6-11 z^4 a^6+7 z^2 a^6-3 a^6+4 z^5 a^5+z^4 a^4$ The A2 invariant $q^{38}+q^{36}-3 q^{34}+q^{32}-5 q^{28}+2 q^{26}-2 q^{24}+q^{22}+2 q^{20}-q^{18}+5 q^{16}-2 q^{14}+2 q^{12}+3 q^{10}-3 q^8+q^6$ The G2 invariant $q^{190}-3 q^{188}+8 q^{186}-16 q^{184}+21 q^{182}-23 q^{180}+9 q^{178}+25 q^{176}-74 q^{174}+131 q^{172}-159 q^{170}+124 q^{168}-16 q^{166}-151 q^{164}+326 q^{162}-410 q^{160}+358 q^{158}-152 q^{156}-149 q^{154}+426 q^{152}-569 q^{150}+496 q^{148}-227 q^{146}-123 q^{144}+405 q^{142}-489 q^{140}+345 q^{138}-47 q^{136}-260 q^{134}+434 q^{132}-410 q^{130}+162 q^{128}+180 q^{126}-491 q^{124}+639 q^{122}-549 q^{120}+251 q^{118}+157 q^{116}-531 q^{114}+731 q^{112}-704 q^{110}+430 q^{108}-19 q^{106}-371 q^{104}+597 q^{102}-569 q^{100}+321 q^{98}+41 q^{96}-335 q^{94}+427 q^{92}-308 q^{90}+21 q^{88}+288 q^{86}-464 q^{84}+445 q^{82}-224 q^{80}-79 q^{78}+349 q^{76}-482 q^{74}+440 q^{72}-267 q^{70}+46 q^{68}+153 q^{66}-266 q^{64}+286 q^{62}-215 q^{60}+119 q^{58}-14 q^{56}-56 q^{54}+84 q^{52}-91 q^{50}+68 q^{48}-38 q^{46}+13 q^{44}+7 q^{42}-12 q^{40}+12 q^{38}-10 q^{36}+6 q^{34}-3 q^{32}+q^{30}$