# 7 1 (KnotPlot image) See the full Rolfsen Knot Table. Visit 7 1's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 7 1 at Knotilus! 7_1 should perhaps be called "The Septafoil Knot", following the trefoil knot and the cinquefoil knot. See also T(7,2).  Interlaced form of 7/2 star polygon or "septagram"  Decorative interlaced form of 7/2 star polygon or "septagram"

### Knot presentations

 Planar diagram presentation X1829 X3,10,4,11 X5,12,6,13 X7,14,8,1 X9,2,10,3 X11,4,12,5 X13,6,14,7 Gauss code -1, 5, -2, 6, -3, 7, -4, 1, -5, 2, -6, 3, -7, 4 Dowker-Thistlethwaite code 8 10 12 14 2 4 6 Conway Notation 

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 3 3-genus 3 Bridge index 2 Super bridge index 4 Nakanishi index 1 Maximal Thurston-Bennequin number Failed to parse (lexing error): \text{$\$\$Failed} Hyperbolic Volume Not hyperbolic A-Polynomial See Data:7 1/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $3$ Topological 4 genus $3$ Concordance genus $\textrm{ConcordanceGenus}(\textrm{Knot}(7,1))$ Rasmussen s-Invariant -6

### Polynomial invariants

 Alexander polynomial $t^3+ t^{-3} -t^2- t^{-2} +t+ t^{-1} -1$ Conway polynomial $z^6+5 z^4+6 z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 7, -6 } Jones polynomial $- q^{-10} + q^{-9} - q^{-8} + q^{-7} - q^{-6} + q^{-5} + q^{-3}$ HOMFLY-PT polynomial (db, data sources) $a^8 \left(-z^4\right)-4 a^8 z^2-3 a^8+a^6 z^6+6 a^6 z^4+10 a^6 z^2+4 a^6$ Kauffman polynomial (db, data sources) $a^{13} z+a^{12} z^2+a^{11} z^3-a^{11} z+a^{10} z^4-2 a^{10} z^2+a^9 z^5-3 a^9 z^3+a^9 z+a^8 z^6-5 a^8 z^4+7 a^8 z^2-3 a^8+a^7 z^5-4 a^7 z^3+3 a^7 z+a^6 z^6-6 a^6 z^4+10 a^6 z^2-4 a^6$ The A2 invariant $-q^{30}-q^{28}-q^{26}+q^{18}+q^{16}+2 q^{14}+q^{12}+q^{10}$ The G2 invariant $q^{168}-q^{136}-q^{134}-q^{128}-q^{126}-q^{124}-q^{118}-q^{116}-q^{102}-q^{96}-q^{94}-q^{92}+q^{88}-2 q^{84}+2 q^{80}+q^{78}+q^{72}+3 q^{70}+2 q^{68}+q^{64}+2 q^{62}+2 q^{60}+q^{58}+q^{54}+q^{52}+q^{50}$