6₂ knot

6₂ knot

Arf invariant	1
Braid length	6
Braid no.	3
Bridge no.	2
Crosscap no.	2
Crossing no.	6
Genus	2
Hyperbolic volume	4.40083
Stick no.	8
Unknotting no.	1
Conway notation	[312]
A-B notation	6₂
Dowker notation	4, 8, 10, 12, 2, 6
Last /Next	6₁ / 6₃
Other
alternating, hyperbolic, fibered, prime, reversible, twist

In knot theory, the 6₂ knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 6₃ knot. This knot is sometimes referred to as the Miller Institute knot,^[1] because it appears in the logo^[2] of the Miller Institute for Basic Research in Science at the University of California, Berkeley.

\Delta (t)=-t^{2}+3t-3-1+3t^{-1}-t^{-2},\,

\nabla (z)=-z^{4}-z^{2}+1,\,

V(q)=q-1+2q^{-1}-2q^{-2}+2q^{-3}-2q^{-4}+q^{-5}.\,

^[3]

The 6₂ knot is a hyperbolic knot, with its complement having a volume of approximately 4.40083.

References

Knot theory (knots and links)

Hyperbolic	Figure-eight (4₁) Three-twist (5₂) Stevedore (6₁) 6₂ 6₃ Endless (7₄) Carrick mat (8₁₈) Perko pair (10₁₆₁) (−2,3,7) pretzel (12n242) Whitehead (52 1) Borromean rings (63 2) L10a140

Satellite	Composite knots Granny Square Knot sum

Torus	Unknot (0₁) Trefoil (3₁) Cinquefoil (5₁) Septafoil (7₁) Unlink (02 1) Hopf (22 1) Solomon's (42 1)

Invariants	Alternating Arf invariant Bridge no. 2-bridge Brunnian Chirality Invertible Crosscap no. Crossing no. Finite type invariant Hyperbolic volume Khovanov homology Genus Knot group Link group Linking no. Polynomial Alexander Bracket HOMFLY Jones Kauffman Pretzel Prime list Stick no. Tricolorability Unknotting no. & problem

Notation & operations	Alexander–Briggs notation Conway notation Dowker notation Flype Mutation Reidemeister move Skein relation Tabulation

Other	Alexander's theorem Berge Braid theory Conway sphere Complement Double torus Fibered Knot List of knots and links Ribbon Slice Sum Tait conjectures Twist Wild Writhe

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