L6n1

(Knotscape image)	See the full Thistlethwaite Link Table (up to 11 crossings). Visit L6n1 at Knotilus!
	[edit L6n1 Quick Notes] L6n1 is $6_{3}^{3}$ in Rolfsen's table of links. It makes three fibers in the Hopf fibration.

One modern form of the Germanic Valknut		Basic depiction		Basic symmetrical depiction		Three squares, as impossible object
Coat of arms of Suchy, Vaud, Switzerland		Rich Schwartz' "98"		Episcopal coat of arms of Dom Jacinto Bergmann (Brazil)		Heraldic badge of Admiral Lord Boyce as Lord Warden of the Cinque Ports		Canadian trade-union federation emblem.

Planar diagram presentation	X₆₁₇₂ X_12,8,9,7 X_4,12,1,11 X_5,11,6,10 X₃₈₄₅ X_9,3,10,2
Gauss code	{1, 6, -5, -3}, {-4, -1, 2, 5}, {-6, 4, 3, -2}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	${\frac {w-uv}{{\sqrt {u}}{\sqrt {v}}{\sqrt {w}}}}$ (db)
Jones polynomial	$q^{4}+q^{2}+2$ (db)
Signature	0 (db)
HOMFLY-PT polynomial	$-z^{2}a^{-2}-3a^{-2}+a^{-4}+2-2a^{-2}z^{-2}+a^{-4}z^{-2}+z^{-2}$ (db)
Kauffman polynomial	$z^{4}a^{-2}+z^{4}a^{-4}+z^{3}a^{-1}+z^{3}a^{-3}-4z^{2}a^{-2}-4z^{2}a^{-4}-3za^{-1}-3za^{-3}+5a^{-2}+3a^{-4}+3+2a^{-1}z^{-1}+2a^{-3}z^{-1}-2a^{-2}z^{-2}-a^{-4}z^{-2}-z^{-2}$ (db)

The coefficients of the monomials

t^{r}q^{j}

are shown, along with their alternating sums

\chi

(fixed

j

, alternation over

r

).

0

1

2

3

4

χ

9

1

7

1

5

1

3

1

3

1

2

-1

2

$\dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}$	$i=-1$	$i=1$	$i=3$
$r=0$	${\mathbb {Z} }^{2}$	${\mathbb {Z} }^{3}$	${\mathbb {Z} }$
$r=1$	${\mathbb {Z} }$
$r=2$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=3$
$r=4$	${\mathbb {Z} }$	${\mathbb {Z} }$