L4a1
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(Knotscape image) 
See the full Thistlethwaite Link Table (up to 11 crossings). 
L4a1 is in the Rolfsen table of links. It frequently occurs in late Roman mosaics and some medieval decorations. In this context, it is called the "Solomon's knot" (sigillum Salomonis) or "guilloche knot". It is also the "Kramobone" symbol (meaning "one being bad makes all appear to be bad") of the Adinkra symbol system. Link L10a101 contains multiple L4a1 configurations. 
Link Presentations
[edit Notes on L4a1's Link Presentations] Why such an ugly Braid Representative?
Planar diagram presentation  X_{6172} X_{8354} X_{2536} X_{4718} 
Gauss code  {1, 3, 2, 4}, {3, 1, 4, 2} 
A Braid Representative  
A Morse Link Presentation 
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...)  (db) 
Jones polynomial  (db) 
Signature  1 (db) 
HOMFLYPT polynomial  (db) 
Kauffman polynomial  (db) 
Khovanov Homology
The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). 

Integral Khovanov Homology
(db, data source) 

Computer Talk
Much of the above data can be recomputed by Mathematica using the package KnotTheory`
. See A Sample KnotTheory` Session.
Modifying This Page
Read me first: Modifying Knot Pages
See/edit the Link Page master template (intermediate). See/edit the Link_Splice_Base (expert). Back to the top. 
