From the generating braid AbACbdCd following families of alternating achiral KLs are derived: 
 
ApbACbdCdp p 1 2 2 1 p ApbAqCrbrdqCdp (((p,q),r)+) (((p,q),r)+) 
AbACpbpdCd  (p,2+) (p,2+)  ApbqACrbrdCqdp (q,p 1,r) (q,p 1,r) 
AbpACqbqdCpd  (p,q,2) (p,q,2)  ApbqArCsbsdrCqdp (q,(p,r),s) (q,(p,r),s) 

From the same palindromic non-alternating generating braid the following families of achiral KLs are obtained: 
 
 
ApBacBDcdp p p ApBacBDcdp 2 p p 2 
AbAcpBpdCd  (p,2) (q,2)  ApbAcqBqdCdp (p 1,q) (p 1,q) 

In the same way is possible to continue the derivation of achiral KLs from other palindromic reduced braids. 

The family of achiral odd crossing number knots discovered by J. Hoste, M. Thistlethwaite and J. Weeks (1998) can be extended to the two-parameter BFR defined by the palindromic braid ABaBqCpBAdcbpcqDcd corresponding to the family of non-alternating achiral odd-crossing knots with  n = 7+4p+4q crossings 

10**(-2p) 0.-1.-2 0.(2q):(-2p) 0.- 1.-2 0.(2q)
 

PreviousContentsNext