From the 637 non-invertible chiral knots, 68 of them are obtained from the families already derived for n=8 and n=10. From the remaining 569 knots, 554 are the generators of the new families of chiral non-invertible knots without additional conditions for parameters. In the following list are given the remaining 15 chiral non-invertible knots, the families of chiral non-invertible knots derived from them, and the conditions for parameters:

 
12a76 .4.2 1 0.2 .(2p).(2q) 1 0.(2r) p r
12a192 .4 1.2 1 0 .(2p) 1.(2q) 1 0 p q
12a201 .4.2 1.2 .(2p).(2q) 1.(2r) p r
12a566 4 1,2 1 1,2 1 (2p) 1,(2q) 1 1,(2r) 1 p r
12a610 4:2 1:2 (2p):(2q) 1:(2r) p r
12a735 5,3,2 1+ (2p+1),(2q+1),(2r) 1+ p q
12a753 5,2 1 1,3 (2p+1),(2q) 1 1,(2r+1) p r
12a782 2 1:4 0:2 0 (2p) 1:(2q) 0:(2r) 0 q r
12a952 2.4.2 0.2 (2p).(2q).(2r) 0.(2s) q s
12a981 .4.2.2 0.2 0 .(2p).(2q).(2r) 0.(2s) 0 p q
12a984 4:3:2 (2p):(2q+1):(2r) p r
12a988 4:2:3 0 (2p):(2q):(2r+1) 0 p q
12a1191 8*4:2 8*(2p):(2q) p q
12a1238 3:4 0:2 0 (2p+1):(2q) 0:(2r) 0 q r
12a1240 4 0:3 0:2 0 (2p) 0:(2q+1) 0:(2r) 0 p r



Every alternating non-invertible knot (except those corresponding to basic polyhedra) is the generator, or the member of the family of non-invertible knots. Based on the properties of its generating KL we can determine if some additional requirements are needed for the whole family of KLs to be non-invertible. For example, even though the generating knot 816 .2.2 0 is invertible, the family it generates .(2p).(2q) 0 will contain only non-invertible KLs beginning from the knot 1085 .4.2 0 provided that p q.

 

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