In the same way, from the following 13-crossing minimal almost alternating representations we obtain the next six non-alternating knots:
 
.-(3,2).2  .(3 1-,2 1).2  .-(2 1,2).2  .(3 1-,3).2 
.2.-(3,2)  .2.(3 1-,2 1)  .2.-(2 1,2)  .2.(3 1-,3) 
.-(3,2).2 0  .(3 1-,2 1).2 0  .2 0.-(3,2)  .2 0.(3 1-,2 1) 

Finally, from 76 non-alternating polyhedral knots, 74 of them are given by almost alternating minimal 12-crossing representations, and for two of them, 2 0.-3.-2 0.2 and 2 0.-2 1.-2 0.2, we have not been able to obtain non-alternating representations:

 
-2 2:2:2  2 1 1 1-0:2:2  -2 2 0:2:2 0  2 1 1 1-:2:2 0 
-2 2:2 0:2 0  2 1 1 1-0:2 0:2 0  -2 2:-2 0:-2 0  2 2 0:2 1-:2 
2 2:-2 0:-2 0  2 1 1 0.2 0.1-.2.2  -2 1 1:2:2  2 2 1-0:2:2 
-2 1 1 0:2:2 0  2 2 1-:2:2 0 
-2 1 1:2 0:2 0  2 2 1-0:2 0:2 0  -2 1 1:-2 0:-2 0  2 1 1 0:2 1-:2 
-4 0:2:2  3 1 1-:2:2  -4:2:2 0  3 1 1-0:2:2 0 
-4 0:2 0:2 0  3 1 1-:2 0:2 0  -4 0:-2 0:-2 0  4:2 1-:2 
-3 1 0:2:2  4 1-:2:2  -3 1 0:2 0:2 0  4 1-:2 0:2 0 
-3 1 0:-2 0:-2 0  3 1:2 1-:2  -2 1 1 0:2:2  2 2 1-:2:2 
-2 1 1:2:2 0  2 2 1-0:2:2 0  -2 1 1 0:2 0:2 0  2 2 1-:2 0:2 0 
-2 1 1 0:-2 0:-2 0  2 1 1:2 1-:2  -3 0:2 1:2  2 1 1-:2 1:2 
-3 0:2 1:-2 0  2 0:2.2 1.1-.2 1 0  -3 0:2 1 0:2  2 1 1-:2 1 0:2 
-2 1 0:3:2  3 1-:3:2  -2 1 0:3 0:2  3 1-:3 0:2 
-2 1 0:-3 0:-2 0  2 1:3:2 1- -2 1 0:2 1:2  3 1-:2 1:2 
-2 1 0:-2 1 0:-2 0  2 1:2 1:2 1- 2.-2 1.2.2  2.3 1-0.2.2 
2.2 1.-2.2  2.2 1.2 1-0.2  2.-3.2.2 0  2.2 1 1-0.2.2 0 
2.3.-2.2 0  2.3.2 1-0.2 0  20.3.-2.2  2 0.3.2 1-0.2 
2.-3.-2 0.2 0  8*2 0.2 0.1-.3  2.-2 1.-2 0.2 0  8*2 0.2 0.1-.2 1 
2.2.-2.2.2 0  2.2.2 1-0.2.2 0  2.2.-2.2 0.2 0  2.2.2 1-0.2 0.2 0 
2.2 0.-2.2.2 0  2.2 0.2 1-0.2.2 0  8*-4 0  8*3 1 1-
8*-3 1 0  8*4 1- 8*-2 1 1 0  8*2 2 1-
8*-3 0.2 0  8*2 1 1-.2 0  8*3:-2 0  8*3:2 1-
8*-2 1 0:2  8*3 1-:2  8*-3 0:2 0  8*2 1 1-:2 0 
8*3 0:-2 0  8*3 0:2 1- 8*-2 1 0:2 0  8*3 1-:2 0 
8*2 1 0:-2 0  8*2 1 0:2 1- 8*-3 0:.2 0  8*2 1 1-:.2 0 
8*-2 1 0:.2 0  8*3 1-:.2 0  8*3 0::-2 0  8*3 0::2 1-
8*3::-2 0  8*3::2 1- 8*2 1::-2 0  8*2 1::2 1-
8*2.-2 0.2  8*2.2 1-.2  8*2.-2 0.2 0  8*2.2 1-.2 0 
8*2.2 0.-2 0  8*2.2 0.2 1- 8*2:2:-2 0  8*2:2:2 1-
8*2:2 0:-2 0  8*2:2 0:2 1- 8*2:-2 0:2 0  8*2:2 1-:2 0 
8*2 0:-2 0:2 0  8*2 0:2 1-:2 0  8*2 0:2 0:-2 0  8*2 0:2 0:2 1-
8*2:.-2 0:.2  8*2:.2 1-:.2  8*2:.2:.-2 0  8*2:.2:.2 1-
8*-2 1 0:.2  8*3 1-:.2  8*-3 0::2 0  8*2 1 1-::2 0 
9*.-3  9*.2 1 1- 9*.-2 1  9*.3 1-
9*2.-2  9*2.2 1- 9*2 0.-2  9*2 0.2 1-
9*.2:.-2  9*.2:.2 1- 9*.-2:.-2  8*2 0.2 0.1-.2 0.2 0 
9*.2 0:.-2  9*.2 0:.2 1- 10*-2 0  10*2 1-
10**-2 0  10**2 1-  
2 0.-3.-2 0.2  2 0.-2 1.-2 0.2 
 

In conclusion, for n £ 11 there are only two non-alternating 11-crossing knots, 2 0.-3.-2 0.2 and 2 0.-2 1.-2 0.2, whose almost alternating representations we haven't been able to determine (see Adams, 1994, Unsolved question, page 140, Fig. 5.54). We are only sure that, if such representations exist, they must have more then 16 crossings. Knowing one of them, the other follows immediately. For one of the knots from Adams' question, 9*.-2:.-2, we obtained 12-crossing minimal non-alternating representation 8*2 0.2 0.1-.2 0.2 0.

In the same way, after adding the missing links to the tables derived by J. Conway (1970) and A. Caudron (1982), it is possible to search for almost alternating representations of non-alternating links given in the Conway notation for n ³ 10.


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