As we calculated before by using the PET (see Table 10), from the basic polyhedron 8* we derive 2 source KLs with 1 bigon, 12 with 2 bigons, 34 with 3 bigons, 87 with 4 bigons, 124 with 5 bigons, 136 with 6 bigons, 72 with 7 bigons, and 30 source KLs with 8 bigons. Using these complete lists, we can continue with the derivation of KLs belonging to the P(R)-subworld and to all other subworlds for larger values of n by replacing bigons by the corresponding tangles (R-tangles not beginning by 1, etc). 

By using the external LinKnot program for the derivation of polyhedral source KLs we can try to complete the Table 10 with the missing data for the basic polyhedra 10***, 1413*, and 1451*. The only limiting factor is the size of the input data: 2n source KLs for a basic polyhedron with n crossings, from which we need to extract representatives of non-equal ones. If you use a very fast PC computer, from the basic polyhedron 10*** you will obtain 2 source KLs with 1 bigon, 18 with 2 bigons, 66 with 3 bigons, 237 with 4 bigons, etc.

The LinKnot function fGenKL (webMathematica fGenKL) generates all different alternating KLs with n crossings from a given source KL by rational tangle substitutions. 
 
For example, from each of P-equivalent source links 2.2.20.2, .2.2.2.20, 2.2.20.20, 2.20.2.20, 20.2.20.20 are obtained 6, 27, 100, 334, 1032, 3020, KLs with n=11,...,16 crossings, respectively. 
 
We could be interested not only for particular polyhedral KLs with a given number of crossings, but for their general classes. This illustrates the example of all classes obtained from the basic polyhedron 6* by placing in it rational tangles. 

From the source link 6*2 we derive 6*t1; from the source links 6*2.2, 6*2.2 0, 6*2:.2 0, 6*2:.2 we obtain, respectively:   

6*t1.t1 6*t1.t2
6*t1.t1 6*t1.t2
6*t1:.t1 6*t1:.t2
6*t1:.t1 6*t1:.t2
 


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