The next basic polyhedron 8* is a 4-antiprism, with the graph symmetry group G = [2+,8] of order 16, generated by the rotational reflection 
~
S
 
= (1,2,3,4,5,6,7,8)
and reflection 
R = (1,3)(5,7)(4,8)(2)(6)
containing its axis. We can find the number of different symmetry choices of the vertices (i.e. vertex bicolorings of 8*) by using PET. In this case, 
ZG 1
16
(t18+4t12t23+5t24+2t42+4t8),
and the coefficients of 
ZG(x,1) = 1+x+4x2+5x3+8x4+5x5+4x6+x7+x8
represent, respectively the number of choices of n-8 vertices for 8 £ n £ 16. For 9 £ n £ 12, these choices are:   

{1}; {1,2}, {1,3}, {1,4}, {1,5}; 

{1,2,3}, {1,2,4}, {1,2,5}, {1,3,5}, {1,4,7}; 

{1,2,3,4}, {1,2,3,5}, {1,2,3,6}, {1,2,4,5}, 

{1,2,4,6}, {1,2,4,7}, {1,2,5, 6}, {1,3,5,7}   

corresponding, respectively, to the source KLs of the form   

8*a; 8*a.b, 8*a:b, 8*a:.b, 8*a::b; 

8*a.b.c, 8*a.b:c, 8*a.b:.c, 8*a:b:c, 8*a:.b:.c; 

8*a.b.c.d, 8*a.b.c:d, 8*a.b.c:.d, 8*a.b:c.d, 

8*a.b:c:d, 8*a:b.c:d, 8*a.b:.c.d, 8*a:b:c:d,   

given in the Conway notation. The coefficients of 

ZG(x,x,1) = 1+2x+12x2+34x3+87x4 +124x5+136x6+72x7+30x8

give the number of different source KLs derived from 8* for 8 £ n £ 16. We can divide all the vertex bicolorings obtained into equivalence classes, with regard to their symmetry groups, and then consider only their representatives. According to this, for n = 9 we have the representative 8*a giving 2 source links; for n = 10 the representative 8*a.b (8*a:b, 8*a:.b, 8*a::b) giving 3 source links; for n = 11 two representatives: 8*a.b.c (8*a:b:c, 8*a:.b:.c) giving 6 source links and 8*a.b:c (8*a.b:.c) giving 8 source links; for n = 12 five representatives: 8*a.b.c.d (8*a.b:c.d, 8*.a:b.c:d) giving 10 source links, 8*a.b.c:d (8*a.b:c:d) giving 16 source links, 8*a.b.c:.d giving 12 source links, 8*a:b:c:d giving 6 source links, and 8*a.b:.c.d giving 7 source links, where the other members of equivalence classes are given in parentheses. The list of source links derived from these representatives is given in Table 8: 

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