The next basic polyhedron
8^{*} is a 4antiprism, with the graph symmetry group G = [2^{+},8]
of order 16, generated by the rotational reflection
{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
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:
