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too complicated to be written here. Click on the link to download a text file. 

X(4), X(5), X(6), X(22), X(251), X(2165) Ixanticevian points : see table 23 

This cubic belongs to the pencil of cubics containing the Napoleon cubic, the Kn cubic. It is the only one which contains K, the Lemoine point. It is D(k) with k =  a^2b^2c^2 / (a^4SA+b^4SB+c^4SC). See "Two Remarkable Pencils..." in the Downloads page. It has the same asymptotic directions as pK(X6, X427) and meet the circumcircle at the same points as pK(X6, X343). See also Table 78. 
