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

X(13), X(14), X(216), X(1989), X(3163) midpoints of ABC six equilateral anticevian points. see table 14 feet of the trilinear polar of X(265) E = X(3163), on the inscribed Steiner ellipse and on the Fermat axis. 

Q040 is an example of quartic passing through the six equilateral anticevian points. See table 14. The tangents at A, B, C are the altitudes. 
