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X(2) midpoints of ABC vertices of the antimedial triangle infinite points of the Thomson cubic infinite points of the sidelines of ABC CPCC or Hcevian points, see Table 11 

This curve is related to Table 28 : {X}Cevian and Anticevian points. It contains the {X}Cevian points of any X on the Lucas cubic and in particular the CPCC or Hcevian points. A, B, C are nodes with tangents the bisectors. See Q027, a very similar sextic. 
