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X(4), X(6), X(4846), X(8743) vertices of the Grebe triangle infinite points of the McCay cubic F, F' : foci of the inconic with center X(182) imaginary foci of the Brocard ellipse i.e. common points of the Brocard axis and the Kiepert hyperbola 

K643 is the only circumstelloid passing through the vertices of the Grebe triangle. Its asymptotes are parallel to those of the McCay cubic K003 and concur at X = X(2)X(51) /\ X(4)X(182) /\ X(5)X(6), etc, which is actually the centroid of the triangle OHK. This point is now X(14561) in ETC (20170928). K643 meets its asymptotes on the line X(26)X(32), the satellite line of the line at infinity. K643 is also spK(X3, X182) in CL055. K643 is a member of several pencils of circumcubics, in particular those generated by :
More generally, if P is a point on the Euler line, Q the midpoint of OP, S the reflection of K about Q, then K643 is in the pencil generated by the union of the line K, P and (O), spK(S, Q) of CL055. See also Table 57. 
