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X(4), X(206), X(1676), X(1677)

infinite points of the altitudes of ABC

vertices of the pedal triangle of X(206)

vertices and in/excenters of the Grebe triangle

K642 is a circum-cubic which is the isogonal pK with pivot X(4), isopivot X(206) with respect to the Grebe triangle. See also Table 57.

It has three real asymptotes perpendicular to the sidelines of ABC. See other analogous cubics in Table 58.

It is a member of the pencils of cubics generated by :

• the Darboux cubic K004 and the union of the line at infinity and the rectangular circum-hyperbola through X(3108),

• the Grebe cubic K102 and the union of the circumcircle and the line X(3)X(3589).