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X(3), X(25), X(1073), X(1384), X(1617), X(3167) vertices of the Thomson triangle 

K626 is the isogonal transform of K616. It is a nodal cubic with perpendicular nodal tangents passing through the vertices of the Thomson triangle. See Q091 for a generalization. The nodal tangents are parallel to the asymptotes of the Jerabek hyperbola and to the axes of the Steiner ellipse. 
