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X(6), X(523), X(2574), X(2575) vertices of the Thomson triangle M1, M2 on the Fermat axis and on the rectangular circumhyperbola through X(477) 

K624 is a nK0 passing through the vertices of the Thomson triangle and having three real asymptotes concurring at G. Two asymptotes are parallel to those of the Jerabek hyperbola and one is perpendicular to the Euler line. *** More generally, a nK0 passing through the vertices of the Thomson triangle must have its root on the line at infinity and its pole on the Lemoine axis. It always contains the Lemoine point K = X(6). See K625 for another example. 
