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X(2), X(6), X(98), X(182), X(187), X(385), X(598) foci of the inscribed Steiner ellipse imaginary common points of the circumcircle and the Lemoine axis 

K705 is another example of circumcubic passing through the center and the foci of the Steiner inscribed ellipse. It is the isogonal transform of K353. K705 is spK(P, X2) where P is the reflection of X(385) about X(2). See CL055 and also Table 48. 
