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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 circum-cubic passing through the center and the foci of the Steiner inscribed ellipse.

It is the isogonal transform of K353.

K705 is spK(X7840, X2) where X(7840) is the reflection of X(385) about X(2). See CL055 and also Table 48.

See the related cubics spK(G, G) = K002 (Thomson cubic), spK(X524, G) = K018 (second Brocard cubic), spK(K, G) = K287 (a central cubic), spK(X385, G) = K353 and spK(X599, G) = K729 (Grebe-Steiner cubic).

If P, Q are two finite points on the line GK, distinct from G and symmetric with respect to G, then spK(P, G) and spK(Q, G) are isogonal transforms of each other.