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X(3), X(4), X(20)

isogonal conjugate of X(3543)

its reflection about X(3)

foci of the inscribed Steiner ellipse

their reflections about X(3)

infinite points of pK(X6, X3543)

antipodes of A, B, C on (O)

K706 is a central circum-cubic with center O passing through the foci of the Steiner inscribed ellipse.

K706 is spK(X3543, X2) where X(3543) is the reflection of X(2) about X(4). See CL055 and also Table 48.

The isogonal transform of K706 is K847.

K706 is a member of the pencil of central cubics generated by the Darboux cubic K004 and the union of the Euler line and the circumcircle. These cubics are those in the column P = [X20] of Table 54.