A self-isogonal cubic us a triangle cubic that is invariant under isogonal conjugation. The
term is commonly applied to mean a pivotal isogonal
cubic, in which points 
lying on the conic and their isogonal conjugates are collinear
with a fixed point 
known as the pivot point of the cubic.
Self-Isogonal Cubic
See also
Isocubic, Pivotal Isogonal Cubic, Triangle CubicPortions of this entry contributed by Floor van Lamoen
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References
Yff, P. "Two Families of Cubics Associated with a Triangle." In MAA Notes, No. 34. Washington, DC: Math. Assoc. Amer., 1994.Referenced on Wolfram|Alpha
Self-Isogonal CubicCite this as:
van Lamoen, Floor and Weisstein, Eric W. "Self-Isogonal Cubic." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Self-IsogonalCubic.html