In isogonal pivotal (with pivot at the line of infinity) cubics with respect to a triangle $\triangle ABC$. By a suitable projective transformation, fixing $A$,$B$, and $C$, sending the incenter to the centroid, sends the excenters to their corresponding vertex of the anticomplementary triangle, this "duality" initially suggests some kind of isotomic conjugates points that every isotomic pivotal cubic should pass through analogous to circular points of infinity, but I'm not sure if they share nice properties as the circular points at infinity do.
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$\begingroup$ It is important to give references for readers who don't know what isotomic conjugation is, see here ; about cubics in this world : see there $\endgroup$– Jean MarieCommented Apr 26 at 19:58
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$\begingroup$ Thanks for the references. I'll keep these recommendations in mind in my next questions. $\endgroup$– CuriousCommented Apr 27 at 1:47
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