A circumconic is a conic section through the vertices of a triangle .[more]
Given a triangle , the Thomson cubic of is the set of the centers of circumconics whose normals at the vertices are concurrent . It is a self-isogonal cubic with pivot point at the triangle centroid.
Let , , be the side lengths of the reference triangle and , , be the excenters. Then the equation of the Thomson cubic of triangle in barycentric coordinates is
, where indicates that the sum is taken over all six permutations of , , .
The solution is traced in red. Some of the Kimberling centers on the Thomson cubic are:
, , , , , , , , , , , , , , , , , .
You can drag the vertices , and .[less]
 C. Kimberling, "Triangle Centers and Central Triangles." Congressus Numerantium, 129, 1–295, 1998.
 B. Gilbert. "Thomson Cubic = pK(X6,X2)." (Jul 20, 2022) bernard-gibert.pagesperso-orange.fr/Exemples/k002.html.
 Encyclopedia of Triangle Centers (ETC). https://faculty.evansville.edu/ck6/encyclopedia/etc.html.
 B. Gilbert. "Catalogue of Triangle Cubics." (Aug. 3, 2022) https://bernard-gibert.pagesperso-orange.fr/ctc.html.