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Given a triangle , the Neuberg cubic is the set of all points whose reflections in the sides , and form a triangle perspective to . It is a self-isogonal cubic with pivot point at the Euler infinity point . The name comes from the geometer Joseph Jean Baptiste Neuberg for his 1894 paper.[more]
Let , , be the side lengths of and let , , be the excenters of . Then the equation of the Neuberg cubic of in barycentric coordinates is given by
, where the cyclic sum is over all six permutations of , , .
The cubic passes through the points , , and the Kimberling centers , , , , , , , , , , , , .
You can drag the vertices , and .[less]
Contributed by: Minh Trinh Xuan (August 2022)
Open content licensed under CC BY-NC-SA
 C. Kimberling. "Encyclopedia of Triangle Centers." (Aug 2, 2022) faculty.evansville.edu/ck6/encyclopedia.
 B. Gilbert. "Catalogue of Triangle Cubics." (Aug 3, 2022) https://bernard-gibert.pagesperso-orange.fr/ctc.html.