The Thomson cubic
of a triangle
is the locus the centers of circumconics whose normals at the vertices are concurrent.
It is a self-isogonal cubic with pivot point
at the triangle centroid, so its parameter is
and its trilinear equation is given
by

(Cundy and Parry 1995; Kimberling 1998, p. 240).

It is sometimes called the seventeen-point cubic (Casey 1893, p. 460; Kimberling 1998, p. 240) because it passes through the vertices , ,
, the side midpoints , ,
, the altitude
midpoints ,
, , the excenters , , , the incenter (),
triangle centroid (),
circumcenter (),
orthocenter (),
and symmedian point ().
It also passes through the mittenpunkt (), as well as Kimberling
centers ,
, and (Kimberling 1998, p. 240), as well as and so it is really a 23-point cubic!