The Gibert point can be defined as follows. Given a reference triangle ,
reflect the point
(which is the inverse point of the Kosnita
point in the circumcircle) in each of the side
lines of ,
to obtains the points ,
, and to obtain the triangle . The triangles and are then perspective, with perspector
given by the Gibert point, which is Kimberling center .

Consider the Neuberg cubic, which is the locus of a point
such that the reflections of in the sidelines of a reference
triangle
are the vertices of a triangle perspective to . The locus of the perspector
is the cubic
with trilinear equation

(Gibert). This cubic passes through Kimberling centers for , 5, 13, 14, 30, 79, 80, 265, 621, 622, 1117, and 1141.

The Gibert point is then also the unique point (other than , ,
and ) in which meets the circumcircle.