A pivotal isotomic cubic is a self-isotomic cubic that possesses a pivot point, i.e., in which points P lying on the conic and their isotomic conjugates are collinear with a fixed point Q known as the pivot of the cubic. Let the trilinear coordinates of X be α:β:γ, then X' has trilinear coordinates α^(-1) :β^(-1) :γ^(-1), or equivalently βγ:γα:αβ.

Lucas cubic | pivot point | self-isotomic cubic