Let be trilinear points for , 2, 3. The -vertex of the unary cofactor triangle is then defined as the point

and the -vertex and -vertex are defined cyclically.

The following table summarizes the unary cofactor triangles for common named triangles.

The vertices are the isogonal conjugates of the vertices of the line-polar triangle of the points .

If is a triangle and is its unary cofactor triangle, then , and and are perspective, with the perspector being known as the eigencenter.

A triangle is perspective to iff its unary cofactor triangle is perspective to . Also, triangle circumscribes triangle iff circumscribes (Kimberling and van Lamoen 1999).