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).
