The Stammler hyperbola of a triangle is the Feuerbach hyperbola of its tangential triangle,
and its center is the focus of the Kiepert parabola,
which is Kimberling center 
.
It has trilinear equation
 |
The Stammler hyperbola passes through Kimberling centers 
for 
(incenter 
), 3 (circumcenter 
), 6 (symmedian point 
), 155, 159, 195, 399 (Parry reflection
point), 610, 1498, 1740, 2574, 2575, 2916, 2917, 2918, 2929, 2930, 2931, 2935, and
2948. It also passes through the excenters 
, 
, and 
, as well as through the centers of the Stammler
circles.
The polar triangle of the Stammler hyperbola is the reference triangle.
The anticevian triangle of a point on the hyperbola has vertices on the hyperbola. The vertices of the antipedal
triangles for Kimberling centers 
with 
, 3, 64, 2574, and 2575 also lie on the Stammler hyperbola
(P. Moses, pers. comm., Jan. 24, 2005).
