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).