The Stammler Hyperbola

The Stammler Hyperbola passes through the circumcenter (O), the incenter (I), the three excenters, and the vertices of the tangential triangle. The center of the hyperbola is the Euler reflection point. The asymptotes are the lines joining this point to the intersection points of the Euler line and the circumcircle. The Euler line is tangent to the hyperbola at the circumcenter.