The high symmetry of the double-cone topology of the linear E ⊗ e JT system directly reflects the high underlying symmetry. It is one of the earliest (if not the earliest) examples in the literature of a conical intersection of potential energy surfaces. Conical intersections have received wide attention in the literature starting in the 1990s and are now considered paradigms of nonadiabatic excited-state dynamics, with far-reaching consequences in molecular spectroscopy, photochemistry and photophysics. Some of these will be commented upon further below. In general, conical intersections are far less symmetric than depicted in the figure. They can be tilted and elliptical in shape etc., and also peaked and sloped intersections have been distinguished in the literature. Furthermore, for more than two degrees of freedom, they are not point-like structures but instead they are seams and complicated, curved hypersurfaces, also known as intersection space. The coordinate sub-space displayed in the figure is also known as a branching plane.