“…Of particular relevance to this paper is the so-called "last geometric statement of Jacobi", which asserts (among other things) that the conjugate locus of a non-umbilic point on the triaxial ellipsoid has precisely 4 cusps (see [20] for a historical sketch and list of references). This conjecture was recently proved by Itoh and Kiyohara [13], and a renewed interest in the conjugate and cut locus can be seen in the recent papers providing formal studies ( [11], [24], [14], [15]), simulations ( [23], [8], [21], [22], [20]) and applications ( [6], [5], [3], [4], [7]). It is no surprise that the papers which focused on the triaxial ellipsoid and surfaces of revolution made heavy use of the fact that the geodesic flow on those surfaces is (Liouville) integrable.…”