This spheroid solution is stable up to a certain (critical) angular momentum (normalized by M G ρ ρ r e ), but in 1834 Carl Jacobi showed that it becomes unstable once the eccentricity reaches 0.81267 (or f reaches 0.3302). Above the critical value the solution becomes a Jacobi, or scalene, ellipsoid (one with all three axes different). Henri Poincaré in 1885 found that at still higher angular momentum it will no longer be ellipsoidal but piriform or oviform. The symmetry drops from the 8-fold D 2h point group to the 4-fold C 2v, with its axis perpendicular to the axis of rotation. Other shapes satisfy the equations beyond that, but are not stable, at least not near the point of bifurcation. Poincaré was unsure what would happen at higher angular momentum, but concluded that eventually the blob would split in two.