It has a lower symmetry than cylindrical, but it still has axes of symmetry and planes of symmetry and a center of symmetry.

The equilibrium condition only forces the symmetry condition that the points of intersection between any straight line that passes through the center of rotation with the surface of the body must be equidistant to the center of rotation.

This symmetry condition is satisfied by the symmetry group of the rectangular parallelepiped, which is also the symmetry group of the triaxial ellipsoid.