Here, the seven main types of third-order Möbius plane curves are represented on two spheres. One sphere shows the curves without a colon (V to VII).

To obtain the spherical image of a third-order plane curve, as in the present examples, the curve is positioned naturally with its origin in the x-y plane and made the directrix of a cone whose vertex lies at a suitable distance on the z-axis. The center of the sphere is then placed at the apex of the cone, and the generatrix of the cone intersects the spherical surface in the desired spherical image.