There are many well known examples of CMC-surfaces with large spatial symmetry groups. The classic Delaunay surfaces (see [8]) have a nondiscrete group AutΨ(D) containing the group of all rotations around their generating axis. Other examples are the Smyth surfaces [19], which were visualized by D. Lerner, I. Sterling, C. Gunn and U. Pinkall. These surfaces have an m + 2-fold rotational symmetry in R 3 , where the axis of rotation passes through the single umbilic of order m. More recent is the… CONTINUE READING