A sphere with two puncture points can be deformed into the infinitely extended hourglass form of a catenoid.
Until the work of Hoffman and Meeks, the plane, catenoid and helicoid (imagine a soap film stretching along the curves of an infinitely long helix or spiral) were the only known examples of complete, embedded, minimal surfaces of finite topology.
Mathematical clues indicated that the surface contained two catenoids and a plane that all somehow sprouted from the center of the figure.
However, the Laplacian of the Gauss map of several surfaces and hypersurfaces, such as catenoids and right cones in [E.
For instance, when [alpha] = 0, the generalized catenoids of the first and the third kind have proper pointwise 1-type Gauss map of the first kind.