Constant Negative Gauss Curvature

The surface of a ball (a sphere) has the same positive Gauss Curvature in every point. It is very interesting that there are also surfaces with the same negative Gauss Curvature in every point. Some are surfaces of revolution, but there are also some other surfaces with this property (at least away from some singular curves). The object shown here looks similar to a hyperboloid of one sheet at first sight. But the constant netative curvature property makes the shape look much more fascinating.