Here is a pseudosphere created with openSCAD.
For a description see http://mathworld.wolfram.com/Pseudosphere.html
The openSCAD code can also be used to generate pseudosphere sections. Two bowls, with pleasing curved surfaces, were formed from such sections. Stl files are:
OpenSCAD code is included.
The pseudosphere needs to be printed on a raft with support. My Replicator produced a nice smooth print except for a small dimple where the sphere touched the build surface.
The other 3 files can be printed directly on the build platform. An alternative to printing the pseudosphere is to print two half spheres and glue them together.