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:

pseudosphere.stl
pseudosphere_half.stl
bowl_3.stl
bowl_4.stl

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.