Make an Open Polysurface (Mesh) smooth

How would one go about smoothing a Mesh that is either an Open Mesh or a Open Polysurface?

See below mesh and render result:

Meshes and surfaces/polysurfaces are different types of objects in Rhino. A surface in Rhino is a NURBS object and a polysurface is two or more surfaces with coincident edges which are joined together. Many Rhino commands only work on surfaces and polysurfaces, not on meshes.