A set of single untrimmed surfaces that are all at least tangent to its neighbour surfaces. Ideally they all have the same control point structure at shared edges. As a working title I call this thing MultiNURBS objects. The specivic object on the left might also be called hexosphere while the "sharpness" can be changed to make it look more like a rounded box.
| Edge Continuity
The example shows a flattened sphere which is represented by six surfaces with curvature continuity at the shared edges. It is possible to make other basic shapes for example a smoothed cylinder or a torus. If I have some time I will make more MultiNURBS shapes and offer to download.
In other modeling software these kind of objects usually can be controlled by a cage, but I think this is a limitation to Rhino's real NURBS. I prefer to select the points with the help of macros or VBscript. That way you don't have to subdivide the surfaces that much.