Bending an object over a surface

The term Geodesic Sphere comes to mind.
These pages may be of interest:

TaffGoch’s Geodesic Help Group
https://groups.google.com/forum/#!topic/GeodesicHelp/DolXrzpzAQs

TaffGoch’s 3D Warehouse Collection

Domerama
http://www.domerama.com/