These are some great tests I must say - they really get you to think nurby-nurby! 
 
 
As Michael said, I'm seeing a sphere with a portion of the surface extracted - the edges however sound like a loft or something dealing with a profile. 
 
The indentations seems to me look like they should be created seperately (using circles of differing levels and perhaps a profile curve used as a 2-rail sweep?  This is then somehow boolean'ed or blended onto the main surface (definitely not sure of that one?) 
 
Figuring this one out would definitely be a great lesson! 
 
-Will 
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