[airdave]

Ring or Petal, are your two options for "spherical" shapes.
These are the two most common methods of creating compound curved shapes.

Since paper can not/will not bend in two directions (compound curving),
you must resort to more sections/more seams to build up a curved panel or shape.

Biggest lesson to learn is all about pre-forming/pre-shaping parts before you try to glue things together.
If a part will hold its shape without gluing, it will assemble better and easier with better looking results.

Thats my two cents.