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Just as the title says: is there a formal name for a convex polygon on a sphere, of which the vertices are connected not by great circle but by small circle segments?

My end goal is to intersect two (or more) of such shapes, and find the area of the shape where the two small-circle polygons overlap. It would therefore be helpful to get to know some basic and/or special properties of such shapes, what equations apply, etc.

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Why not just "spherical polygon" as in "spherical triangle" en.wikipedia.org/wiki/Spherical_trigonometry –  Maesumi Oct 11 '12 at 14:33
    
@Maesumi: because such shapes are defined to be connected by great circle segments (the spherical analogue of a straight line); see the first sentence in the paragraph "Lines and angles on a sphere" in your link. –  Rody Oldenhuis Oct 11 '12 at 14:35
    
I see. Finally! I don't have an answer but in flat 2D there are specialized cases like en.wikipedia.org/wiki/Reuleaux_triangle and the more general "circular triangle", a triangle whose sides are circles. –  Maesumi Oct 11 '12 at 16:18
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