Take the 2-minute tour ×  I recently found that there were some
things that could be said about the digon, the polygon with 2
vertices and 2 edges; in particular, the Wikipedia article notes
that “in spherical geometry a nondegenerate digon (with a
nonzero interior area) can exist if the vertices are antipodal.”
It seems to me that there is another case, in which the digon is
irregular, which consists of two vertices (not necessarily
antipodal) lying on a single line (great circle), so that the
interior consists of exactly half of the sphere. Is there a
reason why this does not qualify as a nondegenerate digon?
share|improve this question add comment  2 Answers  Since both
edges are on the same great circle, they are actually the same
edge. You cannot define a digon this way.  It is like defining a
quadrilateral in an euclidean space using four vertices, out of
which three are on the same line - this is not a quadrilateral
but a triangle.  share|improve this answer I think you mean
"vertices" rather than "e