There are an infinite number.
If you draw two great circles, no matter how close together they are,
I can always draw a great circle ... or 2 or 3 or 10 ... between them.
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A sphere has no corners, it is a 3-D circle.
A sphere has no vertices. It also has no edges.
None. A sphere does not have any angles.
The ancient Greek mathematician Archimedes proved that the volume of a sphere is four times that of the cone with base equal to a great circle of the sphere and height the radius of the sphere. Maybe this is what the poser of the question meant.
A sphere has one side. Not tricky! Unless the sphere is hollow, which would have two sides, inside and outside.