The answer will depend on the shape under consideration.
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There is no limit to the number of vertices nor edges.
Sphere ( 0 faces , 0 edges , 0 vertices )
Faces + Vertices = Edges + 2
the formula is (vertices+faces)- 2= edges
There is not a specific formula fro vertices and edges. The Euler characteristic links the number of vertices, edges AND faces as follows: E + 2 = V + F for a simply connected polyhedron.