If I understand what you mean, then another way to say is "No two of its vertices can form a line segment that falls outside of the polygon". In that case, it is called a convex polygon.
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A polygon can have three or more edges and exactly the same number of vertices. All polygons have one face.
5 vertices
No
A sphere has no edges or edges but its face is globular.
Vertices= 24 Edges=36 Face=14