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From the formal definition of edges, faces and vertices: no simply connected solid object because, according to the Euler's characteristic of such shapes you are not topologically equivalent to a sphere, a torus (sphere with one hole through it), or a sphere with any number of holes.

Using a more casual approach to these definitions, I would suggest a convex lens - or two spherical sections joined together.

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Q: If you have 1 edge 2 faces and 0 vertices what would i be?
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