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As far as I can make out, none.

According to the Euler characteristic F + V = E + 2 for a 3-D polyhedron where

F = number of Faces

V = number of Vertices

E = number of Edges

If F=V=E then the Euler characteristic implies that F=V=E=2

But you cannot have a solid object with 2 faces.

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Q: What 3d object has an equal number of faces vertices and edges?
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