Presumably the question refers to a POLYHEDRON, not a polygon.
By the Euler characteristic for a simply connected polyhedron, V + F = E + 2 so the number of vertices would be 8. (It is a parallelepiped.)
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A prism with 10 faces would have 16 vertices. A pyramid with 10 faces would have 10 vertices. Since your figure is neither of these, you need to tell us what it is. In case your numbers were incorrect, here are the formulas: A prism with an n-sided base will have 2n vertices, n + 2 faces, and 3n edges. A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges.
A cube or a cuboid both would fit the given description both of which have 8 vertices, 12 edges and 6 faces.
Well, it has 24 edges, 10 faces, and finally,16 vertices's
A square-based pyramid would fit the given description. (A triangular prism would have 9 edges and 6 vertices)
According to Euler none; for all 3d shapes: Vertices + Faces = Edges + 2 ⇒ 12 + 8 = 19 + 2 ⇒ 20 = 21 So unless 20 does equal 21, no 3d shape has 8 faces, 19 edges and 12 vertices. Any 3d shape with 8 faces would be an octahedron.