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A (genus-0) polyhedron must satisfy Euler's formula:

V + F - E = 2.

Setting V, E, F equal to the same value, say, X, we get

X + X - X = 2

X = 2.

A solid with two edges, vertices and faces is called a "digonal hosohedron", but it is not usually considered a three-dimensional figure, in euclidean space.

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Q: What 3 dimensional figure has the same number of faces edges and vertices?
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