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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A rhombus is a two dimensional figure while the concept of {faces, vertices and edges} is relevant to 3-dimensional shapes.
A trapezium has 4 vertices and 4 edges or sides. It is a two dimensional figure so it has only one "face".
It is a cube.
A cube
A hexagon is a plane (2-dimensional) figure with 1 face, 6 vertices and 6 sides (which may be called edges).