When a polyhedron is formed by a plane cut through a cube, it will have one face created by the cut. Its other faces will be formed from all or part, of some or all, of the six faces of the cube.It follows that the polyhedron can have at most one more face than the cube, that is, at most seven faces. Therefore it is not possible to obtain a polyhedron with eight faces.

The diagram on the right shows a cube with a plane cut through points on three adjacent edges of the cube.

It can be seen that this produces a tetrahedron which has four faces, and a second polyhedron.

The second polyhedron has three square faces which are faces of the original cube, threepentagonal faces formed by removing a triangular corner from the other three faces of the cube, and the triangular face created by the cut. It is therefore a polyhedron with seven faces.

This shows that neither option A nor D is correct.

The diagram on the right shows a plane cut through two adjacent vertices and two points on the bottom edges of a cube.

One of the polyhedra created by this cut is a triangular prism. This has five faces.

The other polyhedron is a prism whose end faces are trapeziums. This has six faces.

This shows that neither option B nor C is correct.

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