There are infinitely many shapes that do.
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A cylinder and a cone - are two entirely different 3D shapes. A cylinder has three faces & two edges. A cone has two faces and one edge.
6 faces, 12 edges
The rule applies to POLYHEDRA (3D shapes) not Polygons, which are 2D Faces + Vertices - Edges = 2
Such a shape does not exits. See the attached link for all 3d shapes with 6 plane faces.
A triangular prism has nine edges, three edges that are parallel to each other on the top and bottom of the prism, and three surrounding edges. It also has five faces and six vertices.