A heptohedron
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Faces: 7 Vertices: 7 Edges: 12
What has 7 faces 12 edges 5 vertices
The number of vertices does not determine the number of faces. If the shape with 6 vertices was a quadrilateral based bipyramid, it would have 8 faces. A hexagonal based pyramid has 7 vertices and 7 faces. So more vertices does not necessarily imply more faces.
A pentagonal prism has 7 faces, 10 vertices and 15 edges.
Faces:4 Edges:7 Vertices:5