A hexagon based pyramid.
Well, a triangular prism has 5 faces and 6 vertices, but it has 9 edges. So I'm not sure.
Faces: 7 Vertices: 7 Edges: 12
What has 7 faces 12 edges 5 vertices
A pentagonal prism would seem to fit the given description.
a square
A hexagon based pyramid.
pentagonal prism
It is a pentagonal prism
pentagonal prism
What has 7 faces 7 edges 11 vertices
It cannot be a simply connected 3d shape because it does not satisfy the Euler characteristic.
Well, a triangular prism has 5 faces and 6 vertices, but it has 9 edges. So I'm not sure.
7 faces 7 vertices 12 edges
It has 7 faces, 12 edges, and 7 vertices
7 faces 12 edges 7 vertices
7 faces,12 edges, 7 vertices