There is no such 3-d shape if it also has flat faces.
A pyramid
cube
cube
A 3D shape that has 6 edges is called a hexagonal prism.
It cannot be a simply connected 3d shape because it does not satisfy the Euler characteristic.
It is a pentagonal prism.
A square base pyramid
corners of a 3d shape
It is a square based pyramid that has 5 faces, 8 edges and 5 vertices
triangular prism
Triangular prism
A triangular prism