CUBE
a square pyramid
cube
A cube.
square
a square
A cube.
It is not clear whether the question means the shape has ten faces of which 4 are square and 6 are not, or 6 faces of which 4 are square. In the first case the shape would be a 16-hedron. The second is impossible.
a cube
square
It is a cube that has 6 identical square faces, 12 edges and 8 vertices.
This is a cube.
square based Pyramid