Of course in your case you will need 6 planes at right angles to each other each with a square defined as the intersection region. You will also need to solve for the ray intersection point so that you can detect if it intersects the plane behind your eye and is thus unseen. Later you can give the plane reflective properties and bounce the ray around the scene and/or map a picture into the seen region and give it some nice texture. Don't forget about specular highlights at reflective angles that pass close to to a light source since in the real world nothing can completely absorb light.
