[math-fun] How do I reverse-project 2D points into 3D? (special case)

I have 4 2D points in (computer) screen-space, and I need to reverse-project them back into 3D space. I know that each of the 4 points is a corner of a 3D-rotated rigid rectangle, and I know the size of the rectangle. Is it possible to recover the original 3D coordinates from this? If so, how? (I originally heard this problem here: http://stackoverflow.com/questions/76134/how-do-i-reverse-project-2d-points-... )