You can only cut along edges, and the shape must be in one piece and flat. By unique, I mean rotations and reflections don't count.

This problem can be analogized to four dimensions as well. How many unique 3-dimensional shapes can be made by "unfolding" a 4-dimensional hypercube into 8 cubes? This problem is significantly more difficult than the first.

Well, thanks Tristan. In a way, it does give me some ideas, but as I went on reasing to the part on the hypercube, boom! I am lost again. Anyway, thank you for taking time explaning, though I still do not understand. Plus, as you said, the image is distorted...

Thanks anyway!