How many unique shapes can you get by unfolding a paper cube?

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, I have heard of it before, but I do not know what 4d means. Can some explain to me?

Posted by Vee-Liem Veefessional on 2004-07-31 04:30:38