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.

I think theres 10 3D to 2D cubes, struggling a bit with the 4D to 3D though

[]
[][][][]
[]

[]
[][][][]
  []

[]
[][][][]
     []

[]
[][][][]
        []

  []
[][][][]
  []

  []
[][][][]
     []

[][][]
     [][][]

[]
[][][]
     [][]

  []
[][][]
     [][]

     []
[][][]
     [][]

Posted by Juggler on 2004-07-22 14:18:39