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Unfolding cube (Posted on 2004-07-22) Difficulty: 4 of 5
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.

  Submitted by Tristan    
Rating: 3.1667 (6 votes)
Solution: (Hide)
There are 11 ways of unfolding a cube.
 _ _ _    _ _     _ _    _ _      _       _
|_|_|_|  |_|_|_  |_|_|  |_|_|   _|_|_   _|_|
  |_|      |_|_|   |_|_   |_|  |_|_|_| |_|_|_
  |_|      |_|     |_|_|  |_|_   |_|     |_|_|
  |_|      |_|     |_|    |_|_|  |_|     |_|

 _       _       _       _        _
|_|_ _  |_|_    |_|_    |_|_     |_|
|_|_|_| |_|_|_  |_|_|   |_|_|_   |_|_
  |_|     |_|_|   |_|_    |_|_|  |_|_|
  |_|     |_|     |_|_|     |_|    |_|
                                   |_|

There are 261 ways of unfolding a hypercube. A good explanation is at
http://members.rogers.com/peter.turney/unfolding/index.html

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(2): 4d???Vee-Liem Veefessional2004-08-01 02:30:06
Hints/Tipsre: 4d???Tristan2004-07-31 11:47:53
Question4d???Vee-Liem Veefessional2004-07-31 04:30:38
re(2): For the first partJuggler2004-07-22 22:58:32
Solutionfirst partrixar2004-07-22 21:03:41
SolutionmethodCharlie2004-07-22 15:24:54
re: For the first partSing4TheDay2004-07-22 14:53:45
For the first partJuggler2004-07-22 14:18:39
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