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 Unfolding cube (Posted on 2004-07-22)
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

 Subject Author Date re(2): 4d??? Vee-Liem Veefessional 2004-08-01 02:30:06 re: 4d??? Tristan 2004-07-31 11:47:53 4d??? Vee-Liem Veefessional 2004-07-31 04:30:38 re(2): For the first part Juggler 2004-07-22 22:58:32 first part rixar 2004-07-22 21:03:41 method Charlie 2004-07-22 15:24:54 re: For the first part Sing4TheDay 2004-07-22 14:53:45 For the first part Juggler 2004-07-22 14:18:39

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