perplexus.info :: Shapes : Unfolding cube

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

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2024-06-11 12:31:12
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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