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How to fold a cube from a square sheet

Take a 1-by-1 sheet, and fold 16 squares. Then add diagonal foldings according following figure. (dotted-line: mountain-fold, straight: valley-fold).
   +---------+---------+---------+---------+
   | \      6|         |2      / |      3/1|
   |   \     .         .     /   |     .   |
   |     \   |         |   /     |   /     |
   |6      \ .3        . /      2| .       |
   +---------+---------+---------+ - --- - +
   |         |         |       / |         |
   |         |         |     .   |         |
   |         |         |   /     |         |
   |         |         | .       |         |
   +---------+---------+---------+---------+
   |       / |         |         |         |
   |     .   |         |         |         |
   |   /     |         |         |         |
   | .       |         |         |         |
   + - --- - +---------+---------+---------+
   |5      / |         | .       . \       |
   |     /   |         |   \     |   \     |
   |   /     |         |     .   .     \   |
   | /      5| 4       |      4\ |       \1|
   +---------+---------+---------+---------+
Short instructions: Detailed instructions, for those who are not very experienced.
   A---------B---------C---------D---------E
   | \       |         |       / |       / |
   |   \     .         .     /   |     .   |
   |     \   |         |   /     |   /     |
   |       \ .         . /       | .       |
   F---------G---------H---------I - --- - J
   |         |         |       / |         |
   |         |         |     .   |         |
   |         |         |   /     |         |
   |         |         | .       |         |
   K---------L---------M---------N---------O
   |       / |         |         |         |
   |     .   |         |         |         |
   |   /     |         |         |         |
   | .       |         |         |         |
   P - --- - Q---------R---------S---------T
   |       / |         | .       . \       |
   |     /   |         |   \     |   \     |
   |   /     |         |     .   .     \   |
   | /       |         |       \ |       \ |
   U---------V---------W---------X---------Y
(Thanks to Ralph Dratman for his comments.)

Instruction video by Jorge Jaramillo

Jorge Jaramillo has made an instruction video showing how to fold the video including a colour diagram showing where to make all the folds before putting it together.

About the fold

This fold was found by a number of people independently, but is not a well known fold, which is rather surprising as it is a very elegant folding. I too found it by myself.

It was published in the book `Origami for the Conoisseur', where it can be found on page 58. It says that it was independently invented by Haga and Kunihiko Kasahara.

Jeannine Mosely told me that she invented it in 1974 on her own.

Origami pages

For other ways to fold boxes look here in the The garden of Origami by Victoria Beatty. See also Joseph Wu's Origami Page, and a Guide to Paperfolding Instructions on the Web.


How to fold a cube from two square sheets

Take two 1-by-1 sheets, and fold them according to the following figure. (dotted-line: mountain-fold, straight: valley-fold).
   +---------A-------------------L---------+
   |       /   \               / | \       |
   |     .       .           /   |   .     |
   |   /           \       /     |     \   |
   | .               .   /       |       . |
   I-------------------H         |         G
   | \               /   \       |       . |
   |   \           /       \     |     /   |
   |     \       /           \   |   .     |
   |       \   /               \ | /       |
   |         B                   F         |
   |       / | \               /   \       |
   |     .   |   \           /       \     |
   |   /     |     \       /           \   |
   | .       |       \   /               \ |
   C         |         D-------------------K
   | .       |       /   .               . |
   |   \     |     /       \           /   |
   |     .   |   /           .       .     |
   |       \ | /               \   /       |
   +---------J-------------------E---------+
Now fold, at the same time, A to B, C to D, E to F, and G to H for both sheets. You will get two semi-boxes where the points I, J, K, and L stick out.

The two semi-boxes can be put together, such that the points I, J, K, and L of the one semi-box go inside the other semi-box touching the points A, C, E, and G.

As an alternative, you can also join one of the above with the following:

   +---------A---------+---------B---------+
   |       /   \       .       /   \       |
   |     /       \     |     /       \     |
   |   /           \   .   /           \   |
   | /               \ | /               \ |
   C                   x                   D
   | \               /   \               / |
   |   \           /       \           /   |
   |     \       /           \       /     |
   |       \   /               \   /       |
   +-.-.-.-.-x                   x-.-.-.-.-+
   |       /   \               /   \       |
   |     /       \           /       \     |
   |   /           \       /           \   |
   | /               \   /               \ |
   E                   x                   F
   | \               / | \               / |
   |   \           /   .   \           /   |
   |     \       /     |     \       /     |
   |       \   /       .       \   /       |
   +---------G---------+---------H---------+
The first tricky thing about this fold is to get the diagonal folds at the right place. Now fold A to B, C to E, D to F, and G to H. This will give you a box with one open side. The second thing is to make this one join with a paper folded according to the previous diagram. There is only one way to do it, but I cannot describe it accurately.