The Origami Forum

Hello everyone here,
I'm hoping someone will be able to assist me. I used to be a primary school teacher and loved teaching the children origami. I had many books to assist and more often than not, there'd always be one child who would become so brilliant that they'd be teaching me wonderful new models to make! One such model was a closed cube made from a single A4 sheet with no cuts, no glue, no resizing just folding. I have searched the net numerous times to try and find this ingenious design, but to no avail. If anyone knows of this model I'd greatly appreciate a link to either the book or the instructions.
thanks in advance,
Moonthing.

Right out of my head I don't remember a closed cube from an A4 sheet, but there is a pretty ingenious one from a square: https://erikdemaine.org/thok/delian.html

Thanks so much for the reply! The cube from the A4 looks exactly the same... I remember that the initial folding for the design involved thirds along the 21cm side and the longer side into quarters, which gives you 12 squares (vs 16 with the cube you've provided)... and like the pattern for the square paper it's a series of diagonal valleys and mountains in each square, followed by a very puzzling assembly!

Well, A4 is not quite 3x4, but close enough. There are probably a dozen ways to fold a cube from a 3x4 grid, but here is a simple one with clean outer edges: https://photos.app.goo.gl/LGyS9i423DM7uXud6
First make your grid. Then add the six diagonals as shown with orange being mountain and green valley folds.
Start collapsing on the right side by making the rightmost mountain and valley fold at the same time. The two valley folds that outline the rightmost square come to lie atop each other forming a pocket for later.
The next step is exactly the same but mirrored with the second square from the left.
Finally on the leftmost square the diagonal is made as a valley fold creating a flap that is folded outward into the pocket created earlier.

Oh, one thing I should mention, the word diagonal that I used is technically speaking wrong in this case, because what you really want are angle bisectors starting at the inner corners.