A Yoshimoto Cube is a cube that infinitely folds over itself. You can fold it either way but you will never run into a problem while folding that will make you have to go the other way. In this Instructable, I will teach you how to make the cubes used to make this and how to connect them. Folding it is pretty straight forward. If you have another method of making cubes that you would like to try, you may use it as this method is just used to make strong cubes and add paper to connect them. As you will see, you can use paper to connect the cubes or tape.
Step 1: Selecting Paper
I used some papers I had lying around my house. They are 8.5x11". You can use rectangular papers (just try not to get too big or too small, I have done that and they are hard to fold) but we are going to make them into a square for this.
You will need three (3) pieces of paper to make the cubes and two (2) more for connecting the cubes if you don't want to use tape
If you have selected square paper, skip the next step.
If you have another method of making the cubes or you know how to make these cubes, skip to step 6.
Step 2: Squaring the Paper
To make it a square, have your paper portrait . Fold the top left corner to the right long edge. Line up the top edge with the side edge and crease (Image 1).
Next, take the excess on the bottom and fold it over to line up with the piece you just folded over. Crease it (Image 2). Cut that rectangle off then unfold the triangle to reveal the square (Image 3).
Step 3: Making the Grid
In this step, we are creating an 8x8 grid with the paper by folding and creasing. After every fold, you will be creasing then unfolding the paper in this step. Start by folding in half both horizontally and vertically (Images 1 & 2). Then fold the bottom edge up to the middle crease and repeat that all the way around and you will have a 4x4 grid (Image 3). Now fold up the bottom edge to the first crease. Do that all the way around the paper. Then fold the bottom edge up to the 1/4 crease (should be the second crease from the top) (Image 4).
Your paper should now look like image 5 with the 8x8 grid folded into it.
Step 4: Making the Strips
You have made an 8x8 grid but your strips need to be 6x1 so you need to take off an 8x2 section (Images 1 & 2).
After that, you will want to start taking off 6x1 strips (Image 3). SAVE THE 8x2 SECTION. I suggest using the fold and tear (adding moisture with water or saliva to the crease will help) or using a paper cutter or a metal ruler and a knife to cut these. Scissors will leave you with curved lines and in my experience, they don't cut on the line even if you want them to when your line is a fold. From this piece, you will end up with eight (8) strips (Image 4).
Now take your 8x2 strip and cut off a 2x2 section from the end (Images 5 & 6). Then cut the 6x2 section into two (2) 6x1 strips (Image 7). From one (1) paper, you have made 10 strips (Image 8).
Step 5: Creating the Cube
You will need three (3) strips for each cube (Image 1) and eight (8) cubes total.
In image 2, you see two strips laid down (paper clips are just there to hold the strips for the picture and will not be used in this project). The horizontal strip MUST be on the bottom. There are three (3) squares on the left, one (1) under the other strip, and two (2) on the right. The vertical strip has four (4) squares on top, one (1) above the other strip, and one (1) on the bottom.
Image 3 shows the third strip starting with one end on the right as the strip wraps around the others. To do this, you will need to fold the strips up around the overlapping squares. The other end should end up in the front of the cube (Image 4).
Now there are three pieces of strips sticking out the top. Image 5 shows that the one that has one (1) square up gets folded in. Image 6 shows that the one that has two (2) squares sticking out gets folded over that and tucked into the opening on the other side.
Images 7 & 8 show the last piece of a strip sticking out going into an opening on the bottom.
Images 9 & 10 are what you should've ended up with.
Repeat this step until you have eight (8) cubes (Image 11).
These strips can be tucked away the other way, the longer one first, then the short one and the one with two (2) squares last. I suggest doing it that way if you want to use strips to put them together.
Step 6: Connecting the Cubes
Arrange the cubes in a 4x2 block (Image 1). Take two (2) at a time and connect them together one (1) edge to one (1) edge. DO NOT CONNECT THE SIDES. Images 2, 3, and 4 show how to do it with strips. Image 5 shows the cubes connected on the bottom right. When you have completed this part of the step, you should have four (4) groups of two (2) cubes (Image 6). Arrange them as shown in image 7 with the edge that is connected on top.
Connect the two middle cubes on the long edge together on the outside. Switch to the opposite side for the other two so they are also connected on the outside (Images 8 & 9).
Flip the whole thing over (if you flip the connected sets individually, the parts from images 8 and 9 will be on the inside and it won't work). Now you need to connect the two (2) sets of four (4) cubes together. This is achieved by connecting the cubes on both short ends together on the TOP.
Step 7: Play!
If you have successfully made the cubes and connected them correctly, you now have a Yoshimoto Cube that will infinitely fold. If you play with it too much, the paper will wear and tear. You can either replace it or tape it. Tape will wear and tear too. When I make these, I use paper then reinforce them with tape.
Have fun! I hope you enjoyed this Instructable!