I connected 14 cubes together to create the rainbow cube chain seen above. It took 168 sheets of paper.
You can make an open cube of your own using just 12 sheets of paper and few simple folds. These open cubes are pretty fun to make and look good in both solid color and rainbow.
All you will need to make a open cube is 12 pieces of origami paper.
Fold the paper in half then unfold. Fold the edges into the middle to meet at the center crease. Turn the model over.
Fold the bottom right corner up to meet the top edge. Unfold that turn the model over. Grab the bottom left corner and bring it up a bit while opening it. Smash it down to create the triangle with a missing corner as show in the last picture.
Fold down the top right corner then undo that fold. Fold the right corner tab up as shown in the third picture. Now fold the entire right corner down again on the crease you made before. Tuck the tabbed corner you folded under the flap.
Fold the entire model in half the long way. Fold the triangle tabs in half as shown. The unit is now complete.
Make 12 of these units.
Begin assembling the units but connecting three of them together. Insert one piece into the other as shown in the first picture. Once inserted, the crease on the tip of the inserted one should line up with the main crease of the one it was inserted into.
Attach a third unit to lock these in place. Again, you'll know it's in the right way when the creases match up.
Keep attaching units, 3 to a corner, to form a cube. After you've attached all 12 you'll have a fun open cube, good job!
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