The base unit you are working with is a hyperbolic paraboloid, which is a surface talked about in multivariable calculus and other fields of math. Don't let its mathematical underpinnings scary you, it is a simple shape to fold.
This instructable is inspired by the work of Professor Erik Demaine. I HIGHLY recommend going to his website to see how he folds a hyperbolic paraboloid. The instructions here for folding a hyperbolic paraboloid are more of a supplement to Demaine's instructions. The main focus of this instructable is making a hyperbolic paraboloid cube using 24 hyperbolic paraboloid units.
Step 1: Gathering Knowledge and Supplies
Things you will need for this instructable:
24 sheets of square paper - The color does not matter. I color coded the sides for this instructable to make it easier to see the different sides of the finished "cube". Also, if you can, use good paper. It's completely possible to use cheap paper for this, as I did, but it will be much sturdier if you use good quality paper.
Double-sided tape - This is the best method I could think of for attaching the hyperbolic paraboloid units together. You could use glue or some other tape, but I highly recommend double-sided tape.
Thread, a needle, and masking tape - This is optional and only needed if you plan on hanging your finished sculpture.
Step 2: Folding a Hyperbolic Paraboloid
In total, you need 24 of these, 4 per side. Color-cordinate as you wish.
Step 3: Making a Side of the Cube
The way in which you join the edges of these 4 hyperbolic paraboloids is the same method used to join hyperbolic paraboloids for the rest of this project. The key to joining the hyperbolic paraboloids is making sure you are joining the CORRECT sides, hence this instructable and many pictures.
Once you have one side, make 20 more hyperbolic paraboloids units for the 5 other sides.
Step 4: Attaching the First Five Sides
Step 5: Attaching String for Hanging (optional)
Ideally, you would sow through the side that is to be attached last (which is the red side on this cube.)
There is no need for attaching thread if you plan on not hanging your cube.
Step 6: The Last Side!
Step 7: It's Done!
I recommend hanging your master piece in a place of honor. Alternatively, if you used a sturdy enough paper, you can just let the sculpture sit around for people to look at and hold.
You could also make into hat or the worst fish bowl ever.