Alex Lamb/Experiments/Origami
My wife and I spent many silly evenings a few years ago building giant polyhedral shapes out of Sonobe modules. These modules are very easy to make and fun to build with. The problem with them though, is that you can only join them together in a very limited number of ways. You can make little pointed three-sided turrets, rhombic hats, and flat squares. And that's about it. Of these, I found the three-sided turret the most useful, as you could use them to make any shape that could be made out of equilateral triangles (so long as you didn't mind having a little stubby tetrahedron in place of a each triangle). Eventually, though, our interest waned. (Though not before making some things the size of beachballs with over three hundred components. :) )
I wanted to find a single module that I could combine to make three, four, and five-sided faces with equal ease. I couldn't find one online, so I decided to invent one. About fifty crumpled bits of paper later, I came up with something. I'm no Origami specialist, and suspect that my module lacks elegance. However, it's very versatile and can be used to construct large models without the need for tape or glue, as it includes hooks that link each piece together and enforce rigidity. It's sort of an engineer's module.
Here's how to build it. If you can't stand the suspense, feel free to scroll to the bottom to see a picture of the modules in action.
Take a piece of square paper and crease it corner to corner. Then fold the corners back in to the middle so you get something that looks like this.
Now take each one of those folded-in corners in turn, and fold it back in to the center again. The result should look a bit like a quilt.
Now take two opposite corners and fold them in to the center along the creases you've made to make a kind of narrow strip with pointed ends that opens in the middle like a pair of doors.
Next, take the two ends and fold them back along the creases you've already got that touch the base of each end-diamond. If that doesn't make any sense, take a look at this:
Now turn the shape over so you're looking at a plain rectangle with a seam up the middle. Then fold one corner up to meet the opposite. Ideally, bottom left to top right. You should get something like the following.
We're getting to a tricky part, this is, so here are some more picutres of the same, so you can make sure you got it right.
Okay, the hard part. Unfold your shape back to the rectangle with the seam running down the middle. It should look a bit like the diagram below (either that or its mirror image), where the crease is the line that runs from B to E.
Now fold lines from B to F and A to E, folding away from you, so that on either side of your diagonal crease you get an isosceles triangle. Here are some more pictures so you can figure out what the hell I mean.
I hope that's sort of clear. Now you should have two isosceles triangles, each decorated with a little diagonal seam, that meet at the base. Each triangle should have a flap sticking out of it to the right. Now take each of those flaps and fold the ends down about halfway along, parallel to the edge of the triangle. (This step requires that you make a rough guess of where to fold. You want the flaps long enough that they will reach the seams in the faces of adjacent modules, as shown later on.) You should end up with a small hook parallel to the triangle's edge.
Now you've got your first module! Make two of them and slot them together as shown below, fitting the little hook from one triangle into the seam of its neighbor.
Three modules fit together the same way, making a spike that should be quite rigid once you have the hooks tucked into the flaps of the neighboring pieces.
If you've got this far, then the world is your oyster! Simply attach shapes the same way in groups of three, four, five or even six to make turrets of different shapes.
And here's the result: a shape inspired by the rhombicosidodecahedron, with three, four and five sided points. Hoorah! Nerd joy! Suddenly hours of toil pay off as disposable paper weirdness!
If these instructions seem completely garbled and strange, feel free to email me at the address shown on my contacts page to demand clearer guidelines and I will endeavor to help.