Introduction: A Rectangular Tetrahedron
Once you know how, this is a simple project - turning a flat rectangular piece of paper into a full tetrahedral solid.
Step 1: Thirty-Six by Five
That's the secret - you need a rectangular piece of paper or light card with sides in the ration of 36:5.
It can be 36cm x 5cm, 9" x 1.25", whichever you like. Obviously, the larger the piece of paper, the larger the model you can make. You can, if you want, use two pieces that are in the ratio of 18:5, then tape them end-to-end to make a larger piece*.
If you have some sort of graph paper, your job will be made a lot easier, because all you need to do is count squares.
* The next steps will assume you are using a single, long piece of paper, but if you've got the brains to check this footnote, you're able to adapt the instructions to using two separate pieces.
Step 2: Preparation
Draw dotted lines to divide the length of the rectangle into four equal parts. If you are using a piece that is "36 squares" long, then each section will be "9 squares" long.
Draw another dotted line from corner-to-corner of each of the smaller rectangles. Pay attention to the images below - they must alternate in direction, so your paper looks like a pair of broad arrow-heads.
Carefully crease along each dotted line, both valley and mountain fold, so that the paper bends easily both ways.
Step 3: Construction.
Fold the rectangle round into a loop, and tape the ends together.
Then you fold it into a tetrahedron. It's really hard to describe - you sort of aim for a simple boat-shape, then lift the bow and stern up towards each other - Look at the photos one after the other to get the idea.
Once you've got it figured out, the folding is easy (if #2 son can do it, so you can too!). If you make paper models, the tetrahedron is a useful shape to be able to quickly make.
My boys also draw eyes and teeth on these, to make simple puppet-monsters they can keep in their pocket, and it doesn't matter if they get lost.