A Rectangular Tetrahedron




About: Find me on Reddit, Tumblr and Twitter as @KitemanX. Buy my projects at bit.ly/LWLaser

Once you know how, this is a simple project - turning a flat rectangular piece of paper into a full tetrahedral solid.

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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.

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    37 Discussions


    10 years ago on Introduction

    sweet! going to make an army of these to unleash on. . .my..er..any volunteers? :-]


    10 years ago on Step 1

    It will also work, like with most paper (in America, at least) with 11" X 1.528". With any given length of paper, all you have to do is take the length and multiply it by the result (different calculators will give different results) of the equation 5/36. My calculator gave me 0.13888888888888888888888888888889 which I then multiplied my length, 11", by; 0.13888888888888888888888888888889*11, my calculator gave me 1.5277777777777777777777777777778 There you are, my own formula (and probably the one in use by Kiteman) for finding Kiteman's magical tetrahedron length:height ratio.


    Reply 11 years ago on Introduction

    np I'm gonna make it after i clean my room tomorrow. *ps do you want before and after pics of my room lol its kind hard to walk in there atm.*


    11 years ago on Introduction

    This is great. It works because 9 is very close to the actual value of 8.66 for a regular tetrahedron. And the way it can store flat in your wallet is very cool. Nice Instructable and fun to play with.

    1 reply

    Reply 11 years ago on Introduction

    If you use public transport, try sitting on the bus and taking one of these out of your pocket, flat. Play with it a few times and then hand it to anybody who was pretending not to watch you.

    Then watch everybody else watch them. Priceless.


    Reply 11 years ago on Introduction

    Thanks :P, I turned my screen off to use as a black background, but for some reason my fingers are really white in the 3rd pic ?:P