Introduction: A Rectangular Tetrahedron

Picture of 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

Picture of 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

Picture of 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.

Picture of 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.


Kite builder (author)2014-04-26

I know this, a friend of my famely gave me a redy one

Spycrab (author)2009-09-02

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

chriskarr (author)2009-01-02

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.

PKTraceur (author)2008-11-30

Schweet! d4!

knexfan9182 (author)2008-07-27

thats cool i might make it. +5*

Kiteman (author)knexfan91822008-07-27


knexfan9182 (author)Kiteman2008-07-27

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.*

Kiteman (author)knexfan91822008-07-28

LOL, sounds like my youngest's room.

knexfan9182 (author)Kiteman2008-08-06

hmm how much of the year can he/she walk in it with out stepping on something?

Kiteman (author)knexfan91822008-08-06

About twenty minutes...

footer0 (author)Kiteman2008-09-25

i knew you liked D&D; >:D

dombeef (author)Kiteman2008-08-12


iectyx3c (author)2008-07-29

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.

Kiteman (author)iectyx3c2008-07-29

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.

=SMART= (author)2008-06-29

Here is My Tetrahedron, I made the larger size and drew it out by hand. Cool instructable 5*

Kiteman (author)=SMART=2008-06-29

Very nice - well photographed as well.

=SMART= (author)Kiteman2008-06-29

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

Kiteman (author)=SMART=2008-06-29

Washed out by camera-flash?

=SMART= (author)Kiteman2008-06-29


YummyPancakes (author)=SMART=2008-07-15

Or you're just nerdier than you think you are 8-)

gmjhowe (author)2008-06-30

nice, good job!

=SMART= (author)2008-06-29

I added this to the Papercraft Group too :D

Kiteman (author)=SMART=2008-06-29

Oh? That's fine.

=SMART= (author)2008-06-29

Haha very nice, mines printing now :P Looks cool, and good pictures

Kiteman (author)=SMART=2008-06-29

Thank you, but you could have just drawn it, like I did. (I made the image in step 1 by using Corel to draw over a scan of the hand-drawn rectangle I use in the photos).

LinuxH4x0r (author)2008-06-28

*golf clap* Very nice!

Kiteman (author)LinuxH4x0r2008-06-28

Thank you, but what is a "golf clap", anyway?

Lithium Rain (author)Kiteman2008-06-28

It's a very polite, quiet clap (because we wouldn't want to break the golfer's concentration!). I don't think he meant it rude.

Kiteman (author)Lithium Rain2008-06-28

Oh! Jake Tobak's link said it was sarcastic, like a slow clap.

Sorry Linux.

(Climbs down off high horse.)

Lithium Rain (author)Kiteman2008-06-28

No, just polite and quiet-kinda like the British. Ducks head

=SMART= (author)Lithium Rain2008-06-29


Kiteman (author)LinuxH4x0r2008-06-28

OK, now I know what a golf clap is, what is your problem with the 'ible?

LinuxH4x0r (author)Kiteman2008-06-28

No problem. I didn't know it was sarcastic. I liked it. I have no clue why. tired. go away. stop asking hard questions

smheath (author)2008-06-28

You mean 9" x 1.25".

Kiteman (author)smheath2008-06-28

Oops, thanks for catching that!

Kiteman (author)Kiteman2008-06-28


About This Instructable




Bio: The answer is "lasers", now, what was the question? If you need help, feel free to contact me. Project previews on Tumblr & Twitter: @KitemanX
More by Kiteman:Fallen Astronaut 2Custom laser cut metal business cardsDashboard Phone Stand
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