A Rectangular Tetrahedron

 by Kiteman
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.
Spycrab says: Sep 2, 2009. 12:49 PM
sweet! going to make an army of these to unleash on. . .my..er..any volunteers? :-]
chriskarr says: Jan 2, 2009. 6:20 PM
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 says: Nov 30, 2008. 7:23 AM
Schweet! d4!
knexfan9182 says: Jul 27, 2008. 12:00 PM
thats cool i might make it. +5*
Kiteman (author) in reply to knexfan9182Jul 27, 2008. 2:53 PM
Thanks!
knexfan9182 in reply to KitemanJul 27, 2008. 8:31 PM
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) in reply to knexfan9182Jul 28, 2008. 3:52 AM
LOL, sounds like my youngest's room.
knexfan9182 in reply to KitemanAug 6, 2008. 9:05 AM
hmm how much of the year can he/she walk in it with out stepping on something?
Kiteman (author) in reply to knexfan9182Aug 6, 2008. 9:48 AM
About twenty minutes...
footer0 in reply to KitemanSep 25, 2008. 5:16 PM
i knew you liked D&D >:D
dombeef in reply to KitemanAug 12, 2008. 5:17 PM
YEA HA!
iectyx3c says: Jul 29, 2008. 8:34 AM
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) in reply to iectyx3cJul 29, 2008. 8:46 AM
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= says: Jun 29, 2008. 8:56 AM
Here is My Tetrahedron, I made the larger size and drew it out by hand. Cool instructable 5*
SNC11536.JPGSNC11534.JPGSNC11535.JPG
Kiteman (author) in reply to =SMART=Jun 29, 2008. 9:08 AM
Very nice - well photographed as well.
=SMART= in reply to KitemanJun 29, 2008. 9:31 AM
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) in reply to =SMART=Jun 29, 2008. 10:13 AM
Washed out by camera-flash?
=SMART= in reply to KitemanJun 29, 2008. 10:21 AM
Probbaly
YummyPancakes in reply to =SMART=Jul 15, 2008. 3:57 PM
Or you're just nerdier than you think you are 8-)
gmjhowe says: Jun 30, 2008. 4:37 AM
nice, good job!
=SMART= says: Jun 29, 2008. 9:32 AM
I added this to the Papercraft Group too :D
Kiteman (author) in reply to =SMART=Jun 29, 2008. 10:14 AM
Oh? That's fine.
=SMART= says: Jun 29, 2008. 3:52 AM
Haha very nice, mines printing now :P Looks cool, and good pictures
Kiteman (author) in reply to =SMART=Jun 29, 2008. 4:01 AM
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 says: Jun 28, 2008. 8:56 AM
*golf clap* Very nice!
Kiteman (author) in reply to LinuxH4x0rJun 28, 2008. 12:18 PM
OK, now I know what a golf clap is, what is your problem with the 'ible?
LinuxH4x0r in reply to KitemanJun 28, 2008. 1:08 PM
No problem. I didn't know it was sarcastic. I liked it. I have no clue why. tired. go away. stop asking hard questions
Kiteman (author) in reply to LinuxH4x0rJun 28, 2008. 9:15 AM
Thank you, but what is a "golf clap", anyway?
Lithium Rain in reply to KitemanJun 28, 2008. 1:30 PM
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) in reply to Lithium RainJun 28, 2008. 1:44 PM
Oh! Jake Tobak's link said it was sarcastic, like a slow clap.

Sorry Linux.

(Climbs down off high horse.)
Lithium Rain in reply to KitemanJun 28, 2008. 2:07 PM
No, just polite and quiet-kinda like the British. Ducks head
=SMART= in reply to Lithium RainJun 29, 2008. 3:53 AM
WWWWWHHHHAHAAATTTTTTTT!?!?!?!?!?!? lol
JakeTobak in reply to KitemanJun 28, 2008. 9:55 AM
smheath says: Jun 28, 2008. 10:32 AM
You mean 9" x 1.25".
Kiteman (author) in reply to smheathJun 28, 2008. 12:14 PM
Oops, thanks for catching that!
Kiteman (author) in reply to KitemanJun 28, 2008. 12:16 PM
Fixed.
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