[old] Umulius Rectangulum (Thoki Yenn): Instructions

Adams, Sara
Difficulty Level: 
Low intermediate
Model type: 
6 units
Paper ratio: 
1 : sqrt(2) (A-sized)

Origami "Umulius Rectangulum" by Thoki Yenn

Sadly, Thoki Yenn passed away in 2004. His son, Thomas S√łndergard, was kind enough to give me permission for making this video available to you.

Update: This structure has the name "Borromean Rings": three rings linked in a way that by removing any one ring the other two aren't linked anymore, either.


is there a specific size the paper should be because ive been just dividing a square in half to get a rectangle


I do mention it at the beginning of the video, but I guess not everyone knows what A-sized paper is. Each module needs a paper that's half an A-sized paper. So if you use normal printing paper from Europe and divide it lengthwise, you'll be fine. In the US and Canada standard printing paper is letter-sized. The instructions in the video do assume you're using A-sized paper, although other rectangles can be used accordingly.
If you don't have A-sized paper or don't know what I'm talking about, try 6 sheets sized 3in by 8.485in, or 74mm by 210mm. Hope this helps.

I just found a method to make a square paper in an a4 format.
The diagrams are at origami.com

Hi Sara! I'm just here to say that this site really is helping me improve my origami skills. I'm currently in Korea and I bought some origami paper. It's about the size of the paper you used in "Can Love Be Squashed?" So, I am wondering, instead of going through all that fuss, can I just use whatever thin piece of paper like yours? Not exact, but close. Because, I just think that cutting my origami paper in half is better.

Please reply!:)

Sorry, a sheet of 2 by 1 paper (half a square) won't do. You can use normal printing paper (A4), and cut that in half lengthwise - or in quarters crosswise. As far as I can see, Korea uses A4 sized printing paper, so it should be easy for you to get that sized paper, and it's usually sold in many colours. By the way, normal printing paper should be thin enough to work well for this model, but try not to go for thicker versions. Hope this helps,

-- Sara

Thank you so much for posting this video! Your video was very easy to understand, and I had finished my model in no time at all. This model is very neat the way the different pieces hold each other together. Thanks again!

hi sara
i have been stuggling with this diagram without knowing how to collpase it. your video did the mracle. i have done it . thANKS A LOT . keep going best wishes have a woderful day

This video seems simple but I still didn't start this umulius rectangulum becase I had a doubt. Was the paper size you mentioned A4 or A-size??? I had this ddoubt because you mentioned it A4 in the video but in the paper ratio coloumn it was given A-sized. Please clear this doubt of mine by replying.

Well, A4 paper is A-sized paper with a length of about 29.7cm and width of about 21cm. But you can vary the length/width of paper. Basically, you can use any paper with a ratio of 1 by square root of 2 - which is what I call A-sized. For this model you indeed have to cut an A-sized paper in half lengthwise, so the ratio will be 1 by 2*sqrt(2) - but that's included in the video.

Hope this helps,

-- Sara

I thanf you. MUST APPRECIATE THE EFFORT!!! I made one like yours.I have one more doubt. where do you get your coloured papers? I don't have any shos nearby that sels coloured paper. Should I PUT EXTRA EFFORT AND PAINT THE PAPER MYSELF??? I would be glad if you would clear this doubt of mine too!!!

For this model you can simply use coloured printing paper. You should be able to get that in just about any stationary store.

Hey Sara!
I just want to share something funny regarding this model that I folded and my friends.
I was showing this to some of my friends:
Friend: "Wow, thats cool, but how'd you get the rings together? It's impossible the way they are set up isn't it?"
Me:"......."*pulls rings apart slightly*
Friend: "WOW!!!!! Thats cool man!!"
Are my friends stupid?
Nice Model.

No, they're not stupid. It's exactly what the model was designed for. That in the first moment you ask yourself how that is ever possible. And your friend appreciated it for its nice, hidden locking. I'd say he's smart for that. I know that some would respond that it's just fake and be disappointed. That'd probably be the less smart answer, as clearly there has to be a trick for it to work. :)

-- Sara

Thanks for your opinion!

So do i just cut a sheet of printer paper in half?

If it's A4 paper (which is used basically everywhere except for the US and Canada), then - yes, just cut a sheet of printer paper in half.

-- Sara

This was great! I was not coordinated enough to get the fifths accurately. So I marked fifths on the sides, scored the line and the long folds went much easier for me. Although, I thought the constructing of the fifths was mathematically interesting, my folding was not sufficiently precist. Thanks for this video.

Sara? I was just wondering... For this model you use A4 sheets of paper and cut that in half... Is that the same ratio as a A sized paper? I live in the U.S., so... yah.. Thanks!

First an answer to your question: Yes, A4 paper is A-sized.

Now a bit more:
The wonderful property A-sized paper has is that if you cut the long side in half each half will again have that aspect ratio. Cutting an A4-paper in half results in 2 A5 sheets, cutting an A5 in half results in two A6 sheets (about postcard size). That's why I usually talk about A-sized. In other words, I mean paper with a ratio of 1 by square root of 2.

-- Sara

Oh... Okay, thanks1 yah, I was just looking at the paper ratio and you A4, but it said A-sized, but now i get it, so THANKS!

Thanks for uploading this video!
I really loved the finished model (:
- You're awesome!

Hi Sara.

I tried the Umulius Rectangulum today... and I've done a few others from your instructional videos. You're very good - thank you for posting the viedos. On my first try I was able to complete this project and I thought it came out pretty good. In order to get the aspect ratio of the A4 paper (the length divided by the width is 1.4142), I cut a U.S. standard 8-1/2 x 11 inch paper to 7.7782 x 11 inches... i.e. slightly more than 7-3/4 x 11 inches. It worked nicely. Thanks again, I can't wait to try some more new ones!

hey can i use letter sized paper for the umulius rectangulum?

You can use letter-sized paper, but the instructions will be slightly different (although not by much). In essence, the areas that will overlap when joining two modules will be slightly shorter with letter-sized paper. I fear I haven't worked out the precise sequence that will be necessary, but it shouldn't be too hard. Concentrate on the amount of paper that's between the center of the paper and the creases that form the angles of the "pipe", rather than the distance from the edge of the paper and the creases that form the angles.

-- Sara

You could probably use letter sized paper, because it is very close to A4 sized paper.

Well, given that I posted that video about 3 years ago... you'd think I'd improve in 3 years of practicing. ;)

-- Sara

I LOVE YOU SARA MARRY ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!thanks for all the origami stuff

can you just cut a printer paper in half divide that into fith and you get the picture. but if you don't anyways.

That depends on what the format of the printer paper is. In the US and Canada it's usually letter, everywhere else it's A4. With A4 it works, with letter the folding sequence will have to be slightly different. However, then you can cut the paper to the right size and still follow the video. Check: http://erikdemaine.o...

Ummm.... What if I have some great origami paper that I think would go good with this model but it is in square format. Can I cut one third off and get the same length:width ratio? And If it is easier for you can you tell me the length:width ratio of the 1/2 A4 piece?


Thanks, That was easier than I thought it would be!!!

it's a really nice model and you demonstrated how to fold it wonderfuly :)

I am folding this modle with origami paper that I cut to the right ratio but I dont know which side i should start with facing up.
Please help!!!!!

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