Phizz Unit Origami: Torus
by Chaunce Dolan on Thursday, September 2nd, 2010
The Phizz unit torus happens to be one of the most stunning, yet challenging, modular origami pieces I have done yet. It has 360 total units and took me a few months to complete. Once complete though, the design itself is surprisingly rigid and is really fun to look at and hold.
There are a few reasons why it took so long to complete. First, the paper I used was old velum. While giving it a vintage look, the paper was also more fragile and a lot of pieces tore resulting in having to fold more units than necessary. Second, I had no diagram to complete this. I only had a small picture that I found while browsing the Web. I had mapped the design out in my head as well as on paper a few different times, each time realizing that my mapping was wrong. I finally figured it out after 5 different iterations. The third reason it took so long was due to frustration. Rebuilding it over and over forced me to stop and start over a bunch of times which really taxed my patience.
Even though it was the most difficult modular piece I have done yet, it still inspires me to build another one with different paper and a fun color design.
Phizz Unit Diagram
Torus Directions
To complete this design, I have a few of suggestions that will help the process:
- Use the torus diagram to the right as a map on how to build each shape and its surrounding shapes
- The numbers in the diagram tell how many sides each shape has not how many to build
- Build the next shape onto the one previously built
- Keep connecting shapes until you build a ring
- To build the other half, start replicating the wireframe on the inner edge of the first ring
- Build shapes until it connects to the outer side, creating the first ring of the torus
- Keep building more connecting shapes, the rest builds itself from there
- Be patient, it’s awesome when it’s done
Close Ups
Hi,
Ive just finished my torus like yours (following your very useful diagram), but I used 288 Phizz Units instead of your 360 and got 24 Pentagons and 24 Heptagons (like yours i believe).
Just wondering if you might have made an error when you counted how many Phizz units you used?
Thanks.
I had done it about a year before writing this post and I knew it was around 300. I also had to replace a lot as it was made out of old velum which was really brittle.
Ah, thanks for your help on this matter.
I’ve made about 1 3rd and only need to make 70 units (I made the first 180 on 1 weekend). I think I’ve finally understood the matter.
I’ve finally made it. Shame that out of the three colours I used only yellow is strong enough to not fall apart at the lightest touch.
It would be great to see a pic of yours if you can. What was the final count of modules that you used?
This is beautiful
Thank you for sharing the diagram
360 precisely.
Hi,
A quick query – when you talk about using the wireframe diagram to build ‘a half’ first , do you mean that the ‘half’ resembles a shape like you would get if you cut a bagel in half to toast it? then the second stage of the build is essentially to gradually add the other half on top? I’m unsure whether the hexagons on the bottom of the wireframe diagram above are meant to wrap straight around to the hexagons on the top of the wireframe diagram or not (I don’t think this is the case, but just wanted to check)
Thanks!
Thanks
You are correct with the bagel analogy. I hadn’t even though about someone building the half in the other way. Thanks for pointing that out
Thanks! – finished it this afternoon. It is an awesome structure, really strong. Worked out a few tricks in the process to speed up the build/make the phizz units super uniform (which also really helped the build) – thanks again
Glad to hear that it came out well for you. It happens to be my favorite piece. I was really surprised when I had finished building it how strong it was too. How long did it take you to complete it?
Once I had made all of the units the build was surprisingly quick – maybe 10-12 hours – I also used vellum, it gives a nice effect and doesn’t pick up dirt like post-it notes would. Mine was new with a marbled pattern, so I had no problems with splitting etc. i can imagine that would be pretty frustrating
I spent probably longer on the building of the actual units, but worked out a couple of ways to make the manufacturing of them more efficient given I wasn’t able to source vellum squares.
1. I took an A4-sized template in powerpoint, then divided it into 12 70mmx70mm squares, and each of those squares into 4 rectangles each measuring 70mm/3 x 70mm. Powerpoint is brilliant for this as you can dial in the exact dimensions and go from there, rather than using a ruler etc to get the same effect. There is a bit of shifting of the grid pattern needed to be done on spare paper as the printer isn’t necessarily exactly aligned with the template, but its pretty easy to get the pattern directly on there accurately. Then I loaded the print cassette with 30 A4 sheets of marbled vellum and printed the grid directly onto the vellum. If you use a really light grey line, you can’t see it on the vellum unless you are really, really look for it but it serves the purpose for stage 2. (I couldn’t get vellum squares so this was a workaround)
2. Then I scored each printed line on each vellum sheet with a scalpel – each 4th line I cut right through, and then two vertical cuts leave you with 12 vellum squares scored across each of the first stage folds. The good thing I found about doing it this way was that the pieces were very uniform, and folding them was a lot easier because if the scoring has just the right amount of pressure then as you bend the vellum a sharp crease forms right across the edge.
3. Once I’d got the folded rectangles they got put in the pages of a big book with a load of other books to make sure they were all folded down nice and tight
4. Then I formed the phizz units and again replaced them between the pages of the books as I made them to again lock in the creases.
5. I then found that the build was pretty easy, because the scoring left the creases so sharp, and the pieces were so uniform, that they tended to want to regain their form when they were in position.
All in all I reckon the 360 units maybe took me 20 hours so maybe 35 hours for the whole thing.
The tips you had above on the build were very useful. There is a timelapse build of a torus on youtube but the person doing it on there builds it differently, almost like he is winding the shapes around a torus, rather than building one half and then the other. That was why I was getting confused on the build process, I preferred your method.
Photos of mine on http://www.flickr.com/photos/91049302@N00/sets/72157627369539467/with/6065191561/
there’s another 3-D piece I did from paper on there that you might find interesting. Not origami but still a bit of planning involved and its fun to look at.
I enjoy so much doing modular origami! Thank you for including the instructions and details… Without further delay, I will start folding!
I successfully completed the first half-although I used more than 1/2 of the units to complete it, ironically-and having trouble with making the second. Should there be two different rings of heptagons and pentagons?
That is correct, you will use more than half of the units because the inner and outer edges share edges with the other half.
Start with the one half you have built then continue to build on to the inner edges repeating the pattern and thus creating the other half.
I finished it last night, but only used 288. It looks fine- I used 24 heptagons and pentagons, but when recreating the pattern, I left one row of hexagons (the row in which they are directly adjacent to each other- at the very bottom on your diagram). Do you know of any other complex origami creations (preferably modular) that are of higher level or the same as the torus?
I am not aware of any others. I created this design from a really bad picture that someone had posted in a forum. I haven’t seen any other complex designs like this. Although, I have though of creating some I haven’t gotten around to doing that yet.
If you ever do I’d love to see your diagrams!