Origami Tessellations

Hello All,

Here are some newly created diagrams for perhaps my only “easy” origami model, a simple fan made from an A4-sized sheet of paper. I’m quite fond of this little fan, it uses a unique method of radial pleating to create a very useable result!

As with all of my diagrams, these are released under a Creative Commons BY-NC-SA 3.0 License, which allows you to share them and re-use them with appropriate attribution and sharing. (Find out more on Creative Commons licenses)

Download the PDF diagrams here, and feel free to share them with others!

Additionally, if you want to take this model up a notch in style and complexity, divide the paper into 16ths instead of 8ths, and it will make a more pleasing curved fan and a skinnier handle as well. For more advanced folders only!

I hope you enjoy this model as much as I do.

Eric

This post comes from my partner, Ioana Stoian, and is one of the 16 models we’ve been working on (and that I’ve been diagramming) for her upcoming book, “Origami for All: Elegant Designs from Simple Folds“, to be published sometime in the next few months. I really enjoy the models she creates, as they are all “pureland” origami, although just by coincidence… very elegant, simple models, which she folds out of her handmade paper. Our house is filled with these creations and I feel like my tessellation work is now outnumbered!

From her website:

• Seeing as Valentine’s day is just around the corner, I can’t think of a better time to share my simple heart origami model with you. It should be rather easy to fold even if you have no paperfolding experience. Just take your time and follow the diagrams carefully.The simple heart is one of the models that will be included in my upcoming origami book, which should be available for purchase in the next few months. Please feel free to send me your comments. You can find out more information about the book on its website: www.origamiforall.com.
  Happy Valentine’s Day!

  Download: Ioana Stoian – Simple Heart PDF

  

I participate in several web forums on origami, and recently in one of them someone asked questions about tips for folding square & triangular grids. Being somewhat of a specialist on the subject, I posted these thoughts:

• Hi,well, nobody necessarily likes pre-creasing grids, including me. So you’re not alone there. However, I think it’s important to think of it more as a meditative process, and instead of as a chore; it’s a task which you must do to fold a model, and it is, to some extent, an integral part of the model, so it’s worth taking the time to do it well and not rush through it to “get it out of the way”.As others have mentioned to you, if things are getting too small, you need to use larger paper. Also, and perhaps equally as relevant, you should be using better paper… higher quality paper will yield much better results from the same folding process, and is much more likely to give you a better looking result while also giving you less headache while folding. I highly recommend stronger natural papers made from fibers like mulberry or abaca, they work well; or commercial papers like elephant hide. (Japanese/Thai/etc “washi” paper is usually from some kind of mulberry fiber and are pretty inexpensive.)As far as precreasing goes, my personal method is the following:
  • * fold the paper in half
  • * reverse the fold
  • * fold each section in half, to the center (like this: VV)
  • * reverse each new fold
  • * fold each new section in half again (like this: VVVV)
  • * reverse each new fold
  • * repeat, repeat, repeat until finished

  Typically I will do one direction until 1/8ths, then the others, just because the paper will deform if you fold all of 1/32 or 1/64 in one direction and not any others. It’s good to spread the folding around, so I’ll usually fold to 1/8, all the other directions, then continue to 1/16, then the same for the other directions, then to 1/32 etc.

  Reversing the folds is important, as it gives a neutral fold orientation to each crease, and makes it infinitely easier to collapse the model later when doing the final folding. You certainly don’t have to do this, but not doing it often leads to big headaches, and it’s something I really recommend to do. It’s more important also with stronger paper which retains more “fold memory” and crease orientation; if you’re using flimsy cheap origami paper, then it’s not as important because too much folding will destroy your paper. (to put it in context, a strong sheet of washi can withstand thousands of back-and-forth foldings and creasings along the same line before it starts to separate, whereas a wood-pulp sheet of origami paper will only last about 4 times when I fold it…)

  Also, doing the “dividing in half” routine rather than accordion-folding, zig zagging, fold-overs, etc is good, because the dividing routine reduces errors in your folding by dividing them into lesser errors, whereas the other folding methods magnify the errors with each continued fold- so your edge creases will really look horrible, things won’t match up, and so on. Mathematically speaking it’s much, much better to divide the paper as you go along. I stress this in all my classes as I feel it’s quite important.

  I am a slow folder, so I don’t make grids very quickly; a 1m x 70cm sheet of elephant hide takes me several hours to get to a 32-division triangular grid. dividing that further into 64 takes the same amount of time again, as it’s the same number of creases to be made! bear that in mind, the step between 32 and 64 is a doubling 🙂 I always seem to forget this fact.

  To fold a small sheet of paper though, like an A4 sheet (or american letter size paper) into 32 triangular divisions… I think probably an hour? I don’t really measure time while folding, I try to sort of trance out and get into the rhythm of folding and not think about anything. I find it very enjoyable this way.

  Recently I had to fold a lot of grids, making a big piece- I divided 42 one meter sheets into squares about 1cm in size. it took me literally a month to do this, and my hands hated it! many thousands of pleats. I find that I like to work at larger scales, as they are more interesting visually; I can’t really fold pleats any smaller than about 5mm in size, below that the paper just turns to mush. I prefer to fold paper when it’s got some springiness left in it, don’t you? So I prefer to have pleats about 1cm or so, given a choice. This requires larger paper but as stated above I prefer this anyway. I used to fold on the bus, and that required working with 15cm/6inch paper, and that was fine for starting out but very very limiting as time went on. Help yourself out and use bigger paper, it will save you a lot of frustration!

  linked below are two videos of me pre-creasing a square grid and a triangular grid, if you’d like to see the technique I use (bear in mind these are thicker papers, so they required a lot more force than is normally needed.)

  Hopefully there’s some information in here that you will find useful or at least informative! Best of luck and happy folding!

I’ve also created this PDF document to better explain how to fold these grids, and my personal methods for achieving best results.

How-To: Best Methods for Precreasing Square Grids

I also included links to the following two YouTube videos of mine, showing some pre-creasing videos (speeded up, of course:)

http://www.youtube.com/watch?v=Q3ddAYOdUrQ

http://www.youtube.com/watch?v=Y05JUFZ0CMM

Hopefully all of this will help those of you looking for some more information about pre-creasing techniques!

-Eric