Diagrams for geometric folds

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gila o
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Post by gila o »

mleonard wrote:Your wish is my command...

Image

The light grey lines are for guidance only - they mark the centre of the square (obviously) and the quarter-points of two opposite sides. Begin by pinching the quarter points in order to locate the diagonal lines through the centre of the square.

I have thought about extending this pattern onto a long rectangle, so that it will wrap round on itself, but haven't actually done it yet.
Hello,
I am new in this forum.I hope to manage with the tecnical options.
I like to fold tessellation.here I have some pictures of my folds.
http://www.origamitips.com/gallery.php? ... =Oren+Gila
I've tried to fold the diagram that Mark designed.I understood how to fold the centrel diagonal lines ,but didn't know how to continue,so I've printed The crease pattern .Collapsing the model was quiet challanging.
Can anyone help me with the the other diagonal lines??
Thanks to Mark Leonard for the crease Pattern.
Gila.

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Brimstone
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Post by Brimstone »

Well I guess this is one of those models that have no specific method to do. Those are the bad news. The good news are that it is not very complicated to do. It seems terribly challenging but it is actualy just challenging.

Repeat what you did in the center on other places. I found that folding the waterbomb bases that are diagonal to the center piece make it easier. I know this instructions do not sound like good directions, but that's all you have to do (and all I have to offer). Do not try to collapse the whole thing at once. Work by areas (diagonal areas worked best for me). As you go by previous areas will unfold a little but they will keep some their shape. Once you have folded all of them try to "close" the whole thing and try keep it folded using the rest of your fingers. Try it and if you don't succeed keep on trying.
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I'll have to try my hand at this

Post by EricGjerde »

I'm not usually one for folding square-based tessellations, but I've seen Gila's versions of this and it's tempting me to give it a try. I know that John McKeever has a pile of these sorts of folds, so I suppose I ought to try them out and see what I get as a result.
gila o
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Post by gila o »

Brimstone wrote:Well I guess this is one of those models that have no specific method to do. Those are the bad news. The good news are that it is not very complicated to do. It seems terribly challenging but it is actualy just challenging.

Repeat what you did in the center on other places. I found that folding the waterbomb bases that are diagonal to the center piece make it easier. I know this instructions do not sound like good directions, but that's all you have to do (and all I have to offer). Do not try to collapse the whole thing at once. Work by areas (diagonal areas worked best for me). As you go by previous areas will unfold a little but they will keep some their shape. Once you have folded all of them try to "close" the whole thing and try keep it folded using the rest of your fingers. Try it and if you don't succeed keep on trying.
Thank's for the reply-Brimstone.
I think I didn't explain my Question well,collapsing the model was challenging but I succeded.I need help to mark the other diagonal lines after marking the middle one,in the stage of creasing before collapsing.
THank's anyway.If I will not understand Iwill continue to print the model.
Gila.
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Post by Brimstone »

gila o wrote:Thank's for the reply-Brimstone.
I think I didn't explain my Question well,collapsing the model was challenging but I succeded.I need help to mark the other diagonal lines after marking the middle one,in the stage of creasing before collapsing.
THank's anyway.If I will not understand Iwill continue to print the model.
Gila.
Sorry for doubting your skills. You mean knowing where to precrease the diagonals?

I'll tell you my method. If you take a close look at the cp and check the rows and columns of it, you will notice that the diagonals are separated 3 squares from the next one. So you can start by doing the central diagonals and then the four that revolve around the central one. From then on you can count 3 squares in all directions and you will know where to place the other diagonals.

I hope I understood your question this time.
gila o
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Post by gila o »

Brimstone wrote:
gila o wrote:Thank's for the reply-Brimstone.
I think I didn't explain my Question well,collapsing the model was challenging but I succeded.I need help to mark the other diagonal lines after marking the middle one,in the stage of creasing before collapsing.
THank's anyway.If I will not understand Iwill continue to print the model.
Gila.
Sorry for doubting your skills. You mean knowing where to precrease the diagonals?

I'll tell you my method. If you take a close look at the cp and check the rows and columns of it, you will notice that the diagonals are separated 3 squares from the next one. So you can start by doing the central diagonals and then the four that revolve around the central one. From then on you can count 3 squares in all directions and you will know where to place the other diagonals.

I hope I understood your question this time.
O.K -It's getting closer.If you still didn't give up trying to understand me so I meant -where to preacrease the long blue diagonals?
If you gave up :cry: thanks for your try untill now.
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Post by Brimstone »

I must be dumb

Closely look at the Cp. You will notice some clear gray marks. They are located at 1/4 from the lower right border. There is another one at 1/4 of the top left corner. If you join these two points you will get a diagonal. Repeat the process on the other side and you will get your second diagonal. From then on you just have to find the 1/2, 1/4, 1/8 etc of the diagonals.

If this wasn't what you were asking, come again.
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mleonard
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Post by mleonard »

I suppose I ought to try and explain this, since I drew the CP...

Once you've put the first two diagonals in place, there are lots of ways to divide the paper into a grid - just remember that all the lines have to be equidistant and meet each other at right angles. You can choose almost any arbitrary reference point, put a line through it parallel to your first line, and continue from there. Depending on what reference you choose, you will wind up with a larger or smaller number of squares in the final grid.

The reference point I used in the CP above is found by bringing the corner of the square to meet the first line (which we may as well call the centre line, since it runs through the centre of the square). Do this with all 4 corners, and then divide into halves and then quarters.

I'm pretty sure that John uses this method to arrive at the one in his picture (link somewhere at the start of this thread...) - it makes the final model quite a nice 6x6 tessellation, without too much wasted paper. Unfortunately, it means that the intersection points at the edge of the grid don't coincide with the edges of the paper, so you get a tiny left-over triangle each time.
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Post by JMcK »

I've just posted a crease pattern for the Dome of 36 Squares to my Yahoo! photo album.

Crease pattern
Finished model

It's pretty similar to Mark's pattern, except that I have a margin of extra paper around the 36 squares where the tessellation stops and you just get alternating parallel creases instead. (This is to avoid partial squares being formed at the edges; I think it makes the model look a bit tidier, but it's just a matter of taste.)

The crease pattern only shows the folds that are used in the final collapse, which is why a lot of the creases don't go the whole way across the paper. (When I'm precreasing I fold the whole way across.)
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JMcK
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Post by JMcK »

I started folding these waterbomb-type tessellations because of a posting that Kenneth Kawamura made to the origami mailing list back in 2001.

You can read his post here: Link

My only innovation was to rotate the folded grid, thus allowing the squares to line up with the edges of the paper.

Kenneth said in a later posting that these tessellations were influenced by Ron Resch. If you scroll down to the bottom of The Geometry Junkyard's origami section you can find a few Resch links, including a crease pattern for a triangular waterbomb tessellation. (And the world's largest easter egg!)
The Geometry Junkyard: Origami
gila o
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Post by gila o »

Thank's all of you for the explanation.I think I found(at last...)the solution for my question.After creasing the central diagonal line who cross the middle of the square(by using the quarter of the edge) I didn't know where to crease the parallel line.Mark said I can put it in any distance that I choose as long that it will be parallel.I didn't know how to do it without ruler.Acording to John c.p I can use the 1/3 point and than to devide to 6.
If I am wrong I give up.Printing is easier although less Fun!
Mean while I have practice my english,and have much to read in John link to the o list .I have to find also the c.p of the triangulal waterbomb tessellation.
THank's again,
Gila.
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Post by Brimstone »

Why not trying exact divisions of those diagonals? I mean take the point of that diagonal that is farther from the center and fold it to the center (by doing this you will have 1/2, continue creasing the halves of creases you find until they are about the size you want).

A model from a printed Cp would not be as cool (pure or whatever you want to call it) as one done just by folding.
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mleonard
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Post by mleonard »

JMcK wrote:I've just posted a crease pattern for the Dome of 36 Squares to my Yahoo! photo album.

Crease pattern
Finished model

It's pretty similar to Mark's pattern, except that I have a margin of extra paper around the 36 squares where the tessellation stops and you just get alternating parallel creases instead.
Aah... now I understand what you did with the edges.

There's also an interesting bit of maths hidden in this crease pattern. If you start as with my CP by marking the quarter points and fold the first diagonal ("centre line"), you will find that the points where the edges of the paper meet each other are the one-third points.
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Post by gila o »

After few days that our c driver has crashed and we had to reconstruct almost all the information we had -here is The Triangular Waterbomb tesselation that I Iv'e folded.
http://www.flickr.com/photos/87477835@N00/31685638/
This time I have no question about creasing it.I had enough With the last model....
Thank's to John McKeever for turning me to the crease pattern of Ron Resch.
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Post by mleonard »

I've been playing around with these things a bit more, and I've realised that you don't have to stick to squares, or indeed triangles. If you use 2x1 rectangles as the basic element, you can get a "brick wall" pattern or a "herringbone" pattern:

Image
Image

(I have shaded the "bricks" for clarity)

Or if you mix single squares with 2x2 squares, you can get this:

Image

The first 2 patterns don't "twist", so the starting grid should line up with the edges of the square. The last pattern should really be at a slope of 4 to 1, but I haven't worked out a neat way of doing this yet.

All this suggests to me that any tessellation made up of squares and rectangles of different sizes can be turned into a crease pattern of this kind. I wouldn't know how to go about proving this, though.
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