The Origami Forum

Here are some examples:

box pleating
hex pleating
uniaxial box pleating
wetfolding
dry/wet folding
crumpling
tesselating
modular folding
curved crease tension folding
quilling


Those are all pretty broad innovations, but try to come up with something that is a combination of existing techniques or a moderately different deviation from an existing method (such as a new style of crumpling, or a new approach to box pleating).

And even if you haven't fully fleshed it out, feel free to share it here. That way folks could provide feedback or collaborate.

Here is an idea I had: There should be 3D symmetric tessellations from a single sheet of paper. I'm not talking about tessellations that pop out of the page. I'm talking about tessellations that tessellate in all three dimensions. For example: a 3D checkerboard of cubes, or a menger sponge.
It should be designed in such a way that by using a larger piece of paper (or folding smaller), the model could be always be made with more units in all directions.

I haven't really figure out the math to design the above, and I'm most likely not going to spend the time in order to do so, but I wanted to put the idea out there.

A figure such as a Menger Sponge would be practically impossible due to the limited amount of edge on the paper. Same with a 3D checkerboard (assuming you mean cubes connected at the corners) because the total amount of angles adds up to 540 degrees, and paper only allows for a total of 360. That doesn't mean there aren't other tessellations or fractals (such as a Koch Snowflake or a Penrose Triangle) that can't be folded.
However, I've experimented a little with folding "modular" figures from one square (i.e. the Enigma Cube)--haven't had much luck though. But I'm pretty sure it wouldn't be that difficult if one set his/her mind to it.

Hmm, would the 3D tessellation thing work if you attached six squares together to form a paper cube? Who wants to try origami with a 3D starting shape?

As for new «folding style», I personally find multi-piece representational origami to be quite interesting. It gives new options for colors and details.
As an example, see «Prince Katamari» in my gallery: the face is implemented in the head. Another one would be Beth Jonhson's sheep: it'd be much less elegant and efficient if it were done with one sheet.
I wouldn't classify characters holding stuff in this category, however. That's just too easy and boring to do.

A 3D starting shape is a great idea! Now I'm imagining taking a spherical piece of paper and folding a wrap-around tesselation onto it.

A figure such as a Menger Sponge would be practically impossible due to the limited amount of edge on the paper. Same with a 3D checkerboard (assuming you mean cubes connected at the corners) because the total amount of angles adds up to 540 degrees, and paper only allows for a total of 360. That doesn't mean there aren't other tessellations or fractals (such as a Koch Snowflake or a Penrose Triangle) that can't be folded.

Not sure I'm following the angle logic. I assume you are referring to a corner created by three intersecting planes? Couldn't you do it if there were multiple layers of paper? For example, I could make one such corner by pleating a paper such that it vertical perpendicular protrusions in this pattern: -I-I-


Then I would mountain fold book fold. The result would be three intersecting planes without using the edges of the paper.

Was that what you were referring to or were you referring to something else?

Actually, I think I just figured out the cubes connected at the corners. First you pleat the entire paper with a grid of perpendicular protrusions on one side (similar to repeating the window lattice in my house with windows....see the Flickr link in my signature). Then you fold the paper back and forth in a zigzag. This will result in a cube of cubes connected at the corners. It could be expanded to an infinite number of cubes.

(Note, I left out some steps on making the top and bottom of the paper spacex correctly when doing the zigzag. That is solved leaving some strips without the vertical protrusions in the original grid.)

i gave the idea, so I had to try it out. Yes, tessellations can be done from a cube as a starting shape! Unfortunately, I don't think it can take diagonal folds really well (so triangle tess won't work properly...)



I merely wanted to test this out. I don't think I will be developping this technique, as it is a pain to make the cube and fold it!

I could see a menger sponge being folded from this technique, but you wouldn't be able to hollow the center out.

To clarify, I realized Baltorigamist and I meant different things by cubes connected at the corners. I was referring to cubes close-packed so that they fill 100% of the space (the corner of a cube would intersect with 7 other cubes....if you remove half the cubes' imaginary filling it is a checkerboard but none of the faces change...therefore it is the same shape). I believe Baltorigamist was referring to cubes connected such that each corner intersects with the corner of only one other cube and there are lots of spaces between them.

Sunburst wrote: triangle tess won't work properly...

How about on an octahedron or icosahedron?
(Of course, it might be easier to experiment th a tetrahedron first...)

You know what, Baltorigamist? I think it works as long as the pleats are perpendicular to the edges. Looks like I'll be forced to try it out on a tetrahedron

I'm interested in seeing your result. Good luck!
I think the grid itself will have to be rotated about 30deg, such that the edges of the tetrahedron bisect each grid triangle. Otherwise the pleats wouldn't be perpendicular.

Summary: it works!
The grid is indeed 30° rotated.
Tetrahedras are more fun to fold than cubes. I may do 3D diagrams for the one on the left and send it to as many conventino books as I can as a joke

Sunburst

Please explain how you do the cube or the tetrahedron. Do you take 6 pieces of paper (for the cube) and glue them together?

Do not worry Brimstone, I will probably draw instructions soon for this simple method I've devised for the tetrahedra and post them. It is from an equilateral triangle taped on some areas. The cube is more annoying to make: I took two 1:3 rectangles and taped them together.

In other news, more tetrahedra tests!

New type of fold: vertex twist



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