sheet of square based pyramids

[farmgirljane]

Not sure that my title really explains what I am looking for so please look at this link -

http://blog.hostagenyc.com/2010/03/fash ... ant-garde/

I am wanting to achieve similair 3 d for an art project. I have been able to make some linked pyramids using hexagons, octogons, pentagrams but I have been told that it is possible to use a full sheet of paper/fabric etc to create this look in one piece but have been unable to find instructions.

Hoping some one can help - thanks[/url]

[garrasdecaiman]

it is not impossible but will be tremendously difficult since the paper is flat, and could be considered as having no curvature, to obtain the pyramids or any 3D shape you will have to "cut" or hide paper from the final shape, in some simple models these can be tiled to correspond with multiple volumetric subpeices (which works great in box pleating), but sometimes these leftovers do not correspond with each other leaving more and more exess which becomes unmanageable very promptly or requires huge amounts of paper.

I myself have not come upon a satisfactory pyramid tiling, especially in a triangular fashion (there are some egyptian great giza pyramids in box pleating) but the angular shape forces an angular reduction of paper which in turn consumes a great amount of paper before the paper lies flat again.

Anyway I do not believe it to be impossible, but just technically very difficult to obtain a large amount of pyramids tiled in single paper origami.
the graduation of the pyramids in the picture would just add a whole level of complexity but could be managed if you allow the final design to be curved and not lie in a plane.
X

[HankSimon]

Not positive where you want to end up, but:

1. On p. 104 of Genuine Origami by Jun Maekawa, there is an infinite folding Pyramid.

2. On p. 194 ff of ODS by Robert Lang , there is Pleated Textures, including scales...

- Hank Simon

[ahudson]

Something like the center part of this, maybe?



It's not that hard actually, and you can use any triangle you want for the sides. The grid lines are quite visible in the photo, you should be able to figure it out. All of those use the same corner intersection, just different areas on top.