I have been recently coming across several examples of origami influenced shapes and even whole projects in architecture. The complex level of thinking and preparation behind the final outcome is of a great interest to be studied.
Here is a video of Deployable/Transformable structures by Daniel Piker, with an almost (is difficult to read and understand if not familiar with complex origami folding) helpful diagram explaining the different folds of every structure.
Pay a visit to his blog if interested in this kind of forms (+)
“Some of my old experiments with deployable, transformable and bistable structures, auxetics and linkages. One day I might get back to developing some of these further, but until then I thought rather than let them sit and gather dust I’d put them up here, in case anyone else is interested. I’d be happy to share the folding/cutting patterns if you want to make your own.”
Daniel Piker

In addition, although the first video can probably have only a “skin” approach to real life architecture the next two videos make us think of moving-with a twisted mechanic aesthetic-components that could be easily applicable within a project.
What is interesting in those explorations is that the shapes are “rigidly foldable”, meaning there is no deformation of the faces while folding. The geometry and mathematical approach behind the final outcome is something I aim to analyse (as far as I am able to) in a few days time on another post.
Finally for now, there are some examples of a realistic spatial concepts deriving from origami structures
*(human size rigid origami installation* click here (+)

Hi Daniel,
my name is Gianluca Cicala and I am Professor at University of Catania. I am also President of CHISMATECH a start up focused on the development of our proprietary technology for production of auxetic composites.
We are interested, as start up, to investigate featured applications for our product. If you are interested and you can help us to find potential investor I can send you a presentation of our start up.
Regards