I wonder if the geometry of crinkled aluminum foil has been studied?
The above is a photo of foil I flattened to reuse. It might be described as a partition into nearly-uncreased polygons, each polygon of not too many sides, and arranged in a rather un-Voronoi like pattern. It superficially resembles a rugged mountain terrain seen from a great height.
I searched a bit for some mathematical analysis of this pattern without luck. Has anyone seen such an analysis? There might be some interesting mathematics here...
Here is Fig.1 from the PNAS article that jc identified, "Three-dimensional structure of a sheet crumpled into a ball," by Anne Dominique Cambou and Narayanan Menon,
slices through an equatorial plane of three crumpled spheres: