Folding and Cutting: an Intriguing Diversion.

The Economist recently mentioned applications of origami to Mathematics and Engineering.

The inspired a web search that yielded this site that indicates ways of getting interesting shapes by folding paper and then making a single cut. Apparently it is in principle possible to use this method to obtain any shape or set of shapes, provided that the boundaries are made of straight lines. The star is easy, but I had quite a struggle  folding for the swan.

There's also  a course of lectures here.