The traditional Japanese origami crane is such an unusual shape, it makes one wonder why whoever first folded decided on calling it a crane, and also, why they gave it that particular shape.
Well, now we know the answer: it's shaped that way because that's its skeleton, as the photo below shows.
This fantastic model arrived in my inbox from 3D modeler extraordinaire Joaquin Baldwin (with a little help from Shapeways). You can see more of this design and more work by Joacquin on the Shapeways website.
There must be a special affinity between origami and 3D printing; there are some other pretty cool 3D things on the Shapeways site that have an origami connection.