You may wonder what the two have to do with each other.
Short answer: Dr. Robert Lang.

I read an article recently in Smithsonian Magazine about Robert Lang, a laser physicst who has worked in NASA's Jet Propulsion lab, and has authored 40 patents and 80 publications He has been an origami buff since childhood. He has mastered the art of making mind-numbingly complex folds based on complex computation of geometric shapes using math.

Now, how does this connect to the space telescope?

Lang has also consulted with engineers at California's Lawrence Livermore National Laboratory on a new generation space-based telescope dubbed Eyeglass. The goal is to put huge telescopes—up to 328 feet in diameter—into orbit for purposes that include the viewing of planets outside our solar system. Getting such a behemoth into space poses a problem because the hold of the space shuttle measures a slim 15 feet in diameter. Lang devised a folding pattern for a 16-foot-diameter prototype that can be folded for transport, then unfurled like a flower coming into bloom once in space.

Also, see a related New Yorker article.