I was reading a book about Mobius band and I read about turning a sphere inside out, without making a hole in it. Though this appears impossible, it is actual possible when you follow some rules. Looking over the web I found a very good movie showing and explaining how it’s done. For those interested in mathematic curiosities, this 20 minutes video worth watching.
http://video.google.com/videoplay?docid=-6626464599825291409