In differential topology, Smale's paradox states that it is possible to turn a sphere inside out in 3D-space with possible self-intersections but without creating any crease, a process often called sphere eversion, (i.e.to turn a sphere inside out).
Here's an interesting video of how it's possible to turn a sphere inside out, it's 20 minutes long but fun if you're in to topology, geometry or simply just curious.
