Really. It's called a Mobius Strip.
A normal piece of paper has two sides. You can prove that by coloring it two different colors. Also, if you want to trace a line around it you have to go over an edge - another proof that it has two sides. But just twist it and rejoin it, you have an object with one side - not two. That's a Mobius strip. Like this:
Very weird. Not only can't you color it two different colors but you can trace a line all the way around it without lifting the pencil. (Just imagine the yellow car towing a pencil.) Try that with a regular sheet of paper. How is it possible? Like I said, it has only one side!
Engineers often take advantage of this property when designing drive belts or conveyor belts. If you put a twist in the belt you double the surface area and so it wears out half as fast. Or, thinking of it another way, you don't have the problem of wear on one side or the other because there is only one side! In fact B.F. Goodrich Co. patented the Mobius Twist for conveyor belts.
Check it out for yourself with a strip of paper and some tape. Then make yourself a buck by betting a friend that you can make one side of a piece of paper disappear from the universe!