Below is a Moebius Strip (a a one sided surface in 3-space) that exists in virtual reality (vrml). Click at any point in the vrml window on your left mouse button to change your viewpoint.

Click on the right mousebutton for a menu that allows many options such as changing the colors and spining the strip around. I particularly recommend the "navigation" submenu that allows switching between spinning motion, walking motion, fixed point motion, and sliding motion. I'll let you figure out the rest on your own...

Don't try to cross an edge, because it won't get ya anywhere.