"the earth was a Möbius Strip"

Möbius Strip
Creative Commons Attribution Share AlikeMöbius Strip - Credit: David Benbennick
The Möbius Strip, also known as the Möbius band, is a sort of loop with a half-twist that has only one side, and can be travelled from one side to the other without crossing an edge, as would be necessary if the strip did not have the half-twist. Here are instructions to make your own.