Möbius Scarf

A warm scarf, formed into a Möbius strip. Like every Möbius strip it has only one side: put your finger anywhere on it, draw a line, and you'll cover every surface without ever lifting your finger.

The zipper is there for the other famous property. Cut a Möbius strip down the middle and you don't get two halves, you get one much longer loop. So when the scarf isn't quite long enough to coil around your neck the way you want, unzip it and it's twice as long. It is also, underneath all that, a scarf: a study of Finnish military recruits found that wearing one made them 2.1 times less likely to get frostbite on their ears.