The Möbius band (or Möbius Twist) was originally named for the German mathematician August F. Möbius in 1905.  It is a dynamic, three-dimensional, flat-sided circle which has only one surface — the outside turns to become the inside, which then twists to become the outside again.  

My version of this form incorporates a gentle angling which is very comfortable when worn on the hand.  I make my Möbius and split Möbius rings in two weights to suit a variety of tastes.