The mobius strip, also known as a lemniscate, is a unique shape having only one side and one edge. The shape was invented almost simultaneously by two German mathematicians in 1858. It became popular as a prop for magical parlor tricks in the late 19th century, and perhaps this is how Laban encountered it.
You can make one yourself by twisting a strip of paper and joining the ends. A normal band (think of a rubber band or a simple bracelet) has an inner surface and an outer surface and two edges. But the mobius strip has only one surface and one edge. That is, if you start tracing a line on the outer surface, your pencil will move to the inner surface and return to the outer surface without ever lifting the pen. Similarly, if you start running a finger along one edge and circuit the strip twice, you travel along both edges without interruption.
In other words, the outer becomes the inner and the inner becomes the outer.
Laban writes about lemniscates in Choreutics and even maps a couple in the kinesphere using direction symbols. Does Laban mean for this to be taken literally, as a spatial trace-form? Of is this a symbolic form? Find out more in the forthcoming MoveScape Center course, “Decoding Choreutics.”