Geometric Model of A. Harry Wheeler, Immersion of a Moebius Band (One-Sided Polyhedron)

Wheeler, Albert Harry · ca 1940

Taking a long, thin rectangle and attaching the short sides with a half-twist produces a surface called a Moebius band. It has neither inside nor outside (that is to say, it is non-orientable), and has only one boundary component—tracing starting from one point on the edge takes one around both long edges of the rectangle. For most closed polyhedra, the Euler characteristic of the polyhedron, which equals the number of vertices, minus the number of edges, plus the number of faces the number, is 2. For a Moebius band, it is 0.