PPT Slide
It is possible to draw a map of the world on a Moebius strip. The map must be drawn on both sides of the paper, inverting the image on one side. The resulting map, when one uses the Lambert cylindrical projection, with the poles at the edges of the strip, has the curious property that a pin pushed through the map exits at the antipodal point.
W. Tobler, & Kumler, M., 1986, “Three World Maps on a Moebius Strip”, Cartography and Geographic Information Systems, 18(4):275-276.