Tiling of a Möbius strip can be performed immediately by carrying over a tiling of a rectangle with the same two-sided surface area. However, additional tilings are possible by cutting tiles across glued edges. An example of such a tiling is the strip constructed from a 5×1 rectangle consisting of two halves of a width 2 square (which are rejoined when edges are connected) separated by a 1×1 square. Unfortunately, since the long top and bottom edges must be glued together, this example is not constructible out of paper. It also suffers from having the unit square share a boundary with itself. In 1993, S. J. Chapman found a tiling free of the latter defect (although still suffering from the former) which can be constructed using five squares. No similar tiling is possible using fewer tiles.

cylinder dissection | Möbius strip | perfect square dissection | torus dissection