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 
rectangle consisting
of two halves of a width 2 square (which are rejoined when edges are connected) separated
by a 
square (Stewart 1997). 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 (Stewart 1997).
