A Klein bottle dissection into unequal squares can be obtained by gluing the edge of a Möbius strip dissection. Stewart (1997) asserted that all such dissections with six or fewer squares arose this way and that the seven- and eight-square cases were unknown. Morley (2014) refuted the first claim by exhibiting four-square dissections not obtained from a Möbius strip dissection. He also gave examples with seven and eight distinct squares, resolving the cases Stewart had described as unknown.
The Klein bottle dissections illustrated above are two of Morley's four-square examples, each using squares of sides 1, 2, 3, and 4.
The left-hand example has a rectangular fundamental
domain of dimensions 
, with one pair of opposite sides identified
in reverse orientation. The arrows indicate the identifications of opposite sides
(Morley 2014).
