Any quadrilateral
tiles the plane. The tiling is formed by rotating
by 180° about the midpoints of its sides. The same process is then applied to the four new quadrilaterals, and so on.
Another approach is to use the parallelogram
formed by joining the midpoints of
's adjacent sides. Tile the plane with
in the obvious way. Translate the parts of
from the copies of
adjacent to
across
into the opposite copy of
. Then copy the three different patterns in the copies of
to form the same tiling as before.
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