ABSTRACT
Symmetry occurs all around us in faces and flowers and
snowflakes. The craftwork and art of most cultures in-
volves symmetry, often in the design of backgrounds,
borders, and focal points. Symmetry involves the rep-
etition of a basic pattern. The most common repe-
tition is called a translation, in which the basic pat-
tern moves along a line by a specific amount, leav-
ing the pattern unchanged. We can use translations
to classify symmetry patterns into three broad cate-
gories. A rosette pattern has at least one point that
is not moved by any of the symmetry transforma-
tions, and thus has no translations. Frieze patterns, fre-
quently used for fabric and paper borders, have trans-
lations in two directions along one line. Wallpaper
patterns have translations in each direction along two
intersecting lines.
