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Abstract
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In this work, a regular polygon with n sides is described by a periodic
(circular) sequence with period n. Each element of the sequence represents
a vertex of the polygon. Each symmetry of the polygon is the rotation of the
polygon around the center-point and/or flipping around a symmetry axis.
Here each symmetry is considered as a system that takes an input circular
sequence and generates a processed circular output sequence. The system
can be described by a permutation function. Permutation functions can be
written in a simple form using circular indexation. The operation between
the symmetries of the polygon is reduced to the composition of permutation
functions, which in turn is easily implemented using periodic sequences. It
is also shown that each symmetry is effectively a pure rotation or a pure flip.
It is also explained how to synthesize each symmetry using two generating
symmetries: time-reversal (flipping around a fixed symmetry axis) and unit-
delay (rotation around the center-point by 2/n radians clockwise).
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