Chirality in Two Dimensions
In two dimensions, every figure which possesses an axis of symmetry is achiral, and it can be shown that every bounded achiral figure must have an axis of symmetry. (An axis of symmetry of a figure is a line, such that is invariant under the mapping, when is chosen to be the -axis of the coordinate system.) Consider the following pattern:
> > > > > > > > > > > > > > > > > > > >This figure is chiral, as it is not identical to its mirror image:
> > > > > > > > > > > > > > > > > > > >But if one prolongs the pattern in both directions to infinity, one receives an (unbounded) achiral figure which has no axis of symmetry. Its symmetry group is a frieze group generated by a single glide reflection.
Read more about this topic: Chirality (mathematics)
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