Problem: Symmetries

In Figure 1.5, two ``crystals'' (a and b) and a polygon (c) are shown. Identify the point group symmetry operations of the three objects (assume that the crystals are of infinite size). Show that the point groups of the two crystals are different, and that one of them has the equivalent point group as the polygon.

  
Figure 1.5: Two-dimensional objects with four-fold rotational symmetry.