text: Point groups in two dimensions, sometimes called rosette groups.
  They come in two infinite families:
  # Cyclic groups C of n-fold rotation groups
  # Dihedral groups D of n-fold rotation and reflection groups
  Applying the crystallographic restriction theorem restricts n to values 1, 2, 3, 4, and 6 for both families, yielding 10 groups.
  The subset of pure reflectional point groups, defined by 1 or 2 mirrors, can also be given by their Coxeter group and related polygons. These include 5 crystallographic groups. The symmetry of the reflectional groups can be doubled by an isomorphism, mapping both mirrors onto each other by a bisecting mirror, doubling the symmetry order.