Figure 3: The equilateral triangle with its 3 axes of symmetries. The reflections and
generate the entire symmetry group. We have pictured the vectors and
orthogonal to the axes of reflection and chosen to make an obtuse angle. The shaded region
is a fundamental domain for the action of the group on the
triangle. Note that the fundamental domain for the action of the group on the entire Euclidean plane
extends indefinitely beyond the triangle but is, of course, still bounded by the two walls orthogonal
to and .
|