Figure 3

Figure 3: The equilateral triangle with its 3 axes of symmetries. The reflections s1 and s2 generate the entire symmetry group. We have pictured the vectors α1 and α2 orthogonal to the axes of reflection and chosen to make an obtuse angle. The shaded region {w |(w|α1) ≥ 0} ∩ {w |(w |α2) ≥ 0} 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 α1 and α2.