  The problem of computing the exact stretch factor (i.e., the tight bound on
the worst case stretch factor) of a Delaunay triangulation is one of the
longstanding open problems in computational geometry. Over the years, a series
of upper and lower bounds on the exact stretch factor have been obtained but
the gap between them is still large. An alternative approach to solving the
problem is to develop techniques for computing the exact stretch factor of
``easier'' types of Delaunay triangulations, in particular those defined using
regular-polygons instead of a circle. Tight bounds exist for Delaunay
triangulations defined using an equilateral triangle and a square. In this
paper, we determine the exact stretch factor of Delaunay triangulations defined
using a regular hexagon: It is 2.
  We think that the main contribution of this paper are the two techniques we
have developed to compute tight upper bounds for the stretch factor of
Hexagon-Delaunay triangulations.
