  We point out that interesting features in high energy physics data can be
determined from properties of Voronoi tessellations of the relevant phase
space. For illustration, we focus on the detection of kinematic "edges" in two
dimensions, which may signal physics beyond the standard model. After deriving
some useful geometric results for Voronoi tessellations on perfect grids, we
propose several algorithms for tagging the Voronoi cells in the vicinity of
kinematic edges in real data. We show that the efficiency is improved by the
addition of a few Voronoi relaxation steps via Lloyd's method. By preserving
the maximum spatial resolution of the data, Voronoi methods can be a valuable
addition to the data analysis toolkit at the LHC.
