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 sig
nal 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 Lloyds 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.
