The Delaunay tessellation in hyperbolic space

Abstract

AbstractThe Delaunay tessellation of a locally finite subset of the hyperbolic space ℍnis constructed via convex hulls in ℝn+1. For finite and lattice-invariant sets it is proven to be a polyhedral decomposition, and versions (necessarily modified from the Euclidean setting) of the empty circumspheres condition and geometric duality with the Voronoi tessellation are proved. Some pathological examples of infinite, non lattice-invariant sets are exhibited.