  The Delaunay tessellation of a locally finite subset of hyperbolic space is
constructed using convex hulls in Euclidean space of one higher dimension. 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.
