  A jammed packing of frictionless spheres at zero temperature is perfectly
specified by the network of contact forces from which mechanical properties can
be derived. However, we can alternatively consider a packing as a geometric
structure, characterized by a Voronoi tessellation which encodes the local
environment around each particle. We find that this local environment
characterizes systems both above and below jamming and changes markedly at the
transition. A variety of order parameters derived from this tessellation carry
signatures of the jamming transition, complete with scaling exponents.
Furthermore, we define a real space geometric correlation function which also
displays a signature of jamming. Taken together, these results demonstrate the
validity and usefulness of a purely geometric approach to jamming.
