  Relativistic spin networks are defined by considering the spin covering of
the group SO(4), SU(2) times SU(2). Relativistic quantum spins are related to
the geometry of the 2-dimensional faces of a 4-simplex. This extends the idea
of Ponzano and Regge that SU(2) spins are related to the geometry of the edges
of a 3-simplex.
  This leads us to suggest that there may be a 4-dimensional state sum model
for quantum gravity based on relativistic spin networks which parallels the
construction of 3-dimensional quantum gravity from ordinary spin networks.
