  We study the symplectic reduction of the phase space of two twistors to the
cotangent bundle of the Lorentz group. We provide expressions for the Lorentz
generators and group elements in terms of the spinors defining the twistors. We
use this to define twistor networks as a graph carrying the phase space of two
twistors on each edge. We also introduce simple twistor networks, which provide
a classical version of the simple projected spin networks living on the
boundary Hilbert space of EPRL/FK spin foam models. Finally, we give an
expression for the Haar measure in terms of spinors.
