  Given a regular network (in which all cells have the same type and receive
the same number of inputs and all arrows have the same type), we define the
special Jordan subspaces to that network and we use these subspaces to study
the synchrony phenomenon in the theory of coupled cell networks. To be more
precise, we prove that the synchrony subspaces of a regular network are
precisely the polydiagonals that are direct sums of special Jordan subspaces.
We also show that special Jordan subspaces play a special role in the lattice
structure of all synchrony subspace because every join-irreducible element of
the lattice is the smallest synchrony subspace containing some special Jordan
subspace.
