  The Dunkl--Dirac operator is a deformation of the Dirac operator by means of
Dunkl derivatives. We investigate the symmetry algebra generated by the
elements supercommuting with the Dunkl--Dirac operator and its dual symbol.
This symmetry algebra is realised inside the tensor product of a Clifford
algebra and a rational Cherednik algebra associated with a reflection group or
root system. For reducible root systems of rank three, we determine all the
irreducible finite-dimensional representations and conditions for unitarity.
Polynomial solutions of the Dunkl--Dirac equation are given as a realisation of
one family of such irreducible unitary representations.
