  We show that the triple product defined by the spin domain (Bounded Symmetric
Domain of type 4 in Cartan's classification) is closely related to the
geometric product in Clifford algebras. We present the properties of this
tri-product and compare it with the geometric product.
  The spin domain can be used to construct a model in which spin 1 and spin1/2
particles coexist. Using the geometric tri-product, we develop the geometry of
this domain. We present a geometric spectral theorem for this domain and obtain
both spin 1 and spin 1/2 representations of the Lorentz group on this domain.
