The Barrett-Crane intertwiner for the Riemannian general relativity is
systematically derived by solving the quantum Barrett-Crane constraints
corresponding to a tetrahedron (except for the non-degeneracy condition). It
was shown by Reisenberger that the Barrett-Crane intertwiner is the unique
solution. The systematic derivation can be considered as an alternative proof
of the uniqueness. The new element in the derivation is the rigorous imposition
of the cross-simplicity constraint.Comment: 10 page