  The Wigner $3j$ symbols of the quantum angular momentum theory are related to
the vector coupling or Clebsch-Gordan coefficients and to the Hahn and dual
Hahn polynomials of the discrete orthogonal hyperspherical family, of use in
discretization approximations. We point out the important role of the Regge
symmetries for defining the screen where images of the coefficients are
projected, and for discussing their asymptotic properties and semiclassical
behavior. Recursion relationships are formulated as eigenvalue equations, and
exploited both for computational purposes and for physical interpretations.
