  We give a hypergeometric proof involving a family of 2-variable Krawtchouk
polynomials that were obtained earlier by Hoare and Rahman [SIGMA 4 (2008),
089, 18 pages] as a limit of the 9-j symbols of quantum angular momentum
theory, and shown to be eigenfunctions of the transition probability kernel
corresponding to a "poker dice" type probability model. The proof in this paper
derives and makes use of the necessary and sufficient conditions of
orthogonality in establishing orthogonality as well as indicating their
geometrical significance. We also derive a 5-term recurrence relation satisfied
by these polynomials.
