  In this paper, we explore the symmetric nature of the terminating basic
hypergeometric series representations of the Askey--Wilson polynomials and the
corresponding terminating basic hypergeometric transformations that these
polynomials satisfy. In particular we identify and classify the set of 4 and 7
equivalence classes of terminating balanced ${}_4\phi_3$ and terminating
very-well poised ${}_8W_7$ basic hypergeometric series which are connected with
the Askey--Wilson polynomials. We study the inversion properties of these
equivalence classes and also identify the connection of both sets of
equivalence classes with the symmetric group $S_6$, the symmetry group of the
terminating balanced ${}_4\phi_3$. We then use terminating balanced
${}_4\phi_3$ and terminating very-well poised ${}_8W_7$ transformations to give
a broader interpretation of Watson's $q$-analog of Whipple's theorem and its
converse. We give a broad description of the symmetry structure of the
terminating basic hypergeometric series representations of the Askey--Wilson
polynomials.
