  We describe a uniform way of obtaining basic hypergeometric functions as
limits of the elliptic beta integral. This description gives rise to the
construction of a polytope with a different basic hypergeometric function
attached to each face of this polytope. We can subsequently obtain various
relations, such as transformations and three-term relations, of these functions
by considering geometrical properties of this polytope. The most general
functions we describe in this way are sums of two very-well-poised
${}_{10}\phi_9$'s and their Nassrallah-Rahman type integral representation.
