  Elliptic 6j-symbols first appeared in connection with solvable models of
statistical mechanics. They include many interesting limit cases, such as
quantum 6j-symbols (or q-Racah polynomials) and Wilson's biorthogonal 10-W-9
functions. We give an elementary construction of elliptic 6j-symbols, which
immediately implies several of their main properties. As a consequence, we
obtain a new algebraic interpretation of elliptic 6j-symbols in terms of
Sklyanin algebra representations.
