 This came about as a modification of an alternate solution for the six-vertex model; it makes use of elliptic theta functions.The proof relies on the fact that when formula_9 and formula_10, for quantities 
the transfer matrices formula_12 and formula_13 (associated with the weights formula_14, formula_15, formula_16, formula_17 and formula_18, formula_19, formula_20, formula_21) commute.Using the star-triangle relation, Baxter reformulated this condition as equivalent to a parametrisation of the weights given as
for fixed modulus formula_23 and formula_24 and variable formula_25.