We show that the celebrated six-vertex model of statistical mechanics (along
with its multistate generalizations) can be reformulated as an Ising-type model
with only a two-spin interaction. Such a reformulation unravels remarkable
factorization properties for row to row transfer matrices, allowing one to
uniformly derive all functional relations for their eigenvalues and present the
coordinate Bethe ansatz for the eigenvectors for all higher spin
generalizations of the six-vertex model. The possibility of the Ising-type
formulation of these models raises questions about the precedence of the
traditional quantum group description of the vertex models. Indeed, the role of
a primary integrability condition is now played by the star-triangle relation,
which is not entirely natural in the standard quantum group setting, but
implies the vertex-type Yang-Baxter equation and commutativity of transfer
matrices as simple corollaries. As a mathematical identity the emerging
star-triangle relation is equivalent to the Pfaff-Saalschuetz-Jackson summation
formula, originally discovered by J.~F.~Pfaff in 1797. Plausibly, all vertex
models associated with quantized affine Lie algebras and superalgebras can be
reformulated as Ising-type models with only two-spin interactions.}
