  We present an uniform construction of the solution to the Yang- Baxter
equation with the symmetry algebra $s\ell(2)$ and its deformations: the
q-deformation and the elliptic deformation or Sklyanin algebra. The R-operator
acting in the tensor product of two representations of the symmetry algebra
with arbitrary spins $\ell_1$ and $\ell_2$ is built in terms of products of
three basic operators $\mathcal{S}_1, \mathcal{S}_2,\mathcal{S}_3$ which are
constructed explicitly. They have the simple meaning of representing elementary
permutations of the symmetric group $\mathfrak{S}_4$, the permutation group of
the four parameters entering the RLL-relation.
