  We construct an infinite-dimensional solution of the Yang-Baxter equation
(YBE) of rank 1 which is represented as an integral operator with an elliptic
hypergeometric kernel acting in the space of functions of two complex
variables. This R-operator intertwines the product of two standard L-operators
associated with the Sklyanin algebra, an elliptic deformation of sl(2)-algebra.
It is built from three basic operators $\mathrm{S}_1, \mathrm{S}_2$, and
$\mathrm{S}_3$ generating the permutation group of four parameters
$\mathfrak{S}_4$. Validity of the key Coxeter relations (including the
star-triangle relation) is based on the elliptic beta integral evaluation
formula and the Bailey lemma associated with an elliptic Fourier
transformation. The operators $\mathrm{S}_j$ are determined uniquely with the
help of the elliptic modular double.
