  In the paper, we clarify some relations between solutions to the
star-triangle equation via the gauge/YBE correspondence. We consider two
solutions to the star-triangle relation in terms of Euler's gamma function. We
derive these solutions from the reduction of certain basic and hyperbolic
hypergeometric integral identities. These identities can be interpreted as
equality of the supersymmetric partition functions of a specific
three-dimensional N=2 supersymmetric dual theories.
