  It is shown how Yang-Baxter maps may be directly obtained from classical
counterparts of the star-triangle relations and quantum Yang-Baxter equations.
This is based on reinterpreting the latter equation and its solutions which are
given in terms of special functions, as a set-theoretical form of the
Yang-Baxter equation whose solutions are given by quadrirational Yang-Baxter
maps. The Yang-Baxter maps obtained through this approach are found to satisfy
two different types of Yang-Baxter equations, one that is the usual equation
involving a single map, and another equation that involves a pair of maps,
which is a case of what is also known as an entwining Yang-Baxter equation.
Apart from the elliptic case, each of these Yang-Baxter maps are
quadrirational, but only maps that solve the former type of Yang-Baxter
equation are reversible. The Yang-Baxter maps are expressed in terms of
two-component variables, and two-component parameters, and have a natural
QRT-like composition of separate maps for each component. Through this
approach, sixteen different Yang-Baxter maps are derived from known solutions
of the classical star-triangle relations.
