We present PolyChor$\lambda$, a language for higher-order functional choreographic programming—an emerging paradigm for concurrent programming. In choreographic programming, programmers write the desired cooperative behaviour of a system of processes and then compile it into an implementation for each process, a translation called endpoint projection. Unlike its predecessor, Chor$\lambda$, PolyChor$\lambda$ has both type and process polymorphism inspired by System F$_\omega$. That is, PolyChor$\lambda$ is the first (higher-order) functional choreographic language which gives programmers the ability to write generic choreographies and determine the participants at runtime. This novel combination of features also allows PolyChor$\lambda$ processes to communicate distributed values, leading to a new and intuitive way to write delegation. While some of the functional features of PolyChor$\lambda$ give it a weaker correspondence between the semantics of choreographies and their endpoint-projected concurrent systems than some other choreographic languages, we still get the hallmark end result of choreographic programming: projected programmes are deadlock-free by design.