Chapoton introduced several polynomials defined in terms of "Coxeter-Catalan" objects associated to a given root system, and he conjectured several identities among them. These identities were then extended and proved by several authors. Although the polynomials are presented in an abstract combinatorial manner, they have a natural interpretation in terms of Cambrian fans. In this talk, I will present some other fans with no apparent connection to root systems for which Chapoton's polynomials remain combinatorially meaningful. This is from joint work with Alexander Garver.