  This paper completes the project of constructing combinatorial models (called
frameworks) for the exchange graph and g-vector fan associated to any exchange
matrix B whose Cartan companion is of finite or affine type, using the
combinatorics and geometry of Coxeter-sortable elements and Cambrian
lattices/fans. Specifically, we construct a framework in the unique non-acyclic
affine case, the cyclically oriented n-cycle. In the acyclic affine case, a
framework was constructed by combining a copy of the Cambrian fan for B with an
antipodal copy of the Cambrian fan for -B. In this paper, we extend this
"doubled Cambrian fan" construction to the oriented n-cycle, using a more
general notion of sortable elements for quivers with cycles.
