Abstract: Each Dynkin diagram corresponds to a finite type cluster algebra A, a commutative ring with distinguished generators called cluster variables which are grouped into overlapping sets called clusters. "Finite type" means that there are finitely many cluster variables, and these cluster variables are parametrized by the union of all positive roots and negative simple roots of the corresponding root system. Each pair of clusters is connected by a sequence of involutions called mutations. These involutions can be visualized with the exchange graph, which has a vertex for each cluster and an edge for each mutation. The exchange graph of A is the 1-skeleton of a polytope called a generalized associahedron (for type A this is an associahedron, and for type B or C this is a cyclohedron). The faces of the generalized associahedron are indexed by subclusters (subsets of clusters), and the facets are indexed by the cluster variables. In this talk, we will discuss the superunitary region S(A) of A which is the space of ring homomorphisms from A to the real numbers which send each cluster variable to at least 1 (the name “superunitary” was chosen because it means “greater than 1”). This region can be embedded into the positive orthant of the Euclidean space by requiring all cluster variables (which can be written as positive Laurent polynomials) to be bigger or equal to 1. An exciting fact about the superunitary region is that there is a homeomorphism from S(A) to the generalized associahedron of A which sends each subcluster face to the corresponding polyhedral face. An application of this is a uniform proof that there are finitely many Dynkin-type friezes (positive integral-valued functions on repetition quivers, classical combinatorial objects which have been studied since the 70s by Conway and Coxeter). This talk is based on work with G. Muller.