On type cones of g-vector fans

We study the type cone (i.e. the space of all polytopal realizations) of g-vector fans of finite type cluster-like complexes (finite type cluster complexes, nonkissing complexes of gentle algebra, and graphical nested complexes). We show that this cone is often simplicial, which explains an elegant “kinematic” construction of the associahedron as a section of a high dimensional positive orthant by certain affine subspaces parametrized by a low dimensional positive orthant.