  The study of toy models in loop quantum gravity (LQG), defined as truncations
of the full theory, is relevant to both the development of the LQG
phenomenology, in cosmology and astrophysics, and the progress towards the
resolution of the open issues of the theory, in particular the implementation
of the dynamics. Here, we study the dynamics of spin network states of quantum
geometry defined on the family of graphs consisting in 2 vertices linked by an
arbitrary number of edges, or 2-vertex model in short. A symmetry reduced
sector of this model -- to isotropic and homogeneous geometries -- was
successfully studied in the past, where interesting cosmological insights were
found. We now study the evolution of the classical trajectories for this system
in the general case, for arbitrary number of edges with random initial
configurations. We use the spinorial formalism and its clear interpretation of
spin networks in terms of discrete twisted geometries, with the quantum 3d
space made of superpositions of polyhedra glued together by faces of equal
area. Remarkably, oscillatory and divergent regimes are found with a universal
dependence on the coupling constants of the Hamiltonian and independent of the
initial spinors or the number of edges. Furthermore, we explore the evolution
of the associated polyhedra as well as their volumes and areas.
