<p>The tree-level scattering amplitudes for tr(<i>ϕ</i>³) theory can be interpreted as a sum over the vertices of a polytope known as the associahedron. For each graph <i>G</i>, there exists a natural generalisation of the associahedron, which is constructed by considering tubes and tubings of the underlying graph. This family of polytopes are called <i>graph associahedra</i>. The classical associahedra then arise as the graph associahedron for the path graphs. It is therefore natural to associate to each graph associahedron an amplitude-like object, we refer to as the <i>amplitube</i>, defined via a sum over its vertices. Recently, also in the context of tr(<i>ϕ</i>³) theory, progress has been made towards defining a new geometric object, coined the <i>cosmohedron</i>, which computes not the amplitude, but the cosmological wavefunction as a sum over its vertices. This polytope can be constructed by consistently blowing up all boundaries of the associahedron to co-dimension one. Building on these results, in the present paper, we generalise the notion of the wavefunction for arbitrary graphs. These new expressions, which we call <i>cosmological amplitubes</i>, are defined via a sum over the vertices of a corresponding polytope, the <i>graph cosmohedron</i>. The graph cosmohedra are constructed by considering <i>regions</i> and <i>regional tubings</i> of the underlying graph which we introduce. Like the cosmohedron, the graph cosmohedra can be obtained by consistently blowing up all boundaries of the corresponding graph associahedron to co-dimension one. This new family of polytopes constitutes a vast generalisation of the cosmohedron, and we provide explicit embeddings for them, which builds upon an ABHY-like embedding for the graph associahedra.</p>