  Multilevel self-assembly involving small structured groups of nano-particles
provides new routes to development of functional materials with a sophisticated
architecture. Apart from the inter-particle forces, the geometrical shapes and
compatibility of the building blocks are decisive factors in each phase of
growth. Therefore, a comprehensive understanding of these processes is
essential for the design of large assemblies of desired properties. Here, we
introduce a computational model for cooperative self-assembly with simultaneous
attachment of structured groups of particles, which can be described by
simplexes (connected pairs, triangles, tetrahedrons and higher order cliques)
to a growing network, starting from a small seed. The model incorporates
geometric rules that provide suitable nesting spaces for the new group and the
chemical affinity $\nu$ of the system to accepting an excess number of
particles. For varying chemical affinity, we grow different classes of
assemblies by binding the cliques of distributed sizes. Furthermore, to
characterise the emergent large-scale structures, we use the metrics of graph
theory and algebraic topology of graphs, and 4-point test for the intrinsic
hyperbolicity of the networks. Our results show that higher Q-connectedness of
the appearing simplicial complexes can arise due to only geometrical factors,
i.e., for $\nu = 0$, and that it can be effectively modulated by changing the
chemical potential and the polydispersity of the size of binding simplexes. For
certain parameters in the model we obtain networks of mono-dispersed clicks,
triangles and tetrahedrons, which represent the geometrical descriptors that
are relevant in quantum physics and frequently occurring chemical clusters.
