The most stable configurations of clusters with tetrahedral bond coordination are often polyhedral or have the form of several adjacent polyhedra. This paper proposes a new approach to the topological identification of such structures, which is distinguished by the use of explicit formulas for calculating n-membered cycles in the structural graph. Furthermore, a formula that is a generalization of the Euler formula for adjacent polyhedra is used for the first time. Methods for identifying multi-cage structures can find application in working with cluster databases, in probabilistic methods for generating cluster structures, and in interpreting the results of computer simulations aimed at understanding the self-organization processes of molecular systems. The Database of Water Cluster Minima is used as the main dataset Rakshit et al., J. Chem. Phys. 151, 214307 (2019).
M. V. Kirov (Tue,) studied this question.