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The research object is a cyclically symmetric construction of a two-tier dome in the form of a convex polyhedron. Load and deflection critical parameters were determined for this construction pyramidal element. The behavior features of the conservative system in the dome's central assembly vertical displacement critical region value analysis has been carried out. The elastic rod model fluctuating and construction deviations from its equilibrium state reaction have been researched. System's behavior at natural motions and nonlinear restoring force is refined on the base of the findings carried out.