## 5 Conclusions  
This study examined the influence of the initial prestress level on the shape and range of unstable regions of small-scale steel Geiger domes. The behavior depends on the design of the dome, which affects the minimum prestress level. Four different design solutions, known from the literature, were compared, i.e., regular and modified domes with closed (type A) and open (type B) upper sections. Type A domes require a much higher initial prestress level to ensure the appropriate distribution of normal forces in the elements than type B domes. In the first case, the minimum prestress levels are 48% and 70% of the maximum prestress level for regular and modified domes, respectively, while in the second case, it is only 4%. The main unstable regions corresponding to the frequencies depending on the initial prestress were determined. The four selected main unstable regions were presented in this paper. The influence of three initial prestress levels \(S\) on the shape and range of these regions was determined. At this point, it should be noted that in the case of type B domes, the number of frequencies, depending on the initial prestress level \(S\), corresponds to infinitesimal mechanisms. In turn, in the case of type A domes, there are three additional frequencies that depend on the prestress. However, for these frequencies, the boundaries of instabilities coincide. The dynamic stability analysis showed that type B domes are characterized by wider unstable regions than type A domes. In the case of type A domes, unstable regions occur only at low values of initial prestress and completely narrow with the increase in the initial prestress level. In turn, for type B domes, the impact of the initial prestress is weaker. The number of unstable regions depends on the number of infinitesimal mechanisms. Type B domes are characterized by a larger number of infinitesimal mechanisms and thus a larger number of unstable regions. Additionally, they are concentrated close to each other, and some of them coincide, which results in a higher risk of excitation vibrations. Modified type B domes are the most sensitive to changes in resonant frequencies, whereas modified type A domes are the least sensitive. This means that the additional circumferential cables have a negative impact on the dynamic stability of type B domes. For all domes, as the initial prestress level increases, the resonant frequencies also increase. With a high initial prestress level (approximately 70% of the maximum prestress level), the boundaries of instability practically coincide, and the risk of the excitation of motion with increasing amplitudes decreases. The application of tensegrity domes in real structures is a very demanding process. Choosing the initial prestress level in real-world applications is very important; however, it is not easy. The process of optimizing the initial prestress level must be carried out. First, the initial prestress level must ensure an appropriate redistribution of normal forces under actual loading. Second, the load-bearing capacity must be ensured, which means that the allowable stresses must not be exceeded. Third, from the point of view of assessing the dynamics of stability, the risk of the excitation of motion with increasing amplitude must be as low as possible. All these conditions should be taken into account in the optimization process. In addition, in terms of applying these types of structures in real objects, additional analyses must be conducted (including experimental studies). The analyses must include the physical non-linearity of cables and local stability (the local buckling of single elements). Conceptualization, P.O. ; formal analysis, M.S. ; methodology, P.O. ; software, M.S. ; supervision, P.O. ; visualization, M.S. ; writing--original draft and editing, P.O. All authors have read and agreed to the published version of the manuscript. This research received no external funding.