**6. Conclusions**

We presented conceptual models illustrating how cylindrical and spherical symmetries can be applied to reduce the time consumption of numerical simulations in the many-body problem. Often, to obtain practically and theoretically interesting results regarding manybody systems, one needs an extremely long run of corresponding numerical procedures. However, in a normal case, sufficient space for such a run supposes a rather extended system with plenty of interacting particles. It is shown in the present study that periodic boundary conditions corresponding to formal cylindrical symmetry allow for avoiding the problem of a huge number of interacting particles. This trick minimizes the effect of limited boundary conditions and still allows one to obtain reasonably correct results that are interesting from a scientific point of view.

In the second part of the paper, we presented a physically realizable cylindrical configuration and analyzed its advantages and disadvantages for both numerical and physical aspects. Furthermore, the spherical symmetry was studied. In particular, it is stressed that the 2D surface (belt) of the 3D spherical body is a unique natural example of a system, without boundaries at all.

Finally, we present some interesting patterns, which resemble those known from the tectonic history of our planet. It is shown that very realistic continental patterns can be obtained under supposition about perturbations of the planet rotation due to external interplanetary interactions or other extraterrestrial reasons.

**Author Contributions:** Investigation, A.E.F.; Methodology, V.L.P.; Visualization, A.E.F.; Writing— original draft, A.E.F.; Writing—review & editing, V.L.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We acknowledge support by the German Research Foundation and the Open Access Publication Fund of TU Berlin.

**Conflicts of Interest:** The authors declare no conflict of interest.
