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Symmetry number of a complex system

Creation of this applet was inspired by https://www.geogebra.org/material/show/id/fgdnqeby posted by Oktay Haracci — 27. Mai 2019 - 08:17   . How can you prove what this applet illustrates? From the point of view of Steiner's theorem, the result is obvious. Calculations within the applet.