[color=#999999]This activity belongs to the [i]GeoGebra book[/i] [url=https://www.geogebra.org/m/sw2cat9w]GeoGebra Principia[/url].[/color][br][br][br]If we transition from the circle to the sphere (the [i]Thomson problem [/i][url=https://en.wikipedia.org/wiki/Thomson_problem][img]https://www.geogebra.org/resource/scjbyz2p/0tuzuVw455vxurEw/material-scjbyz2p.png[/img][/url], a particular case of one of the eighteen unsolved mathematical problems proposed by mathematician Steve Smale [url=https://en.wikipedia.org/wiki/Smale's_problems][img]https://www.geogebra.org/resource/scjbyz2p/0tuzuVw455vxurEw/material-scjbyz2p.png[/img][/url] in the year 2000), perfect regularity is no longer achievable since there are no Platonic solids with 5 or 7 vertices, for example.[br][br]Moreover, it is not even true that equilibrium is always reached in perfect regularity! In fact, with 8 vertices, the cube is not the configuration that achieves equilibrium. Note also that in most cases, polyhedra with triangular faces appear (but generally not equilateral, hence they are not [i]deltahedra [/i][url=https://en.wikipedia.org/wiki/Deltahedron][img]https://www.geogebra.org/resource/scjbyz2p/0tuzuVw455vxurEw/material-scjbyz2p.png[/img][/url]).

[color=#999999]Author of the construction of GeoGebra: [url=https://www.geogebra.org/u/rafael]Rafael Losada[/url].[/color]