Spherical Confinement Between Repelling Points
This activity belongs to the GeoGebra book GeoGebra Principia.
If we transition from the circle to the sphere (the Thomson problem 
, a particular case of one of the eighteen unsolved mathematical problems proposed by mathematician Steve Smale in the year 2000), perfect regularity is no longer achievable since there are no Platonic solids with 5 or 7 vertices, for example.
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 deltahedra ).
, a particular case of one of the eighteen unsolved mathematical problems proposed by mathematician Steve Smale in the year 2000), perfect regularity is no longer achievable since there are no Platonic solids with 5 or 7 vertices, for example.
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 deltahedra ).Author of the construction of GeoGebra: Rafael Losada.