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Assumptions:

1. The final state of any configuration [n][p] in the charged particle model are stable structures, one of which which will posess an optimal distance and a stable equilibrium.
2. Stable structures with optimal distance are:
   All 2 dimensional p-gons {p}, all forming a structure with a stable equilibrium belonging to the stable configurations [2][p].
   All (p-1)-simplex polytopes {3,3,...,3} in any n-dimensional space where n>=p-1, all forming a structure with a stable equilibrium belonging to the stable configurations [n][p].
   All p-crosspolytopes {3,3,...,4} where p=2*n, all being a structure with a stable equilibrium belonging to the stable configurations [n][2*n].
   The 3 dimensional icosahedron {3,5}, forming a structure with a stable equilibrium belonging to the stable configuration [3][12].
   The 4 dimensional hypericosahedron {3,3,5}, forming a structure with a stable equilibrium belonging to the stable configuration [4][120].
   The regular 4 dimensional 24-cell polytope {3,4,3}, forming a structure with a stable equilibrium belonging to the multi-stable configuration [4][24].
3. Stable structures with a non-optimal point distance are:
   All other regular polytopes namely:
   The dodecahedron {5,3} being a structure with an unstable equilibrium belonging to the multi-stable configuration [3][20].
   The hyperdodecahedron {5,3,3} being a structure with an unstable equilibrium belonging to the multi-stable configuration [3][600].
   All n-dimensional cubes {4,3,...3}, all being a structure with an unstable equilibrium belonging to multi-stable configurations [n][2^n].
4. Any regular polytope which is self-dual with p vertices in n dimensions where p>n are optimal and are structures with a stable equilibrium belonging to configurations [n][p].
5. Any group of regular polytopes having p1 and p2 vertices in n dimensions which are each other's dual, has only one polytope the distance of which is optimal and is a structure with a stable equilibrium belonging to stable configuration [n][p1] and one polytope, the distance of which is not optimal and is a structure with an unstable equilibrium belonging to multi-stable configuration [n][p2].

2003, Symen H. Hovinga

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