The computational model in action:

V 1.4 of the general model as java applet including its source file can be loaded here.

Below you can generate regular convex polytope structures (all use the same applet with different parameters):

2 dimensions

[2][p] will form polygonal structures {p} with a stable equilibrium. Try incrementing/decrementing points by one.

3 dimensions:

Regular structures

[3][4] will form a Tetrahedron structure {3,3} with a stable equilibrium at distance 4*sqrt(6)=9,7979....
[3][6] will form an Octahedron structure {3,4} with a stable equilibrium at distance 6*(2*sqrt(2)+1)=22.9705....
[3][12] will form an Icosahedron structure {5,3} with a stable equilibrium at distance 94.5829....

Irregular structures

[3][8] is a multi-stable configuration and is unlikely* to form a cube structure {4,3} with an unstable equilibrium at distance =8*(sqrt(3)+sqrt(6)+1)=41.4523... , but will show a square anti-prism structure with a stable equilibrium and a greater distance of 41.4730... instead.
* Try incrementing and then decrementing dimensions by one under law 1/R, after trying a few times a cube will show up as a stable structure or remain for a short while and then change to a square anti-prism.
[3][20] is a multi-stable configuration and is unlikely to form a dodecahedron structure {3,5}, but will show a structure with a stable equilibrium and a greater distance of 264.8361... instead.

4 dimensions:

Regular structures

[4][5] will form a Hypertetrahedron structure {3,3,3} with a stable equilibrium at distance 15.8113....
[4][8] will form Hyperoctahedron structure {3,3,4} with a stable equilibrium at distance 8*(3*sqrt(2)+1)=41.9411....
[4][24 will form 24-cell structure {3,4,3}, succeeds about once every eight times with the 24-cell having optimal distance. This is a multi-stable configuration which has at least 2 stable structures with a stable equilibrium at distances 388.1002... and 388.0972... respectively.
[4][120] will form a Hypericosahedron {3,3,5}, with a stable equilibrium at distance 9769.9664...

Irregular structures

[4][16] is a multi-stable configuration and is unlikely to form the regular hypercube structure {4,3,3} with an unstable equilibrium, but will show structures with stable equilibriums and greater distances of 169.0191... and 169.0183... instead.
[4][600] is a multi-stable configuration and is unlikely to form the the regular hyperdodecahedron structure {5,3,3} with an unstable equilibrium, but will show a structure with a stable equilibrium and a greater distance of 244436.9560... instead. (After 50,000 iterations in 1/R^3 law, so be patient!).

5 dimensions and higher*:

Regular structures

[n][n+1] will form n-simplex structures {3,3...,3} with stable equilibriums. Try incrementing/decrementing points and dimensions by one.
[n][2*n] will form n-crosspolytope structures {3,3...,4} with stable equilibrium at distance 2*n*((n-1)*sqrt(2)+1).
Try incrementing/decrementing points by 2 and dimensions by one.

Irregular structures

[n][n^2] are multi-stable configurations and are unlikely to form hyper-n-cubes, {4,3,3,...,3} with unstable equilibriums, but will show structures with stable equilibriums and greater distances instead.

*The current computational model is limited to 100 dimensions and 1000 points.

2004, Symen H. Hovinga

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