### Cube polywell symmetries III

When calculating the electric field of the polywell as in previous experiements one can recognize that the charge values/densities are symmetric. With the linear system method the number of points we can use is limited by both calculation time and memory usage (10000x10000 matrix already takes up 800MB of RAM). The symmetries can be used to reduce the number of points in the linear system.

In cube polywell the increase can be done 48-fold and that is very significant. The only complicated part is the division and cutting of the model into a specific slice. It turns out simply cutting spheres is is not optimal in this application, the best is to construct surfaces specifically for the given slice.

With increased calculation ability we can increase resolution and get a more precise field. A 2000 point slice would symmetrically map into 96000 points.

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