The data for n = 8


The potential
The picture and a description of the configuration
The Gram minimal eigenvalue projection
The Gram middle eigenvalue projection
The Gram largest eigenvalue projection
The Coulomb view
The points in Mathematica format

potential = 19.67528786


The configuration is a twisted cube, i.e. a cube with the top face rotated 45 degrees against the bottom face. The (4,4) bandology is shown by the Gram smallest eigenvalue projection. An "obvious" guess for a local minimum is the regular cube. However, the regular is not analytically stable and a slightly perturbed regular cube starting point will quickly converge to the twisted cube under our algorithm.

[Graphics:n8pic.jpg]

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smallest eigenvalue Gram view

[Graphics:n8g1.jpg]

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second largest eigenvalue Gram view

[Graphics:n8g2.jpg]

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largest eigenvalue Gram view

[Graphics:n8g3.jpg]

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The Coulomb view

[Graphics:n8coul.jpg]

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The points

{{0,0,1.},{0.928283,0,-0.371875},{-0.792339,0.58564,0.170952}, {-0.13596,-0.58564,-0.799088},{-0.135987,0.585619,-0.799098}, {-0.792359,-0.585619,0.17093},{0.464187,0.828181,0.314082}, {0.464176,-0.828181,0.314097}}

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Copyright by Neubauer, Schilling, Watkins and Zeitlin (1998).