### 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.

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smallest eigenvalue Gram view

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second largest eigenvalue Gram view

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largest eigenvalue Gram view

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The Coulomb view

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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).