### The data for n = 24

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 =223.3470692

One of our favorites. The configuration is a BEAUTIFUL AND HIGHLY REGULAR FIGURE, an Archimedean solid.! It is the structure of the protein ferritin. There is a sculpture of this figure in the courtyard of the Beckman Institute at Cal Tech. There are squares positioned at the six positive or negative eigenvector directions and around each square there are equilateral triangles. In each projection there are 6 layers of 4 evenly spaced points, i. e. bandology of (4,4,4,4,4,4). We only noticed this thanks to the eigenvector projections.

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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
{{-0.853997, 0.511087, 0.0973668}, {-0.321737, 0.900638, -0.292123}, {0.117753, 0.40563, 0.906421}, {-0.142552, -0.867828, 0.475976}, {-0.980745, -0.166822, -0.101535}, {-0.044845, 0.474143, -0.879305}, {-0.618068, 0.279805, 0.734644}, {0.743857, 0.16965, 0.646448}, {0.671771, -0.48164, -0.562803}, {-0.571885, -0.814601, -0.0968122}, {-0.582278, -0.372804, -0.722475}, {0.659384, 0.218752, -0.719278}, {0.389757, 0.844032, -0.368373}, {-0.116676, -0.270999, 0.955482}, {0.926903, 0.368667, -0.0702516}, {0.000300573, -0.848696, -0.528881}, {-0.702542, 0.328891, -0.631083}, {-0.744678, -0.398113, 0.535688}, {0.429632, -0.901936, 0.0439063}, {0.0753606, -0.227541, -0.970848}, {0.509369, -0.50697, 0.695359}, {0.463989, 0.815886, 0.345028}, {-0.247505, 0.872505, 0.421279}, {0.939429, -0.331735, 0.0861687}}

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