The data for n = 27


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 =287.3025907


The configuration shows beautiful orderliness in the minimum gram eigenvalue projection with a bandology of (1,5,5,5,5,5,1)--a degree 5 vertex surrounded by 6 degree 6 vertices. This arrangement tempts us to hope for similar structure for n = 2 mod 5.

[Graphics:n27pic.jpg]

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smallest eigenvalue Gram view

[Graphics:n27g1.jpg]

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second largest eigenvalue Gram view

[Graphics:n27g2.jpg]

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largest eigenvalue Gram view

[Graphics:n27g3.jpg]

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The Coulomb view

[Graphics:n11coul.jpg]

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The points

{{-0.921913, 0.0585063, 0.382955}, {0.896492, 0.425153, 0.124689}, {0.747709, 0.00177673, 0.664024}, {-0.374443, 0.576862, 0.725963}, {-0.734423, 0.665653, 0.1324}, {-0.60394, -0.639252, 0.47604}, {0.0278357, -0.691045, -0.722276}, {0.44225, -0.876593, -0.189737}, {-0.899792, 0.232489, -0.36922}, {-0.568146, -0.357761, -0.741092}, {0.783486, 0.283283, -0.553083}, {-0.896495, -0.425145, -0.124694}, {0.671338, -0.385727, -0.632866}, {-0.340864, 0.841616, -0.41892}, {0.639891, -0.632907, 0.435854}, {0.429745, 0.699488, 0.570995}, {-0.423912, 0.300201, -0.854505}, {-0.385348, -0.896484, -0.218684}, {0.109268, -0.485178, 0.867562}, {0.168848, 0.205409, 0.964001}, {-0.0908605, 0.970842, 0.221834}, {0.966321, -0.255507, -0.0306706}, {0.451874, 0.87347, -0.18127}, {-0.0036005, -0.938171, 0.346154}, {0.219651, 0.60536, -0.765045}, {0.163791, -0.0567146, -0.984863}, {-0.474764, -0.0996242, 0.874456}}

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