The data for n = 32


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 =412.2612670


The Coulomb projection has bandology of (1,5,5,5,5,5,5,1) which we suspect is a common form for n=2 modulo 5. The degree 5 points occur the icosahedral pattern (1,5,5,1) and the degree 6 points are in the form of a dodecahedron. In fact this figure is just the addition of midpoints to the faces of either the icosahedron or of the dodecahedron. Adding midpoints to the faces of a stable figure does not always give a stable figure--with the tetrahedron you get the square which is not stable after a small perturbation nor minimal.

[Graphics:n32pic.jpg]

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smallest eigenvalue Gram view

[Graphics:n32g1.jpg]

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second largest eigenvalue Gram view

[Graphics:n32g2.jpg]

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largest eigenvalue Gram view

[Graphics:n32g3.jpg]

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The Coulomb view

[Graphics:n32coul.jpg]

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The points

{{-0.89074, -0.196811, 0.409692}, {0.483794, 0.782744, -0.391477}, {-0.0983049, 0.974077, -0.203738}, {-0.402312, 0.847582, 0.346048}, {-0.964996, 0.0409829, -0.259043}, {0.0110851, 0.623725, 0.781565}, {-0.871869, 0.422802, 0.247151}, {-0.542987, 0.301705, 0.78367}, {0.871862, -0.422818, -0.247147}, {0.964987, -0.0410259, 0.259069}, {-0.306496, -0.907087, -0.288537}, {0.603919, 0.397974, 0.690578}, {0.542988, -0.301676, -0.78368}, {0.098322, -0.974078, 0.203728}, {0.115477, -0.646396, 0.754213}, {-0.60392, -0.397978, -0.690576}, {-0.0789111, -0.0238004, -0.996598}, {-0.66313, 0.686464, -0.298374}, {0.0788847, 0.0238431, 0.996599}, {0.402313, -0.847571, -0.346074}, {0.817969, 0.564651, 0.109983}, {0.663119, -0.686466, 0.298391}, {-0.610706, 0.239619, -0.754733}, {-0.817937, -0.564698, -0.109978}, {-0.483769, -0.782756, 0.391485}, {0.610667, -0.239619, 0.754764}, {-0.0110782, -0.623684, -0.781598}, {-0.433684, -0.327284, 0.839526}, {0.433674, 0.327307, -0.839522}, {0.306534, 0.907083, 0.28851}, {0.890745, 0.196787, -0.409693}, {-0.1155, 0.646402, -0.754204}}

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