Thomson Problem Polyhedra
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J.J. Thomson's question in 1904 focused on the arrangement of electrons on a unit sphere, with proposed solutions for numbers ranging from 2 to 400. The convex hull and its dual are useful polyhedra types for solving this problem. An applet from Syracuse University allows virtual viewing of these polyhedra. To print physical versions, qhull's OFF format is helpful. A program was written to convert OFF format into openSCAD polyhedron commands. The Cambridge Cluster Database offers Thomson problem coordinates, and the openSCAD program from Christmas ornaments displayed electron positions as stars on a sphere. STL files for N=11 solutions, along with instructions for printing them, are provided in the downloadable zip files. Additional solutions can be converted using the provided programs and instructions.
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