Experimental study of energy-minimizing point configurations on spheres

Details Experimental study of energy-minimizing point configurations on spheres Experimental study of energy-minimizing point configurations on spheres

2006-11-15

arxiv.org/abs/math/0611451v3

Experimental Mathematics 18 (2009), 257-283

Mathematics

Metric Geometry

41 pages, 12 figures, to appear in Experimental Mathematics

Scientific paper

10.1080/10586458.2009.10129052

In this paper we report on massive computer experiments aimed at finding spherical point configurations that minimize potential energy. We present experimental evidence for two new universal optima (consisting of 40 points in 10 dimensions and 64 points in 14 dimensions), as well as evidence that there are no others with at most 64 points. We also describe several other new polytopes, and we present new geometrical descriptions of some of the known universal optima.

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