Mathematics – Metric Geometry
Scientific paper
2006-11-15
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.
Ballinger Brandon
Blekherman Grigoriy
Cohn Henry
Giansiracusa Noah
Kelly Elizabeth
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