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Experimental study of energy-minimizing point configurations on spheres. (English) Zbl 1185.68771

Summary: 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.

MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)

Software:

polymake
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