Abstract
In this paper we investigate the problem of finding the maximum volume polytopes, inscribed in the unit sphere of the d-dimensional Euclidean space, with a given number of vertices. We solve this problem for polytopes with \(d+2\) vertices in every dimension, and for polytopes with \(d+3\) vertices in odd dimensions. For polytopes with \(d+3\) vertices in even dimensions we give a partial solution.
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Acknowledgments
The authors are indebted to T. Bisztriczky for his help in understanding the combinatorial properties of neighborly polytopes.
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Communicated by A. Constantin.
Partially supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.
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Horváth, Á.G., Lángi, Z. Maximum volume polytopes inscribed in the unit sphere. Monatsh Math 181, 341–354 (2016). https://doi.org/10.1007/s00605-016-0949-2
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DOI: https://doi.org/10.1007/s00605-016-0949-2