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Optimal Finite Homogeneous Sphere Approximation

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Abstract

The two-dimensional sphere can’t be approximated by finite homogeneous spaces. We describe the optimal approximation and its distance from the sphere. We compare this distance to the distance achieved by all Platonic and Archimedean solids.

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Acknowledgements

Tshacik Gelander and Itai Benjamini offered me this project and opened for me a window to an area in math that was new and exciting for me. I thank both for stimulating discussions. I would also like to thank Tal Cohen. Tal read the first draft of this paper. His comments improved this paper significantly.

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  1. Weizmann Institute of Science, Mizra, Israel

    Omer Lavi

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  1. Omer Lavi
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Lavi, O. Optimal Finite Homogeneous Sphere Approximation. Discrete Comput Geom 67, 1080–1096 (2022). https://doi.org/10.1007/s00454-022-00377-w

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  • DOI: https://doi.org/10.1007/s00454-022-00377-w

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