Abstract
A finite subset of a Euclidean space is called an s-distance set if there exist exactly s values of the Euclidean distances between two distinct points in the set. In this paper, we prove that the maximum cardinality among all 5-distance sets in \(\mathbb {R}^3\) is 20, and every 5-distance set in \(\mathbb {R}^3\) with 20 points is similar to the vertex set of a regular dodecahedron.
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Nozaki, H., Shinohara, M. A Proof of a Dodecahedron Conjecture for Distance Sets. Graphs and Combinatorics 37, 1585–1603 (2021). https://doi.org/10.1007/s00373-021-02318-5
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DOI: https://doi.org/10.1007/s00373-021-02318-5