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arXiv · 1309.2047

Uniqueness of maximum three-distance sets in the three-dimensional Euclidean space

Masashi Shinohara
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Abstract

A subset $X$ in the $d$-dimensional Euclidean space is called a $k$-distance set if there are exactly $k$ distances between two distinct points in $X$. Einhorn and Schoenberg conjectured that the vertices of the regular icosahedron is the only 12-point three-distance set in $\mathbb{R}^3$ up to isomorphism. In this paper, we prove the uniqueness of 12-point three-distance sets in $\mathbb{R}^3$.

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Masashi Shinohara. 2013-09-09. Uniqueness of maximum three-distance sets in the three-dimensional Euclidean space. https://arxiv.org/abs/1309.2047

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