论文标题
距离集的十二面体猜想的证明
A proof of a Dodecahedron conjecture for distance sets
论文作者
论文摘要
如果欧几里得空间的有限子集被称为$ s $ distance set，则如果完全存在欧几里得距离的$ s $值之间的$ s $值。在本文中，我们证明，所有5距离集中的最大基数均以$ \ mathbb {r}^3 $为20，而每一个$ 5 $ distance in $ \ m athbb {r}^3 $ in $ 20 $ coption in $ \ mathbb {r}^3 $都类似于常规的dodecahedron的顶点。
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.
