We present a construction of non-rectifiable, repetitive Delone sets in every Euclidean space $\mathbb{R}^d$ with $d \geq 2$. We further obtain a close to optimal repetitivity function for such sets. The proof is based on the process of encoding a non-realisable density in a Delone set, due to Burago and Kleiner.

翻译：我们提出了一种在任意欧几里得空间 $\mathbb{R}^d$（其中 $d \geq 2$）中构造不可求长且具有重复性的Delone集合的方法。进一步地，我们为此类集合获得了接近最优的重复性函数。该证明基于Burago和Kleiner提出的将不可实现密度编码至Delone集合的过程。