Motivated by a simplified model for atomic structures, and based on the concept of objective structures in ${\mathbb{R}}^3$, we introduce a type of subsets of ${\mathbb{R}}^n$ that we call locally translation-isometric sets (LTI sets). These sets are defined by the property that the $\varepsilon$-neighborhoods around every point in them are isometric copies of each other. For $n=3$, in the case $\varepsilon =\infty$ they are simply objective structures and correspond (for $n\in \mathbb{N}$) to the orbits of symmetry groups with translations. We provide a partial characterization of LTI sets with finite $\varepsilon$, and discuss some interesting examples and results. We generalize the concept further, in particular to locally multi-isometric sets, i.e. sets where the $\varepsilon$-neighborhoods of every point look like one of finitely many sets. We show that these generalizations of objective structures can describe even exotic atomic configurations quite well.

受原子结构简化模型的启发，并基于${\mathbb{R}}^3$，我们引入了一类子集${\mathbb{R}}^n$我们称之为局部平移等距集（LTI 集）。这些集合由属性定义$\epsilon$- 它们中每个点周围的邻域都是彼此的等距副本。为了$n=3$， 在这种情况下$\epsilon =\infty$它们只是客观的结构并且对应（对于$n\in \mathbb{ñ}$) 到具有平移的对称群的轨道。我们提供了有限的 LTI 集的部分表征$\epsilon$，并讨论一些有趣的例子和结果。我们进一步推广这个概念，特别是局部多等距集，即$\epsilon$- 每个点的邻域看起来像是有限多个集合中的一个。我们表明，这些客观结构的概括甚至可以很好地描述奇异的原子配置。