Entangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type. Periodic isotopy classifications are obtained for various families of embedded nets with small quotient graphs. The 25 periodic isotopy classes of depth-1 embedded nets with a single-vertex quotient graph are enumerated. Additionally, a classification is given of embeddings of n-fold copies of pcu with all connected components in a parallel orientation and n vertices in a repeat unit, as well as demonstrations of their maximal symmetry periodic isotopes. The methodology of linear graph knots on the flat 3-torus [0,1)3 is introduced. These graph knots, with linear edges, are spatial embeddings of the labelled quotient graphs of an embedded net which are associated with its periodicity bases.

中文翻译：

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3 周期网络嵌入的同位素类。

定义了纠缠嵌入式周期网和晶体框架，及其尺寸类型、均匀性类型、邻接深度和周期同位素类型。对于具有小商图的各种嵌入式网络族，获得了周期性同位素分类。列举了具有单顶点商图的深度 1 嵌入网络的 25 个周期同位素类。此外，还对 pcu 的 n 重副本的嵌入进行了分类，所有连接的组件均处于平行方向，n 个顶点位于重复单元中，并演示了它们的最大对称性周期性同位素。介绍了平面 3-圆环 [0,1)3 上线性图结的方法。这些具有线性边缘的图结是与其周期性基相关联的嵌入网络的标记商图的空间嵌入。