3-空间的一致分拆及其相关性与嵌入
Uniform partitions of 3-space, their relatives and embedding
摘要：
我们回顾了3-空间的28个均匀划分，以找出它们中的哪些图（骨架）可等距嵌入（或尺度为2）到某些立方格${\bf Z}_n$中。我们还考虑了这28个划分的一些相关的划分，包括Achimedean的Conway-Guy的4-多面体，非紧一致划分，Kelvin划分和具有唯一顶点图形的划分（即Delaunay星）。其中，我们指出了两种连续的非周期性镶嵌半规则的三棱柱体与立方体或正四面体和正八面体。在途中，许多新的分区被添加到这里考虑的不完整的情况下。
英文摘要：
We review 28 uniform partitions of 3-space in order to find out which of them have graphs (skeletons) embeddable isometrically (or with scale 2) into some cubic lattice ${\bf Z}_n$. We also consider some relatives of those 28 partitions, including Achimedean 4-polytopes of Conway-Guy, non-compact uniform partitions, Kelvin partitions and those with unique vertex figure (i.e. Delaunay star). Among last ones we indicate two continuums of aperiodic tilings by semi-regular 3-prisms with cubes or with regular tetrahedra and regular octahedra. On the way many new partitions are added to incomplete cases considered here.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
