Topological density of nets: a direct calculation.
Topological density of nets: a direct calculation.
复制标题
网络的拓扑密度：直接计算。
DOI：
10.1107/s0108767303022037
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
J. Eon
中科院分区：
文献类型：
--
作者：
J. Eon
目前，在确定三维网络的整个配位序列后，即可获得其拓扑密度。本文表明，它的值可以直接从网络商图的循环集合中获得。为此目的开发了一种几何工具，即网络循环图。描述了其作为具有三角形面的凸多面体的构造以及其在拓扑密度计算中的用途。导出了三维网络的精确表达式，并将其扩展到任意 n 维网络。此外，本文还描述了三维晶格和网、n 维金刚石和朗斯代尔石的应用。
The topological density of a three-dimensional net is currently available after determining its entire coordination sequence. This paper shows that its value can be obtained directly from the set of cycles of the quotient graph of the net. A geometrical tool, the cycles figure of the net has been developed for this purpose. Its construction as a convex polyhedron with triangular faces is described as well as its use for topological density calculations. An exact expression is derived for three-dimensional nets and extended to arbitrary n-dimensional nets. Additionally, this paper describes applications to three-dimensional lattices and nets, n-dimensional diamonds and lonsdaleites.