论文标题
立方对称的紧凑型多面体：几何分析和分类
Compact Polyhedra of Cubic Symmetry: Geometrical Analysis and Classification
论文作者
论文摘要
Cutip Point对称性的紧凑型多面体OH，表现出平面截面的表面（面），其特征在于正常矢量家族{abc}，每个均具有多达48个成员，与OH对称性兼容。我们首先专注于一个由一个家庭的正常向量（{100}，{110}和{111}的平面限制的polyhedra。这产生了通用的多面体，这些多面体用于定义一般紧凑型多面体作为三个通用物种的交集。发现它们的结构特性，例如形状，尺寸，体积和表面面，仅由三个多面体结构参数A，B，C。这些多面体可以通过四个多面体结构参数q，a，b，c。所有Polyhedra的几何特性将以分析细节进行讨论，并通过特征示例的可视化来证实。相应的关系也可以用于对观察到的实际紧凑金属纳米颗粒的形状进行分类和估计大小，例如在电子显微镜实验中。
Compact polyhedra of cubic point symmetry Oh, exhibit surfaces of planar sections (facets) characterized by normal vector families {abc} with up to 48 members each, compatible with Oh symmetry. We focus first on polyhedra confined by facets with normal vectors of one family, {100}, {110}, and {111}, separately. This yields generic polyhedra which serve for the definition of general compact polyhedra as intersections of the three generic species. Their structural properties, such as shape, size, volume, and surface facets, are found to be described by only three polyhedral structure parameters A, B, C. In addition, we examine compact polyhedra exhibiting facets defined by normal vectors of only one general {abc} family resulting in up to 48 facets. These polyhedra can be described by four polyhedral structure parameters Q, a, b, c. Geometrical properties of all polyhedra are discussed in analytical detail and substantiated by visualization of characteristic examples. Corresponding relationships can also be used to classify shapes and estimate sizes of real compact metal nanoparticles observed e.g. in electron microscopy experiments.
