存在幻数是团簇的基本特征. 对于以范德瓦尔斯力结合的团簇来说，可以用二十面体模型来描述，并能很好地重现幻数. 虽然二十面体团簇中央原子的配位数为12，但并不是密堆积结构. 为了支撑团簇，沿顶点方向，“原子球”相切.关于二十面体团簇空间利用率的具体计算方法，目前几乎找不到. 我们利用球面几何进行了计算，其空间利用率随着壳层数的增加而减少. 在无穷多层时为68.82%，介于体心立方和面心立方（六方密堆）结构之间. 本文的结果可为从事团簇教学和研究的同行提供参考.

The existence of “magic number” is the fundamental characteristic of clusters. For clusters bound by van der Waals force, they can be described by the icosahedral model, which can well reproduce the magic numbers. Although the coordination number of the central atom of icosahedral clusters is 12, it is not close-packed. To support the cluster, the “atomic spheres” are tangent along the vertex direction. Currently, the detailed calculation about the packing fraction of a regular icosahedron cluster can be hardly found. In this paper, we calculate it by spherical geometry. It decreases as the number of atomic layer increases. When infinite layers are concerned, the packing fraction is 68.82%, which is between the body-centered cubic and face-centered cubic (hexagonal close-packed) structures. The result can be referenced by colleagues engaged in teaching and investigation on clusters.